3D Crack growth simulation - Kolk, Karsten; Kuhn, Günther (Proceedings of the 2nd European Conference on Computational Mechanics, 2001)
UnivIS-Import:2015-04-16:Pub.2001.tech.FT.FT-TM.3dcrac

A calibration method for failure modeling in clinching process simulations - Böhnke, Max; Bielak, Christian Roman; Friedlein, Johannes; Bobbert, Mathias; Mergheim, Julia; Meschut, Gerson; Steinmann, Paul (Materials Research Proceedings, 2023)
In the numerical simulation of mechanical joining technologies such as clinching, the material modeling of the joining parts is of major importance. This includes modeling the damage and failure behavior of the materials in accordance with varying occurring stress states. This paper presents a calibration method of three different fracture models. The calibration of the models is done by use of experimental data from a modified punch test, tensile test and bulge test in order to map the occurring stress states from clinching processes and to precisely model the resulting failure behavior. Experimental investigations were carried out for an aluminum alloy EN AW-6014 in temper T4 and compared with the simulative results generated in LS-DYNA. The comparison of force-displacement curves and failure initiation shows that the Hosford–Coulomb model predicts the failure behavior for the material used and the tests applied with the best accuracy.
CRIS-Team Scopus Importer:2023-04-28
Keywords: Clinching; Damage; Failure

Accelerating molecular dynamics simulations by a hybrid molecular dynamics-continuum mechanical approach - Bauer, Christof; Ries, Maximilian; Pfaller, Sebastian (Soft Materials, 2022)
In this contribution, molecular dynamics (MD) simulations in combination with continuum mechanical (CM) approaches are performed to investigate particle movements under uniaxial deformations of an amorphous polymer at particle resolution. A coarse-grained (CG) model of atactic polystyrene is used as an exemplary model system. We propose a hybrid molecular dynamics-continuum mechanical (MD-CM) approach to simulate the deformation behavior of the polymer. As a reference, purely molecular dynamics systems are used. The methods are compared with regard to the local displacement of the particles and the global stress-strain behavior of the overall system. The good reproducibility of the system's mechanical behavior with the hybrid molecular dynamics-continuum mechanical method is shown. Furthermore, it is demonstrated that CPU time can be significantly reduced with the hybrid calculation model.
CRIS-Team WoS Importer:2022-05-06

Acceleration of 3D crack propagation simulation by the utilization of fast BEM-techniques - Weber, Wilhelm; Kolk, Karsten; Kuhn, Günther (Engineering Analysis With Boundary Elements, 2009)
For the acceleration of the 3D simulation of fatigue crack propagation fast BEM techniques are combined in the present paper. The so-called dual BEM is utilized to separate the coincident crack surfaces. In the present context, the relevant boundary integral equations are evaluated in the framework of a collocation procedure. For the reduction of the numerical complexity of the stress analysis fast BEM techniques are applied. The domain is decomposed in order to obtain a band-structured system matrix. The crack is modeled in terms of the dual discontinuity method. Therewith, the relevant boundary of the domain is reduced by one crack surface. Finally, the adaptive cross approximation, an algebraic matrix compression technique, is utilized to compress the system matrix. The efficiency of this procedure is shown on complex industrial applications. © 2009 Elsevier Ltd. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2009.tech.FT.FT-TM.bem
Keywords: 3D dual BEM; Adaptive cross approximation (ACA); Domain decomposition; Dual discontinuity method (DDM)

Acceleration of the spectral stochastic FEM using POD and element based discrete empirical approximation for a micromechanical model of heterogeneous materials with random geometry - Pivovarov, Dmytro; Steinmann, Paul; Willner, Kai (Computer Methods in Applied Mechanics and Engineering, 2019)
The spectral stochastic FEM with local basis functions in the stochastic domain (SL-FEM) is one of the most flexible and accurate stochastic methods, however, also the most computationally expensive. These expenses are traditionally associated with the extra large tangent stiffness matrix and a huge number of elements which need to be re-integrated in every iteration. In this work we incorporate the proper orthogonal decomposition (POD) into the SL-FEM, thus performing a drastic reduction of the stiffness matrix. In order to reduce the integration costs by hyperreduction, a novel element-based modification of the discrete empirical interpolation, the so-called element-based empirical approximation method (EDEAM), is developed and combined with the POD. Particular advantages of the SL-FEM for order reduction and hyperreduction compared to other stochastic techniques are discussed. The new reduced-order SL-FEM is applied to the computational homogenization of materials with random geometry of the microstructure, i.e. to a general class of problems exhibiting strongly nonlinear, non-smooth and sometimes discontinuous dependency of the solution on some random parameters. The reduced-order SL-FEM demonstrates a high accuracy and a high solution speed, whereby the solution time for the reduced-order SL-FEM is comparable to the solution time of only one single Monte-Carlo sample.
CRIS-Team Scopus Importer:2019-12-03
Keywords: Computational homogenization; Hyperreduction; POD; Random geometry; Reduced order modeling; Stochastic FEM

Accuracy meets simplicity: A constitutive model for heterogenous brain tissue - Filla, Nicholas; Hou, Jixin; Liu, Tianming; Budday, Silvia; Wang, Xianqiao (Journal of the Mechanical Behavior of Biomedical Materials, 2024)
We present a general, hyperelastic, stretch-based potential that shows promise for modeling the mechanics of brain tissue. A specific four-parameter model derived from this general potential outperforms alternative models, such as the modified Ogden model, the Gent model, Demiray model, and machine-learning models, in capturing brain tissue elasticity. Specifically, the stretch-based model achieved R2 values of 0.997, 0.992, and 0.993 (tension, compression, and shear) for the cortex, 0.995, 0.983, and 0.983 for the basal ganglia, 0.994, 0.929, and 0.970 for the corona radiata, and 0.990, 0.896, and 0.969 for the corpus callosum. This work has the potential to advance our understanding of brain tissue mechanics and provides a valuable tool to improve finite element models for the investigation of brain development, injuries, and disease.
CRIS-Team Scopus Importer:2023-12-15

A cohesive crack propagation model: Mathematical theory and numerical solution - Prechtel, Marina; Leugering, Günter; Steinmann, Paul; Stingl, Michael (Communications on Pure and Applied Analysis, 2013)
We investigate the propagation of cracks in 2-d elastic domains, which are subjected to quasi-static loading scenarios. As we take cohesive effects along the crack path into account and impose a non-penetration condition, inequalities appear in the constitutive equations describing the elastic behavior of a domain with crack. In contrast to existing approaches, we consider cohesive effects arising from crack opening in normal as well as in tangential direction. We establish a constrained energy minimization problem and show that the solution of this problem satisfies the set of constitutive equations. In order to solve the energy minimization problem numerically, we apply a finite element discretization using a combination of standard continuous finite elements with so-called cohesive elements. A particular strength of our method is that the crack path is a result of the minimization process. We conclude the article by numerical experiments and compare our results to results given in the literature.
Keywords: Energy minimization; cohesive elements; crack problems.

A comparative assessment of different adaptive spatial refinement strategies in phase-field fracture models for brittle fracture - Rohracker, Maurice; Kumar, Paras; Mergheim, Julia (Forces in Mechanics, 2023)
For the smeared approximation of a discrete crack, phase-field fracture simulations of brittle materials require suitable finite element meshes in regions where crack propagation is expected to get an accurate resolution of the phase-field function. The straightforward option is to pre-refine the mesh in regions of the expected crack paths. However, this could lead to very computationally intensive simulations due to the high number of elements. Alternatively, adaptive spatial refinement of the finite element mesh is utilized based on appropriate error indicators to obtain the required accuracy in the areas of crack propagation. Different error indicators can be used: the most common one for phase-field fracture simulations is the threshold-based approach, in which elements are refined depending on the value of the phase-field function. Alternatively, the Kelly error indicator can be used as a criterion for spatial adaptivity. It considers the jumps in the gradients of the phase-field function between the elements. We additionally introduce here an error indicator based on configurational forces, that depend on the Eshelby stress tensor. For mode I loading in linear elastic fracture mechanics, the configurational forces have a close connection to the J-Integral and the critical fracture energy Gc, respectively. Therefore, a suitable norm of the configurational forces is introduced as an error indicator here. These three error indicators are introduced and compared to each other in terms of accuracy and efficiency by means of numerical examples for crack growth in the single edge notched shear test.
Keywords: Phase-Field Fracture Simulations; Spatial Adaptivity; Brittle Fracture; Single Edge Notched Shear Test

A comparison between a recursive method based on an inverse mechanical formulation and shape optimization for solving inverse form finding problems in isotropic elastoplasticity - Germain, Sandrine; Landkammer, Philipp; Steinmann, Paul (PAMM 2014, 2014)
UnivIS-Import:2015-07-08:Pub.2014.tech.FT.FT-TM.acompa_4

A comparison between inverse form finding and shape optimization methods for anisotropic hyperelasticity in logarithmic strain space - Germain, Sandrine; Steinmann, Paul (Proceedings of Applied Mathematics and Mechanics (PAMM), 2011)
In this paper an inverse mechanical formulation and a Limited-Broyden-Flechter-Goldfarb-Shanno method for shape optimization are compared. Both methods deal with the determination of the undeformed shape of an hyperelastic part knowing its deformed configuration and the applied loads. We consider anisotropic hyperelastic materials that are formulated in the logarithmic strain space. Beside the theoretical aspects, we present a numerical example. We established that no difference could be found between the node coordinates on the undeformed sheets computed with both methods. However the convergence to the solution is faster for the inverse mechanical formulation compared to the L-BFGS algorithm.
UnivIS-Import:2015-04-16:Pub.2011.tech.FT.FT-TM.acompa_8

A Comparison of Atomistic and Enhanced Continuum Approaches at Finite Temperature - Davydov, Denis; Javili, Ali; Steinmann, Paul; McBride, Andrew (Surface effects in solid mechanics, 2012)
UnivIS-Import:2015-04-16:Pub.2012.tech.FT.FT-TM.acompa_7

A Comparison of Different Approaches in the Multi-Scale Computation of Configurational Forces - Mergheim, Julia; Steinmann, Paul; Ricker, Sarah; Müller, Ralf (International Journal of Fracture, 2010)
In the present work the FE2 scheme is extended towards the homogenization of material quantities like the Eshelby stress and material node point forces. Therefore, in contrast to standard computational homogenization schemes volume forces on the micro-and on the macro-level have to be taken into account which emerge in the material motion problem due to inhomogeneities in the material. Different approaches in the determination of the material stresses are compared and it is shown that the direct calculation of the material stresses in terms of averaged material quantities requires an internal extra term to fulfill the energy consistency represented by a Hill-Mandel type condition. Furthermore, two approaches based on the average of the material two-point stress and the Eshelby stress are compared which require a further scale-transition which is performed within a postprocessing step. The influence of different micro-structures onto the macroscopic material quantities is studied within numerical examples. © 2010 Springer Science+Business Media B.V.
UnivIS-Import:2015-03-09:Pub.2010.tech.FT.FT-TM.acompa
Keywords: Computational homogenization; Configurational forces; FE; Multi-scale mechanics

A comparison of material models for the simulation of selective beam melting processes - Burkhardt, Christian; Soldner, Dominic; Mergheim, Julia (Procedia CIRP, 2020)
The focus of this contribution lies on the comparison of different material models for the thermo-mechanical simulation of selective laser melting (SLM) processes. A Finite Element (FE) framework for the analysis of residual stresses and distortions in laser beam melting processes is introduced. The FE solver for the thermo-mechanical problem uses a staggered algorithm, is based on the open source finite element library deal.ii and makes use of heavy parallelization. The most important aspects to be investigated here are the mechanical material behavior and stress relaxation in the range of the melting temperature. Material models, which reset certain variables as stress and plastic strain to zero at a critical temperature are compared to a thermo-viscoplastic constitutive law. Simulations, related to the SLM process of Ti-6Al-4V, are performed to compare the residual stresses and plastic strains predicted by different models after melting and cooling. Furthermore, the validity of geometrically linearized material model is analyzed. <br
Keywords: SLM process; Finite Element simulations; residual stresses; viscoplastic material models; melting; solidification

A comparison of staggered solution schemes for coupled particle-continuum systems modeled with the Arlequin method - Pfaller, Sebastian; Possart, Gunnar; Steinmann, Paul; Rahimi, Mohammad; Müller-Plathe, Florian; Böhm, Michael C. (Computational Mechanics, 2011)
This contribution aims at a systematic investigation of staggered solution schemes for the computation of coupled domains having different resolutions in space, a problem frequently arising in multi-scale modeling of materials. To couple a standard finite element domain with a high resolution atomistic or coarse-grained, i.e. particle-based domain, a so-called bridging domain is considered. In this handshake region a total energy, which is the sum of the weighted energies of both domains, needs to be formulated. Interactions in the particle domain are modeled by potential functions, e.g. a harmonic potential in the simplest case or the Lennard-Jones potential to consider also anharmonic interactions between the particles. The main goal is to separate the computation of finite element and particle domains as much as possible, amongst others to calculate the different domains on several CPUs. In the present work, the governing equations of the coupling method are presented. The energy functions of continuum, particle domain and bridging domain are recapitulated and the coupling constraint is set up. For the sake of simplicity, these relations are reformulated for the case of a one dimensional system. On the one hand, this system is computed monolithically without any separation of domains. On the other hand, various staggered solution schemes are derived systematically. The relevant equations of each scheme are given in detail together with the sequent iteration steps. All staggered schemes are investigated qualitatively, e.g. by their convergence behavior, as well as quantitatively by comparing the staggered solutions with the monolithic solutio
UnivIS-Import:2015-03-09:Pub.2010.tech.FT.FT-TM.acompa_3
Keywords: Atomistic–continuum coupling; Multiscale modeling; Bridging domain method; Domain decomposition; Lagrange multipliers

A complete thermo-electro-viscoelastic characterization of dielectric elastomers, Part I: Experimental investigations - Mehnert, Markus; Hossain, Mokarram; Steinmann, Paul (Journal of the Mechanics and Physics of Solids, 2021)
Dielectric elastomers are a class of solid polymeric materials that are sufficiently soft to deform under the application of an electric field due to the interaction of quasi-static electric charges. Their potential to undergo large deformations renders them promising candidates for the design of energy harvesters, sensors and soft actuators. For their application however, the influence of additional thermal effects should be taken into account as the base materials frequently show a distinct thermal sensitivity that drastically influences their mechanical response. This contribution presents the results of a wide range of experiments conducted on the popular dielectric elastomer VHB 4905™ under a combination of mechanical, thermal and electric loading scenarios. These experiments are performed in such a way that the obtained results are well suited for the identification of the necessary material parameters appearing in a thermo–electro–viscoelastic constitutive model that will subsequently be presented in the second part of the contribution.
Keywords: Dielectric elastomers; Electro-active polymers; Thermo–mechanics; Electro–mechanics

A complete thermo-electro-viscoelastic characterization of dielectric elastomers, Part II: Continuum modeling approach - Mehnert, Markus; Hossain, Mokarram; Steinmann, Paul (Journal of the Mechanics and Physics of Solids, 2021)
A comprehensive experimental study performed under a combination of thermo-electro-mechanical loads applied to a widely used electro-active polymer, is presented in the Part I of this work (Mehnert et al., 2021). Soft polymeric materials, used as base materials in electro-active polymers, are highly susceptible to temperature changes. Hence, thermal influences on their behavior have to be investigated precisely. Constitutive modeling and numerical simulation of electro-active polymers are active fields of current research. However, on the one hand, their experimental study under complex loading conditions is non-trivial. On the other hand, very few constitutive modeling approaches meet with experimental data obtained from thermo-electro-mechanical loading conditions. In this contribution, we aim to develop a thermo-electro-mechanically coupled model, which will closely replicate the response of an electro-active polymer investigated under a combination of thermal, electric and mechanical loads. Once the model is calibrated with the experimental data described in Part I of this contribution, it is validated with a different set of data, which shows excellent agreement with experimental findings.

A comprehensive characterization of the electro-mechanically coupled properties of VHB 4910 polymer - Mokarram, Hossain; Vu, Duc Khoi; Steinmann, Paul (Archive of Applied Mechanics, 2014)
UnivIS-Import:2015-04-14:Pub.2014.tech.FT.FT-TM.acompr

A computational approach to nonlinear dynamics of constrained dynamical systems - Leyendecker, Sigrid; Betsch, Peter; Steinmann, Paul (6th European Solid Mechanics Conference, 2006)

A computational approach to obtain nonlinearly elastic constitutive relations of special Cosserat rods - Arora, Abhishek; Kumar, Ajeet; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2019)
We present a computational framework to obtain nonlinearly elastic constitutive relations of one-dimensional continua modeled as special Cosserat rods. The kinematics of the recently proposed Helical Cauchy–Born rule is used to construct a family of six-parameter (corresponding to the six strain measures of rod theory) helical rod configurations which are subjected to uniform strain field along their arc-length. This uniformity along the rod's arc-length results in the reduction of three-dimensional equations of elasticity to just the rod's cross-section which further allows us to obtain the induced force, moment and stiffnesses of the rod by solving a nonlinear cross-sectional warping problem for every state of strain. The formulation is general in that the rod's material could obey arbitrary three-dimensional hyperelastic constitutive relations. A nonlinear finite element formulation is presented to solve the cross-sectional warping problem and further obtain the induced force, moment and stiffnesses numerically. Several numerical examples are presented illustrating warping due to bending, shearing and torsion in rectangular as well as circular rods and how the warping affects stiffnesses. We also obtain all the stiffnesses of helically reinforced tubes and show the variation in their stiffnesses with the tube's fiber angle.
CRIS-Team Scopus Importer:2019-05-09
Keywords: Elastic constitutive modeling; Helical Cauchy–Born rule; Special Cosserat rod

A computational method for the FE simulation of strong and weak discontinuities - Steinmann, Paul; Mergheim, Julia (Proc. Workshop Gemischte und nicht-standard FE-Methoden, 2005)
UnivIS-Import:2015-04-16:Pub.2005.tech.FT.FT-TM.acompu

A concept for process-oriented interdisciplinary tolerance management considering production-specific deviations - Heling, Björn; Oberleiter, Thomas; Rohrmoser, Andreas; Kiener, Christoph; Schleich, Benjamin; Hagenah, Hinnerk; Merklein, Marion; Willner, Kai; Wartzack, Sandro (Proceedings of the 22nd International Conference on Engineering Design (ICED19), 2019)

A constitutive friction law for sheet-bulk metal forming - Beyer, Florian; Willner, Kai (Journal of Japanese Society of Tribologists, 2016)
Friction has a significant effect on metal forming both in economic and technical terms. This is especially true for sheet-bulk metal forming, which is a combination of bulk metal forming and sheet metal forming. Contact loads of sheet forming processes are typically low to moderate. In contrast, very high contact loads occur in bulk metal forming. Therefore, a friction law, which is applicable for a broad range of contact loads, is necessary, if such a process has to be modelled accurately with the finite element method. A friction law fulfilling this demand is identified with the use of an elastic-plastic half-space model. The half-space model is used to determine the normal contact of rough surfaces and it is validated with experiments. In order to highlight the impact of the identified friction law, a typical sheet-bulk metal forming process is taken into account in the framework of the finite element metho
Keywords: constitutive friction law; simulation; half-space; sheet-bulk metal forming; finite element method; orbital forming

A coupled MD-FE methodology to characterize mechanical interphases in polymeric nanocomposites - Ries, Maximilian; Possart, Gunnar; Steinmann, Paul; Pfaller, Sebastian (International Journal of Mechanical Sciences, 2021)
This contribution introduces an unconventional procedure to characterize spatial profiles of elastic and inelastic properties inside polymer interphases around nanoparticles. Interphases denote those regions in the polymer matrix whose mechanical properties are influenced by the filler surfaces and thus deviate from the bulk properties. They are of particular relevance in case of nano-sized filler particles with a comparatively large surface-to-volume ratio and hence can explain the frequent observation that the overall properties of polymer nanocomposites cannot be determined by classical mixing rules, which only consider the behavior of the individual constituents. Interphase characterization for nanocomposites poses hardly solvable challenges to the experimenter and is still an unsolved problem in many cases. Instead of real experiments, we perform pseudo experiments using our recently developed Capriccio method, which is an MD-FE domain-decomposition tool specifically designed for amorphous polymers. These pseudo-experimental data then serve as input for a typical inverse parameter identification. With this procedure, spatially varying mechanical properties inside the polymer are, for the first time, translated into intuitively understandable profiles of continuum mechanical parameters. As a model material, we employ silica-enforced polystyrene, for which our procedure reveals exponential saturation profiles for Young’s modulus and the yield stress inside the interphase, where the former takes about seven times the bulk value at the particle surface and the latter roughly triples. Interestingly, hardening coefficient and Poisson’s ratio of the polymer remain nearly constant inside the interphase. Besides gaining insight into the constitutive influence of filler particles, these unexpected and intriguing results also offer interesting explanatory options for the failure behavior of polymer nanocomposites.<br
Keywords: polymer nanocomposites; interphase layers; interphase properties; atomistic-continuum coupling

Acquisition of heuristic knowledge for the prediction of the frictional behavior of surface structures created by self-excited tool vibrations - Breitsprecher, Thilo; Hense, R.; Hauer, Franz; Wartzack, Sandro; Biermann, Dirk; Willner, Kai (Key Engineering Materials, 2012)
The selective control of the frictional behavior (tailored friction) in metal forming processes is of high importance with regard to technical and economic aspects. This applies especially for the sheet-bulk-metal forming process. Milling with intentionally invoked regenerative tool vibrations can be applied in order to generate structured surfaces with tailored friction properties on the forming tool. These structures affect the formation of lubrication pockets during the forming process which determine the local frictional properties exceedingly. The full potential of this emerging technology can, however, only be revealed if the heuristic and design-relevant knowledge is acquired and provided to the tool-designer already in the early phases of process development. One thing the tool-designer has to specify is the local frictional behavior on the tool surface. But, however, he does not know which milling parameters lead to the necessary surface structures because in most cases he has no expert knowledge in milling, tribology and forming tools. In this paper data mining is used to determine the frictional behavior based on these parameters. The potential of this method in the described context is revealed by the application on data derived from simulation results, both from milling simulations and contact simulations. The latter are performed by using a Halfspace model for rough surface contact. Both approaches for these simulations, the data mining process and the results are explained to the reader.© (2012) Trans Tech Publications.
UnivIS-Import:2015-03-09:Pub.2012.tech.FT.FT-KLMEFK.acquis
Keywords: Data mining; Halfspace model; Milling with vibrations; Self-learning system

Active Vibration Control of Excited Structures by means of Shape Adaption - Nowak, Alexander; Willner, Kai; Campanile, Lucio Flavio; Hasse, Alexander (International Conference on Adaptive Structures and Technologies, 2017)

Adaptive finite elements based on sensitivities for topological mesh changes - Leugering, Günter; Friederich, Jan; Steinmann, Paul (Control and Cybernetics, 2014)
We propose a novel approach to adaptive refinement in FEM based on local sensitivities for node insertion. To this end, we consider refinement as a continuous graph operation, for instance by splitting nodes along edges. Thereby, we introduce the concept of the topological mesh derivative for a given objective function. For its calculation, we rely on the first-order asymptotic expansion of the Galerkin solution of a symmetric linear second-order elliptic PDE. In this work, we apply this concept to the total potential energy, which is related to the approximation error in the energy norm. In fact, our approach yields local sensitivities for minimization of the energy error by refinement. Moreover, we prove that our indicator is equivalent to the classical explicit a posteriori error estimator in a certain sense. Numerical results suggest that our method leads to efficient and competitive adaptive refinement.
Keywords: Adaptive mesh refinement; Asymptotic expansion; Sensitivity-based refinement; Topological sensitivity

Adaptive harmonic balance analysis of dry friction damped systems - Süß, Dominik; Jerschl, Martin; Willner, Kai (34th IMAC, A Conference and Exposition on Structural Dynamics, 2016, 2016)
One of the most challenging tasks in structural dynamics is given by analyzing and predicting the behavior of jointed structures. In order to perform numerical investigations the Harmonic Balance Method (HBM) is a very mature and efficient technique for estimating the response behavior of such systems in the frequency domain. A better approximation can be obtained by accounting for more harmonic parts and introducing the Multiharmonic Balance Method (MHBM). This leads to a simultaneous reduction of efficiency due to a huge growth of the system dimensions. The goal of this paper is to present an Adaptive Harmonic Balance Method joining together the advantages of both, HBM and MHBM. Therefore the number of harmonics accounted for is adaptively chosen as small as possible, in order to get an efficient procedure and as big as necessary, in order to obtain precise results. The selection is performed by various criteria estimating the most important harmonic parts from an user defined pool of harmonics.
Keywords: Adaptive procedure; FEM; Harmonic balance; Jointed structure; Structural dynamics

Adaptive Poly-FEM for the analysis of plane elasticity problems - Kasi, Balaji; Rajagopal, Amirtham; Steinmann, Paul (International Journal of Computational Methods in Engineering Science and Mechanics, 2017)
In this work, we present an adaptive polygonal finite element method (Poly-FEM) for the analysis of two-dimensional plane elasticity problems. The generation of meshes consisting of n − sided polygonal finite elements is based on the generation of a centroidal Voronoi tessellation (CVT). An unstructured tessellation of a scattered point set, that minimally covers the proximal space around each point in the point set, is generated whereby the method also includes tessellation of nonconvex domains. In this work, we propose a region by region adaptive polygonal element mesh generation. A patch recovery type of stress smoothing technique that utilizes polygonal element patches for obtaining smooth stresses is proposed for obtaining the smoothed finite element stresses. A recovery type a − posteriori error estimator that estimates the energy norm of the error from the recovered solution is then adopted for the Poly-FEM. The refinement of the polygonal elements is then made on an region by region basis through a refinement index. For the numerical integration of the Galerkin weak form over polygonal finite element domains, we resort to classical Gaussian quadrature applied to triangular subdomains of each polygonal element. Numerical examples of two-dimensional plane elasticity problems are presented to demonstrate the efficiency of the proposed adaptive Poly-FEM.
CRIS-Team Scopus Importer:2022-08-05
Keywords: a-posteriori error estimator; Adaptive finite element analysis; polygonal finite elements

Adaptive refinement based on asymptotic expansions of finite element solutions for node insertion in 1d - Leugering, Günter; Friederich, Jan; Steinmann, Paul (GAMM-Mitteilungen, 2012)
We consider refinement of finite element discretizations by splitting nodes along edges. For this process, we derive asymptotic expansions of Galerkin solutions of linear second-order elliptic equations. Thereby, we calculate a topological derivative w.r.t. node insertion for functionals such as the total potential energy, minimization of which decreases the approximation error in the energy norm. Hence, these sensitivities can be used to define indicators for local h-refinement. Our results suggest that this procedure leads to an efficient adaptive refinement method. This presentation is concerned with a model problem in 1d. The extension of this concept to higher dimensions will be the subject of forthcoming publications. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA.

Additive manufacturing of cellular structures: Multiscale simulation and optimization - Mergheim, Julia; Breuning, Christoph; Burkhardt, Christian; Hübner, Daniel; Köpf, Johannes; Herrnböck, Ludwig; Yang, Zerong; Körner, Carolin; Markl, Matthias; Steinmann, Paul; Stingl, Michael (Journal of Manufacturing Processes, 2023)
This paper introduces a multiscale and multi-purpose simulation framework to investigate selective beam melting processes for metallic cellular structures along the complete process chain, up to the topology optimization of components made of cellular materials. Process simulation methods on various length scales are introduced to analyze the relation of process strategies and resulting properties of the cellular materials, as e. g. warpage, residual stresses, material grain structure and surface roughness. Numerical homogenization methods are applied to investigate the influence of the grain structure and the topology of the cellular materials on their mechanical properties. Based on these process-dependent mechanical properties, a two-scale optimization of components made of cellular material is performed, aiming in particular on optimizing the buckling resistance of the structures. The interfaces between the different simulation tools are specified and illustrate the flexibility of the numerical framework. It is shown that consistent simulations of additive manufacturing of cellular materials - from the manufacturing process to the optimized component - provide important insights into process-structure interactions and enable tailored additive manufacturing processes.
CRIS-Team WoS Importer:2023-06-02

Addressing Surface Effects at the Particle-Continuum Interface in a Molecular Dynamics and Finite Elements Coupled Multiscale Simulation Technique - Jain, Yash; Ries, Maximilian; Pfaller, Sebastian; Müller-Plathe, Florian (Journal of Chemical Theory and Computation, 2022)
Atomistic-to-continuum coupling methods are used to unravel molecular mechanisms of polymers and polymer composites. These multiscale techniques advantageously combine the computational efficiency of continuum approaches while keeping the accuracy of particle-based methods. The Capriccio method [Pfaller et al. Comput. Methods Appl. Mech. Eng. 2013, 260, 109−129.] is a well-proven multiscale technique, which connects finite elements (FE) with molecular dynamics (MD) in a partitioned-domain approach. A vital aspect of these multiscale methods is to provide physically sound boundary conditions to the particle domain suppressing any interface effects at the domain boundary occurring due to the coupling. These interfacial coupling artifacts still pose a significant problem, especially for amorphous polymers due to their highly irregular microstructure. We solve this problem by extending the particle-continuum interface by a layer of passive atoms which move with the outer continuum, thereby providing the missing interactions with a surrounding polymer bulk to the inner particle region. This solution allows us to successfully reproduce structural and mechanical properties obtained under conventional periodic boundary conditions, like density, stress, Young’s modulus, and Poisson’s ratio. Furthermore, we demonstrate the application of a nonaffine deformation by means of a simple bending test. In general, our revised method provides a framework to apply complex deformations for molecular scientists, while it allows the engineering community to examine challenging phenomena such as fracture behavior at a molecular level.<br

A Deformational and Configurational Framework for Geometrically Nonlinear Continuum Thermomechanics Coupled to Diffusion - Steinmann, Paul; McBride, Andrew; Bargmann, Swantje; Javili, Ali (International Journal of Non-Linear Mechanics, 2011)
A general framework encompassing both the (conventional) deformational and configurational settings of continuum mechanics is presented. A systematic application of balance principles over a migrating control volume in the undeformed configuration of the continuum body yields the system of governing equations in the bulk, on the surface and on a coherent interface within the continuum. The equations governing the response of the bulk agree with those of the conventional deformational approach. The localised balance equations are expressed in the configurational setting using a pull-back operator and reformulated in terms of the Eshelby stress. The configurational expression of the dissipation elucidates the energy loss associated with configurational changes. The general framework is introduced by considering the problem of coupled deformation, heat conduction and species diffusion within a geometrically non-linear continuum body intersected by a coherent interface. The nature of the coupling is emphasised throughout the presentation and via an example.
UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.adefor

Adhesive removable partial denture attachments made from zirconia ceramic: A finite element analysis and in vitro study - Orujov, Kamran; Winter, Werner; Karl, Matthias; Heckmann, Siegfried; Grobecker-Karl, Tanja (Journal of Prosthetic Dentistry, 2020)
Statement of problem: Whether adhesive zirconia ceramic removable partial denture attachments are feasible with current technology is unclear. Purpose: The purpose of this finite element analysis and in vitro study was to evaluate the effect of the lever arm, tooth preparation, and aging on the loading of the tooth-zirconia attachment interface. Material and methods: Three different finite element analysis (FEA) models allowing for the loading of an adhesive attachment either directly or through a removable partial denture were used. Two models represented a human tooth with 2 different types of attachments, while the third model also included a removable partial denture. For the evaluation of bond strength, a combination of shear and hydrostatic stress was used. In addition, composite resin teeth were fabricated, and zirconia bars were bonded to them with varying tooth preparations and lever arm lengths. In 1 group the influence of aging was analyzed. Fracture load was determined by using a universal testing machine. Statistical analysis was based on the Shapiro-Wilk normality test, ANOVA, and Games-Howell test (α=.05). Results: The maximum stress of 65 MPa occurring in the bonding area was reduced to 37 MPa by adding a retainer to the attachment. Loading of the denture resulted in a maximum stress of 9 MPa. Mean fracture loads ranged from 33.6 N to 209.1 N. Preparing a flat bonding surface showed a nonsignificant increase (P=.197), whereas aging led to a nonsignificant decrease in fracture load (P=.075). A lever arm extended by 2 mm significantly reduced fracture load (P=.002). The addition of an occlusal-distal (OD) cavity led to a nonsignificant increase (P=.186), which became significant when a mesial-occlusal-distal (MOD) preparation was applied (P=.001). Conclusions: Adhesive zirconia attachments should use a MOD cavity and have a cross section of at least 2.5×2.5 mm. The attachment should not extend more than 3 mm.
CRIS-Team Scopus Importer:2020-12-18

A dual Lagrange method for contact problems with regularized contact conditions - Sitzmann, Saskia; Willner, Kai; Wohlmuth, B. I. (International Journal for Numerical Methods in Engineering, 2014)
This paper presents an algorithm for solving quasi-static, non-linear elasticity contact problems without friction in the context of rough surfaces. Here, we want to model the transition from soft to hard contact in case of rough surfaces on the micro-scale. The popular dual mortar method is used to enforce the contact constraints in a variationally consistent way without increasing the algebraic system size. The algorithm is deduced from a perturbed Lagrange formulation and combined with mass-lumping techniques to exploit the full advantages of the duality pairing. This leads to a regularized saddle point problem, for which a non-linear complementary function and thus a semi-smooth Newton method can be derived. Numerical examples demonstrate the applicability to industrial problems and show a good agreement to experimentally obtained results.
Keywords: Constitutive contact equations; Contact; Dual mortar methods; Perturbed lagrange; Rough surfaces; Semi-smooth Newton

A dual Lagrange method for contact problems with regularized frictional contact conditions: Modelling micro slip - Sitzmann, Saskia; Willner, Kai; Wohlmuth, B. I. (Computer Methods in Applied Mechanics and Engineering, 2015)
This paper presents an algorithm for solving quasi-static, non-linear elasticity contact problems with friction in the context of rough surfaces. Here, we want to model the transition from sticking to slipping also called micro slip in a physically correct way in order to reproduce measured frictional damping. The popular dual Mortar method is used to enforce the contact constraints in a variationally consistent way without increasing the algebraic system size. The algorithm is deduced from a perturbed Lagrange formulation and combined with a serial-parallel Iwan model. This leads to a regularized saddle point problem, for which a non-linear complementary function and thus a semi-smooth Newton method can be derived. Numerical examples demonstrate the applicability to industrial problems and show good agreement to experimentally obtained results.
Keywords: Constitutive contact equations; Contact with friction; Dual Mortar methods; Iwan model; Micro slip; Rough surfaces

Advanced simulation of 3D fatigue crack growth by a predictor-corrector procedure considering 3D singularities - Kolk, Karsten; Kuhn, Günther (Proceedings of the 11th International Conference of Fracture, 2005)
An advanced incremental algorithm for the simulation of 3D fatigue crack growth in the framework of linear elastic fracture mechanics is addressed to this paper. The simulation is based on an accurate stress analysis, which is performed by the 3D dual boundary element method (Dual BEM). The utilized fracture mechanics parameters are the stress intensity factors (SIFs) and the so-called T-stresses. They are extracted from the numerical crack near-field by an optimized extrapolation and regression algorithm providing very precise values of both parameters. To answer the still open question concerning a reliable 3D crack growth criterion a predictor-corrector procedure is implemented. This concept is capable of mode-I and three-dimensional mixed-mode conditions. As part of the proposed scheme, 3D corner singularities are considered. They appear especially at the intersection of the crack front and the free surface. Based on these known asymptotic exponents, it is advantageous that the crack front angle is adjusted at such intersection points ensuring a valid square-root singularity and therefore a bounded energy release rate. As a result, the shape of the numerical crack front matches experimentally observed crack fronts locally. After applying a certain number of corrector steps assuming a constant distribution of the energy release rate along the whole crack front a global matching occurs. Finally, a sophisticated re-meshing algorithm updates the numerical model automatically for the next increment.
UnivIS-Import:2015-04-16:Pub.2005.tech.FT.FT-TM.advanc

A family of hyperelastic models for human brain tissue - Mihai, L. Angela; Budday, Silvia; Holzapfel, Gerhard A.; Kuhl, Ellen; Goriely, Alain (Journal of the Mechanics and Physics of Solids, 2017)
Experiments on brain samples under multiaxial loading have shown that human brain tissue is both extremely soft when compared to other biological tissues and characterized by a peculiar elastic response under combined shear and compression/tension: there is a significant increase in shear stress with increasing axial compression compared to a moderate increase with increasing axial tension. Recent studies have revealed that many widely used constitutive models for soft biological tissues fail to capture this characteristic response. Here, guided by experiments of human brain tissue, we develop a family of modeling approaches that capture the elasticity of brain tissue under varying simple shear superposed on varying axial stretch by exploiting key observations about the behavior of the nonlinear shear modulus, which can be obtained directly from the experimental data.
Keywords: Brain mechanics; Hyperelasticity; Large deformations; Combined loading; Constitutive modeling

A fast approach to shape optimization by using the inverse FEM - Landkammer, Philipp; Steinmann, Paul (Key Engineering Materials, 2014)
Inverse form finding aims to determine the optimum blank design of a workpiece whereby the desired spatial configuration that shall be obtained after a forming process, the boundary conditions and the applied loads are known. As a verification of the optimal material configuration a subsequent direct FEM computation has to result in the desired shape of the deformed workpiece. In this contribution the inverse FEM, which formulates the mechanical weak form in the spatial configuration Bt and solves it with respect to the material configuration B0, is used to obtain an admissible blank configuration. An example of applying this inverse method to a contact forming simulation is presented. To this end a FE-code applicable to use the inverse mechanical formulation is coupled with the commercial software MSC. Mentat. In the inverse computation the contact problem is approximated by displacement control. © 2014 Trans Tech Publications, Switzerlan
UnivIS-Import:2015-03-09:Pub.2014.tech.FT.FT-TM.afasta
Keywords: Elastoplasticity; Inverse FEM; Inverse form finding; Optimum blank design

A finite element formulation for a direct approach to elastoplasticity in special Cosserat rods - Smriti,; Kumar, Ajeet; Steinmann, Paul (International Journal for Numerical Methods in Engineering, 2021)
A finite element (FE) formulation is presented for a direct approach to model elastoplastic deformation in slender bodies using the special Cosserat rod theory. The direct theory has additional plastic strain and hardening variables, which are functions of just the rod's arc-length, to account for plastic deformation of the rod. Furthermore, the theory assumes the existence of an effective yield function in terms of stress resultants, that is, force and moment in the cross-section and cross-section averaged hardening parameters. Accordingly, one does not have to resort to the three-dimensional theory of elastoplasticity during any step of the finite element formulation. A return map algorithm is presented in order to update the plastic variables, stress resultants and also to obtain the consistent elastoplastic moduli of the rod. The presented FE formulation is used to study snap-through buckling in a semicircular arch subjected to an in-plane transverse load at its midsection. The effect of various elastoplastic parameters as well as pretwisting of the arch on its load-displacement curve are presented.
CRIS-Team WoS Importer:2021-01-29

A finite element framework for continua with boundary energies. Part III: The thermomechanical case - Javili, Ali; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2011)
This paper, in line with the previous works (Javili and Steinmann [28,29]), is concerned with the numerical implementation of boundary potential energies and the study of their impact on the deformations of solids. Thereby, the main thrust in this contribution is the extension to thermomechanical effects. Although boundary effects can play a dominant role in material behavior, the common modelling in continuum mechanics takes exclusively the bulk into account, nevertheless, neglecting possible contributions from the boundary. In the approach of this contribution the boundary is equipped with its own thermodynamic life, i.e. we assume separate boundary energy, entropy and the like. Furthermore, the generalized local balance laws are given according to Javili and Steinmann [30].Afterwards, the derivations of a generalized weak formulation, including boundary potentials, completely based on a tensorial representation are carried out which is employed for the discretization and finite element implementation. Eventually, numerical examples are presented to demonstrate the boundary effects due to the proposed thermohyperelastic material model. © 2010 Elsevier B.V.
UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.afinit
Keywords: Boundary potentials; Nanomaterials; Surface tension; Thermoelasticity

A Finite Element Framework for Continua with Boundary Energies. Part I: The Two-Dimensional Case - Javili, Ali; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2009)
This contribution deals with the implications of boundary potential energies on the two-dimensional deformations of solids in the framework of the finite element method. Common modelling in continuum mechanics takes exclusively the bulk into account, nevertheless, neglecting possible contributions from the boundary. However, boundary effects sometimes play a dominant role in the material behavior, the most prominent example being surface tension. Within this contribution the boundary potentials are allowed, in general, to depend not only on the boundary deformation but also on the boundary deformation gradient and the spatial boundary tangent. For the finite element implementation, a suitable curvilinear convected coordinate system attached to the boundary is defined and corresponding geometrical and kinematical derivations completely based on a tensorial representation are carried out. Afterwards, the discretization of the generalized weak formulation, including boundary potentials, is performed and eventually numerical examples are presented to demonstrate the boundary effects due to different proposed material models. © 2009 Elsevier B.V. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2009.tech.FT.FT-TM.afinit
Keywords: Boundary potentials; Surface tension

A finite element method for cohesive crack modelling - Mergheim, Julia; Steinmann, Paul; Kuhl, Ellen (Proceedings GAMM'05, 2005)
UnivIS-Import:2015-04-16:Pub.2005.tech.FT.FT-TM.afinit

A Finite Element Method for the Computational Modelling of Cohesive Cracks - Mergheim, Julia; Kuhl, Ellen; Steinmann, Paul (International Journal for Numerical Methods in Engineering, 2005)
The present contribution is concerned with the computational modelling of cohesive cracks in quasibrittle materials, whereby the discontinuity is not limited to interelement boundaries, but is allowed to propagate freely through the elements. In the elements, which are intersected by the discontinuity, additional displacement degrees of freedom are introduced at the existing nodes. Therefore, two independent copies of the standard basis functions are used. One set is put to zero on one side of the discontinuity, while it takes its usual values on the opposite side, and vice versa for the other set. To model inelastic material behaviour, a discrete damage-type constitutive model is applied, formulated in terms of displacements and tractions at the surface. Some details on the numerical implementation are given, concer ning the failure criterion, the determination of the direction of the discontinuity and the integration scheme. Finally, numerical examples show the performance of the method. Copyright © 2005 John Wiley & Sons, Ltd.
UnivIS-Import:2015-03-09:Pub.2005.tech.FT.FT-TM.afinit_6
Keywords: Cohesive cracks; Discontinuous elements; Propagating discontinuities

A finite plasticity gradient-damage model for sheet metals during forming and clinching - Friedlein, Johannes; Mergheim, Julia; Steinmann, Paul (Key Engineering Materials, 2021)
In recent years, clinching has gathered popularity to join sheets of different materials in industrial applications. The manufacturing process has some advantages, as reduced joining time, reduced costs, and the joints show good fatigue properties. To ensure the joint strength, reliable simulations of the material behaviour accounting for process-induced damage are expected to be beneficial to obtain credible values for the ultimate joint strength and its fatigue limit. A finite plasticity gradient-damage material model is outlined to describe the plastic and damage evolutions during the forming of sheet metals, later applied to clinching. The utilised gradient-enhancement cures the damage-induced localisation by introducing a global damage variable as an additional finite element field. Both, plasticity and damage are strongly coupled, but can, due to a dual-surface approach, evolve independently. The ability of the material model to predict damage in strongly deformed sheets, its flexibility and its regularization properties are illustrated by numerical examples.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Damage; Modelling; Regularization

A Finite Strain Framework for the Simulation of Polymer Curing. Part I: Elasticity - Mokarram, Hossain; Possart, Gunnar; Steinmann, Paul (Computational Mechanics, 2009)
A phenomenologically motivated small strain model to simulate the curing of thermosets has been developed and discussed in a recently published paper (Hossain et al. in Comput Mech 43(6):769-779, 2009). Inspired by the concepts used there, this follow-up contribution presents an extension towards the finite strain regime. The thermodynamically consistent framework proposed here for the simulation of curing polymers particularly is independent of the choice of the free energy density, i.e. any phenomenological or micromechanical approach can be utilised. Both the governing equations for the curing simulation framework and the necessary details for the numerical implementation within the finite element method are derived. The curing of polymers is a very complex process involving a series of chemical reactions typically resulting in a conversion of low molecular weight monomer solutions into more or less cross-linked solid macromolecular structures. A material undergoing such a transition can be modelled by using an appropriate constitutive relation that is distinguished by prescribed temporal evolutions of its governing material parameters, which have to be determined experimentally. Part I of this work will deal with the elastic framework whereas the following Part II will focus on viscoelastic behaviour and shrinkage effects. Some numerical examples demonstrate the capability of our approach to correctly reproduce the behaviour of curing materials. © 2009 Springer-Verlag.
UnivIS-Import:2015-03-09:Pub.2009.tech.FT.FT-TM.afinit_9
Keywords: Curing; Elasticity; Finite strains; Polymer

A Finite Strain Framework for the Simulation of Polymer Curing. Part II: Viscoelasticity and shrinkage - Mokarram, Hossain; Possart, Gunnar; Steinmann, Paul (Computational Mechanics, 2010)
A phenomenologically inspired, elastic finite strain framework to simulate the curing of polymers has been developed and discussed in the first part (Hossain et al. in Comput Mech 44(5):621-630, 2009) of this work. The present contribution provides an extension of the previous simulation concept towards the consideration of viscoelastic effects and the phenomenon of curing shrinkage. The proposed approach is particularly independent of the type of the free energy density, i.e. any phenomenologically or micromechanically based viscoelastic polymer model can be utilised. For both cases the same representatives that have been used for the elastic curingmodels, i.e. the Neo-Hookean model and the 21-chain microsphere model, are reviewed and extended accordingly. The governing equations are derived as well as the corresponding tangent operators necessary for the numerical implementation within the finite element method. Furthermore, we investigate two different approaches-a shrinkage strain function and a multiplicative decomposition of the deformation gradient-to capture the phenomenon of curing shrinkage, i.e. the volume reduction induced by the polymerisation reaction which may lead to significant residual stresses and strains in the fully cured material. Some representative numerical examples conclude this work and prove the capability of our approach to correctly capture inelastic behaviour and shrinkage effects in polymers undergoing curing processes. © Springer-Verlag 2010.
UnivIS-Import:2015-03-09:Pub.2010.tech.FT.FT-TM.afinit
Keywords: Curing; Finite strains; Polymers; Shrinkage; Viscoelasticity

A general continuum damage model for soft composites - Zhan, Lin; Wang, Siyu; Qu, Shaoxing; Steinmann, Paul; Xiao, Rui (Journal of the Mechanics and Physics of Solids, 2023)
Soft composites, including filled rubbers, nanocomposite gels, double network hydrogels, and multiple network elastomers, all exhibit stress-softening behavior in loading–unloading cycles, also denoted as the Mullins effect. Though qualitatively this damage behavior shows similar features, the details still vary with material types. In this work, we provide a general approach towards modeling the Mullins effect for soft composites based on continuum damage mechanics. We start with formulating a one-dimensional damage model. A logarithmic damage variable is employed, while a damage potential function is adopted to obtain the evolution law for the damage variable. We then extend the one-dimensional damage model to three-dimensions. The eight-chain type micro–macro transition is used to formulate an isotropic damage model. An anisotropic damage model is constructed based on the full network model, while a new micro–macro mapping is used to determine the micro stretch from the macro deformation. With this new mapping, the full network model appears in a consistent format in that the free energy, dissipation, and stress are respectively given by the average of their directional micro counterparts. In the current approach, two constitutive functions need to be determined: the elastic free energy density and the stored energy limit. Simple forms of these two constitutive functions are provided with only a small set of model parameters. The resulting models are then successfully applied to describe the stress response in loading–unloading cycles and the anisotropic response of predeformed materials for different kinds of soft composites.
CRIS-Team Scopus Importer:2023-04-14
Keywords: Anisotropic damage model; Continuum damage mechanics; Micro–macro mapping; Mullins effect; Soft composites

A generalized anisotropic damage interface model for finite strains - Spannraft, Lucie; Steinmann, Paul; Mergheim, Julia (Journal of the Mechanics and Physics of Solids, 2023)
This contribution presents a generalized mechanical interface model for nonlinear kinematics. The interface's response is non-coherent, i.e. allows for a jump in the deformations and for cohesive failure, and also includes interfacial (in)elasticity, which means that an additional membrane stiffness is introduced in the interface. This can result in a jump in the tractions across the interface and induces membrane stresses for in-plane stretches. An anisotropic cohesive law, i.e. dependent on the spatial interface normal, is formulated which induces for nonlinear kinematics additional shear-like stresses within the interface to satisfy the balance of angular momentum. The cohesive and membrane degradations are coupled via damage variables of the different deformation modes to account for an interaction. It is shown that the model is thermodynamically consistent, fulfills the balance equations and material frame indifference. An interface element with the generalized interface model is implemented as a user element in ABAQUS. Numerical examples illustrate the influence of damage coupling on the mechanical response of adhesive layers.
CRIS-Team Scopus Importer:2023-03-24
Keywords: Anisotropic cohesive zone; Anisotropic material; Damage; Delamination; Finite elements; Finite strain; Generalized interface; Interface (in)elasticity

A geometrically exact continuum framework for light-matter interaction in photo-active polymers I. Variational setting - Mehnert, Markus; Oates, W.; Steinmann, Paul (International Journal of Solids and Structures, 2021)
Molecular photo-switches as, e.g., azobenzene molecules allow, when embedded into a polymeric matrix, for photo-active polymer compounds responding mechanically when exposed to light of certain wavelength. Photo-mechanics, i.e. light-matter interaction in photo-active polymers holds great promise for, e.g., remote and contact-free activation of photo-driven actuators. In a series of earlier contributions, Oates et al. developed a successful continuum formulation for the coupled electric, electronic and mechanical problem capturing azobenzene polymer compounds, thereby mainly focussing on geometrically linearized kinematics [1, 2, 3]. Building on that formulation, we here explore the variational setting of a geometrically exact continuum framework based on Dirichlet's and Hamilton's principle as well as, noteworthy, Hamilton's equations. Thereby, when treating the dissipative case, we resort to incremental versions of the various variational problems via suited incorporation of a dissipation potential. In particular, the Hamiltonian setting of geometrically exact photo-mechanics is up to now largely under-explored even for the energetic case, arguably since the corresponding Lagrangian is degenerate in Dirac's sense. Moreover, in general, the Hamiltonian setting of dissipative dynamical systems is a matter of ongoing debate per se. In this contribution, by advocating a novel incremental version of the Hamiltonian setting exemplified for the dissipative case of photo-mechanics, we aim to also unify the variational approach to dissipative dynamical systems. Taken together, the variational setting of a geometrically exact continuum framework of photo-mechanics paves the way for forthcoming theoretical and numerical analyses.
CRIS-Team Scopus Importer:2021-06-11
Keywords: Coupled systems; Nonlinear continuum mechanics; Photo-mechanics

A geometrically exact formulation of peridynamics - Javili, Ali; McBride, Andrew; Steinmann, Paul (Theoretical and Applied Fracture Mechanics, 2021)
The main objective of this contribution is to develop a geometrically exact peridynamics (PD) formulation wherein the basic elements of continuum kinematics are preserved. The proposed formulation accounts for large deformations and is variationally consistent. We distinguish between one-, two- and three-neighbour interactions. One-neighbour interactions recover the original (bond-based) PD formalism. Two- and three-neighbour interactions are fundamentally different to state-based PD. We account for material frame indifference and provide a set of appropriate arguments for objective interaction potentials accordingly. This contribution is presented in a manner such that the established theory is immediately suitable for computational implementation. From a computational perspective, the proposed strategy is fully implicit and the quadratic rate of convergence associated with the Newton–Raphson scheme is observed. Finally, we demonstrate the capability of our proposed framework via a series of numerical examples at large deformations.
CRIS-Team Scopus Importer:2020-12-25
Keywords: Continuum kinematics; Geometrically exact; Large deformations; Peridynamics; Variationally consistent

A Geometrically Nonlinear FE Approach for the Simulation of Strong and Weak Discontinuities - Mergheim, Julia; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2006)
In the present contribution a discontinuous finite element method for the computational modelling of strong and weak discontinuities in geometrically nonlinear elasticity is introduced. The location of the interface is independent of the mesh structure and therefore discontinuous elements are introduced, to capture the jump in the deformation map or its gradient respectively. To model strong discontinuities the cohesive crack concept is adopted. The inelastic material behaviour is covered by a cohesive constitutive law, which associates the cohesive tractions, acting on the crack surfaces, with the jump in the deformation map. In the case of weak discontinuities an extended Nitsche's method is applied, which ensures the continuity of the deformation map in a weak sense. The applicability of the proposed method is highlighted by means of numerical examples, dealing with both crack propagation and material interfaces. © 2005 Elsevier B.V. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2006.tech.FT.FT-TM.ageome
Keywords: Crack propagation; Discontinuous finite elements; Geometrically nonlinear; Material interfaces; Nitsche's method

A global damping factor for a non-invasive form finding algorithm - Landkammer, Philipp; Steinmann, Paul (Proc. Appl. Math. Mech., 2015)
Inverse form finding based on the finite element method (FEM) aims in determining the optimal material (undeformed) configuration when knowing the target spatial (deformed) configuration in a discretized setting. The strategy is to iteratively update the material coordinates and recompute the spatial configuration by a FEM simulation until the computed spatial nodal positions are close enough to a priori given spatial nodal positions. A form finding algorithm is utilized, which is purely based on geometrical considerations and can be coupled with arbitrary external FEM software via subroutines in a non-invasive fashion. At large deformations degenerated elements can occur when updating the material coordinates. Evaluating the mesh quality of the updated material configuration and adjusting a global damping factor before recomputing the next spatial configuration helps to avoid mesh distortion
UnivIS-Import:2015-10-26:Pub.2015.tech.FT.FT-TM.agloba

A graded interphase enhanced phase-field approach for modeling fracture in polymer composites - Kumar, Paras; Steinmann, Paul; Mergheim, Julia (Forces in Mechanics, 2022)
The superiority of nanosized filler particles in improving the elastic and fracture behavior of polymers, in comparison to microsized inclusions, has been substantiated by several experimental observations. Accurate modeling of crack propagation in such heterogeneous materials, however, involves resolution of complex crack topologies while taking into account the coalescence and branching of multiple cracks. Such complexity renders the traditional sharp crack modeling approaches, such as those based on the idea of partition of unity, to be of limited suitability, especially in 3D, since these involve explicit tracking of the evolving crack surfaces. Consequently, phase-field fracture approaches have come up as an attractive alternative to the traditional sharp crack models, especially when complex crack topologies need to be handled. Furthermore, standard two-phase continuum models, owing to their lack of the necessary length scale, are unable to capture the previously mentioned smaller is stronger size effect. In order to remedy this shortcoming, in context of finite strain hyperelasticity, a graded interphase based enhancement of the standard first-order continuum model was introduced in our previous work. The present contribution extends the idea of graded interphases to the phase-field fracture approach. Herein, an interphase region around filler particles, as observed experimentally, having continuously varying or graded material properties is considered. Fracture behavior of the composite material can be controlled by means of the degree of grading employed in determining the elastic and fracture properties within the interphase region. An optimal combination of the graded interphase parameters yields a tougher macroscopic response, as observed in case of tougher interphases, in comparison to the one obtained with a standard phase-field fracture model, The appropriateness of the introduced technique for modeling a wide spectrum of experimentally observed fracture behaviors, depending upon the degree of adhesion between the filler and the matrix phases, is depicted by means of extensive numerical experimentation.
CRIS-Team Scopus Importer:2022-12-09
Keywords: Graded interphases; Micro-scale modeling; Phase-field fracture; Polymer composites

A gradient micromechanical model to explore flexoelectric copolymers via stochastic chain growth - Moreno Mateos, Miguel Angel (European Journal of Mechanics A-Solids, 2023)
Flexoelectric sensors respond with an electric polarization when they are subjected to inhomogeneous deformation. When these are based on polymeric materials, the electro-mechanical coupling relates to the loss of microstructural symmetries of the polar polymer chains. The object of this work is to explore the mechanisms that induce flexoelectricity in soft (co)polymers via a micromechanical model that explicitly considers the spatial composition distribution of polymer chains. To this end, we analyze the deformation of the Arruda–Boyce 8-chain cell under inhomogeneous deformation and its influence on the overall polarization resulting from the polar monomers. Cells with random-walk chains and tailored degree of entanglement feed Monte Carlo simulations to inform an effective chain dipole that drives the flexoelectric polarization. Homogeneous stretch/compression of the cell accompanying bending deformation reinforce the flexoelectric response. In addition, we focus on stochastic chain-growth processes and the insertion of different types of polar monomers within a same chain. Here, we introduce a model where reactivity ratios of real copolymerization reactions control the resulting flexoelectric coupling. Since the framework allows to relate the effective flexoelectric polarization to any structural isomer distribution, it is especially convenient to model copolymers. Overall, the model is proposed as a versatile framework to explore the intricacies of flexoelectric (co)polymers and to foster the design of flexoelectric devices from real manufacturing parameters.
CRIS-Team Scopus Importer:2023-09-08
Keywords: Constitutive modeling; Curvature-induced polarization; Dielectric polymers; Flexoelectricity; Micromechanics; Non-centrosymmetry

A hybrid analytical–numerical model for calculating the maximum elastic force acting on a flow-driven elastic prolate spheroidal particle during its collision with a rigid wall - Hu, Rongxuan; Liu, Yinshui; Ravnik, Jure; Hriberšek, Matjaž; Steinmann, Paul; Cui, Yan (Computational Mechanics, 2022)
The paper proposes a hybrid analytical–numerical model for calculating the maximum elastic force acting on a flow-driven prolate spheroidal particle during its collision with a rigid wall. This model assumes that the maximum elastic force is a function of normal impact velocity, particle material properties, particle size, particle aspect ratio and particle orientation angle. The relationship between the parameters is determined by dimensional analysis. The remaining unknown coefficients are calibrated by performing finite element (FE) simulations. The solutions for particle aspect ratios of 1.5, 2 and 3 are presented. The proposed model is verified by comparison with independent FE simulation results for different normal impact velocities, particle material properties, particle sizes, particle aspect ratios and particle orientation angles. The results of the comparison between the results of the proposed model and the FE simulation results show a good agreement for small deformations of the particle. The model is valid for any properties of particle material, particle sizes and particle orientation angles.
CRIS-Team Scopus Importer:2022-01-28
Keywords: Elastic force; Finite element simulation; Hybrid analytical–numerical model; Non-spherical particle–wall collision; Prolate spheroidal particle

A Hybrid Discontinuous Galerkin Interface Method for the Computational Modelling of Failure - Mergheim, Julia; Kuhl, Ellen; Steinmann, Paul (Communications in Numerical Methods in Engineering, 2004)
The present contribution is concerned with the computational modelling of failure along well-defined surfaces, which occur for example in the case of light-weight composite materials. A hybrid method will be introduced which makes use of the discontinuous Galerkin method in combination with a finite element interface approach. As a natural choice interface elements are introduced along the known failure surface. The discontinuous Galerkin method is applied in the pre-failure regime to avoid the unphysical use of penalty terms and instead to enforce the continuity of the solution along the interface weakly. Once a particular failure criterion is fulfilled, the behaviour of the interface is determined constitutively, depending on the displacement jump. The applicability of the proposed method is illustrated by means of two computational model problems. © 2004 John Wiley and Sons, Ltd.
UnivIS-Import:2015-03-09:Pub.2004.tech.FT.FT-TM.ahybri
Keywords: Discontinuous Galerkin method; Failure; FE-technology; Interface approach

Alginate-based hydrogels show the same complex mechanical behavior as brain tissue - Distler, Thomas; Schaller, Emely; Steinmann, Paul; Boccaccini, Aldo R.; Budday, Silvia (Journal of the Mechanical Behavior of Biomedical Materials, 2020)
Mimicking the mechanical properties of native human tissues is one key route in tissue engineering. However, the successful cre- ation of functional tissue equivalents requires the comprehensive understanding of the complex and nonlinear mechanical properties of both native tissues and biomaterials. Here, we demonstrate that it is possible to replicate the complex mechanical behavior of soft tissues, exemplary shown for porcine brain tissue, under multiple loading conditions, compression, tension, and torsional shear, through simple blends of alginate and gelatin hydrogels. Alginate exhibits a pronounced compression-tension asymmetry and a nonlinear behavior, while gelatin shows an almost linear response. Blended together, alginate-gelatin (ALG-GEL) hydrogels can resemble the characteristic nonlinear, conditioning, and compression-tension-asymmetric behavior of brain tissue. We demonstrate that hydrogel concentration and incubation effectively tune the stiffness and loading-mode-specific stress relaxation behavior. The stiffness increases with increasing hydrogel concentration and decreases with increasing incubation time. In addition, we observe slower stress relaxation after long incubation times. Our systematic approach highlights the importance of single component, multi-modal mechanical analysis of hydrogels to understand the distinct structure-mechanics relation of each hydrogel component to eventually mimic the response of native tissues. The presented dataset will allow for the structurally derived compositional design of hydrogels for a broad variety of tissue engineering applications.
Keywords: biomechanics; nonlinear material behavior; tissue engineering; brain tissue; alginate-gelatin hydrogels

Algorithms and Data Structures for Matrix-Free Finite Element Operators with MPI-Parallel Sparse Multi-Vectors - Davydov, Denis; Kronbichler, Martin (ACM Transactions on Parallel Computing, 2020)
Traditional solution approaches for problems in quantum mechanics scale as O(M3), where M is the number of electrons. Various methods have been proposed to address this issue and obtain a linear scaling O(M). One promising formulation is the direct minimization of energy. Such methods take advantage of physical localization of the solution, allowing users to seek it in terms of non-orthogonal orbitals with local support. This work proposes a numerically efficient implementation of sparse parallel vectors within the open-source finite element library deal.II. The main algorithmic ingredient is the matrix-free evaluation of the Hamiltonian operator by cell-wise quadrature. Based on an a-priori chosen support for each vector, we develop algorithms and data structures to perform (i) matrix-free sparse matrix multivector products (SpMM), (ii) the projection of an operator onto a sparse sub-space (inner products), and (iii) post-multiplication of a sparse multivector with a square matrix. The node-level performance is analyzed using a roofline model. Our matrix-free implementation of finite element operators with sparse multivectors achieves a performance of 157 GFlop/s on an Intel Cascade Lake processor with 20 cores. Strong and weak scaling results are reported for a representative benchmark problem using quadratic and quartic finite element base

A material model for lamination stacks based on rough contacts - Luchscheider, Vera; Willner, Kai; Maidorn, Mischa (2014 4th International Electric Drives Production Conference, EDPC 2014, 2014)
This contribution presents, how to identify a material model of a lamination stack. The contact behavior between the single sheets is nonlinear and influences the behavior of the whole stack. The Simulation of the contact behavior is performed with contact models for normal and tangential direction. Due to the fact that calculating all sheets with contact is computational very expensive, a FE2-method is presented. With this method the calculation of the stack's behavior is based on a representative volume element. Further it is possible to identify a material model for the whole stack, which has got a linear and a nonlinear part. The linear part is caused by the material of the sheet, whereas the nonlinear part is a result of the contact behavior.
Keywords: lamination stack; material model; multiscale homogenization; normal and tangential contact behavior

A matrix-free approach for finite-strain hyperelastic problems using geometric multigrid - Davydov, Denis; Pelteret, Jean-Paul; Arndt, Daniel; Kronbichler, Martin; Steinmann, Paul (International Journal for Numerical Methods in Engineering, 2020)
This work investigates matrix-free algorithms for problems in quasi-static finite-strain hyperelasticity. Iterative solvers with matrix-free operator evaluation have emerged as an attractive alternative to sparse matrices in the fluid dynamics and wave propagation communities because they significantly reduce the memory traffic, the limiting factor in classical finite element solvers. Specifically, we study different matrix-free realizations of the finite element tangent operator and determine whether generalized methods of incorporating complex constitutive behavior might be feasible. In order to improve the convergence behavior of iterative solvers, we also propose a method by which to construct level tangent operators and employ them to define a geometric multigrid preconditioner. The performance of the matrix-free operator and the geometric multigrid preconditioner is compared to the matrix-based implementation with an algebraic multigrid (AMG) preconditioner on a single node for a representative numerical example of a heterogeneous hyperelastic material in two and three dimensions. We find that matrix-free methods for finite-strain solid mechanics are very promising, outperforming linear matrix-based schemes by two to five times, and that it is possible to develop numerically efficient implementations that are independent of the hyperelastic constitutive law.
CRIS-Team Scopus Importer:2020-03-20
Keywords: adaptive finite-element method; finite-strain; geometric multigrid; hyperelasticity; matrix-free

A mechanical approach to explain cortical folding phenomena in healthy and diseased brains - Budday, Silvia; Steinmann, Paul; Kuhl, Ellen (PAMM, 2014)
The development of the human brain with its characteristically folded surface morphology remains an intensively discussed topic. Impressive advancements in different fields of research have enhanced the understanding of the brain. However, the mechanism that underlies the folding process in healthy and diseased brains remains undetermined. Here, we hypothesize that growth induced mechanical instabilities drive folding. Using the nonlinear field theories of continuum mechanics supplemented by the theory of finite growth [1], we model the human brain as a bi-material with the cerebral cortex, a morphogenetically growing outer layer of gray matter, and the subcortex, a strain-driven growing inner core of white matter [2]. This approach integrates the two popular but competing hypotheses that cortical folding is either driven by differential growth or by axon elongation. Through systematic sensitivity analyses, we identify the critical process parameters of cortical folding and quantify their impact on brain morphology. We further simulate phenomena causing malformations like lissencephaly and polymicrogyria [3], which are associated with neurological disorders, including severe retardation, epilepsy, schizophrenia, and autism. Understanding the mechanisms of cortical folding during brain development might facilitate the diagnostics and treatment of malformed brains. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
UnivIS-Import:2015-07-08:Pub.2014.tech.FT.FT-TM.amecha_7

A mechanical model predicts morphological abnormalities in the developing human brain - Budday, Silvia; Kuhl, Ellen; Raybaud, Charles (Scientific Reports, 2014)
The developing human brain remains one of the few unsolved mysteries of science. Advancements in developmental biology, neuroscience, and medical imaging have brought us closer than ever to understand brain development in health and disease. However, the precise role of mechanics throughout this process remains underestimated and poorly understood. Here we show that mechanical stretch plays a crucial role in brain development. Using the nonlinear field theories of mechanics supplemented by the theory of finite growth, we model the human brain as a living system with a morphogenetically growing outer surface and a stretch-driven growing inner core. This approach seamlessly integrates the two popular but competing hypotheses for cortical folding: axonal tension and differential growth. We calibrate our model using magnetic resonance images from very preterm neonates. Our model predicts that deviations in cortical growth and thickness induce morphological abnormalities. Using the gyrification index, the ratio between the total and exposed surface area, we demonstrate that these abnormalities agree with the classical pathologies of lissencephaly and polymicrogyria. Understanding the mechanisms of cortical folding in the developing human brain has direct implications in the diagnostics and treatment of neurological disorders, including epilepsy, schizophrenia, and autism.
UnivIS-Import:2015-03-09:Pub.2014.tech.FT.FT-TM.amecha

A mixed variational formulation for a class of contact problems in viscoelasticity - Matei, Andaluzia Cristina; Sitzmann, Saskia; Willner, Kai; Wohlmuth, B. I. (Applicable Analysis, 2018)
We consider a deformable body in frictionless unilateral contact with a moving rigid obstacle. The material is described by a viscoelastic law with short memory, and the contact is modeled by a Signorini condition with a time-dependent gap. The existence and uniqueness results for a weak formulation based on a Lagrange multipliers approach are provided. Furthermore, we discuss an efficient algorithm approximating the weak solution for the more general case of a two-body contact problem including friction. In order to illustrate the theory we present two numerical examples in 3D.
CRIS-Team Scopus Importer:2022-08-05
Keywords: 3D numerical examples; Dual lagrange multipliers; Primal-dual active set strategy; Unilateral contact; Viscoelasticity

A Model for Translation and Rotation Resistance Tensors for Superellipsoidal Particles in Stokes Flow - Štrakl, Mitja; Hriberšek, Matjaž; Wedel, Jana; Steinmann, Paul; Ravnik, Jure (Journal of Marine Science and Engineering, 2022)
In this paper, forces and torques on solid, non-spherical, orthotropic particles in Stokes flow are investigated by using a numerical approach on the basis of the Boundary Element Method. Different flow patterns around a particle are considered, taking into account the contributions of uniform, rotational and shear flows, to the force and the torque exerted on the particle. The expressions for the force and the toque are proposed, by introducing translation, rotation and deformation resistance tensors, which capture each of the flow patterns individually. A parametric study is conducted, considering a wide range of non-spherical particles, determined by the parametric superellipsoid surface equation. Using the results of the parametric study, an approximation scheme is derived on the basis of a multivariate polynomial expression. A coefficient matrix for the polynomial model is introduced, which is used as a tunable parameter for a minimization problem, whereby the polynomials are fitted to the data. The developed model is then put to the test by considering a few examples of particles with different shapes, while also being compared to other, currently available solutions. On top of that, the full functionality of the model is demonstrated by considering an example of a pollen grain, as a realistic non-spherical particle. First, a superellipsoid, which best fits the actual particle shape, is found from the considered range. After that, the coefficients of the translation, rotation and deformation resistance tensors are obtained from the present model and compared to the results of other available models. In the conclusion, a superior accuracy of the present model, for the considered range of particles, is established. To the best of the authors knowledge, this is also one of the first models to extend the torque prediction capabilities beyond sphere and prolate particles. At the same time, the model was demonstrated to be simple to implement and very conservative with the computational resources. As such, it is suitable for large scale studies of dispersed two-phase flows, with a large number of particles.
CRIS-Team Scopus Importer:2022-03-25
Keywords: Boundary Element Method; Drag; Non-spherical; Particle; Resistance tensor; Rotation tensor; Stokes flow; Torque

A multi-scale approach to model the curing process in magneto-sensitive polymeric materials - Mokarram, Hossain; Chatzigeorgiou, Georgios; Meraghni, Fodil; Steinmann, Paul (International Journal of Solids and Structures, 2015)
We propose a magneto-mechanically coupled multi-scale model for simulating the curing process of polymers. In the case of magneto-sensitive polymers, micron-size ferromagnetic particles are mixed with a liquid polymeric matrix in the uncured stage. The polymer curing process is a complex process that transforms a fluid to a solid with time. To transfer the constituent parameter information from the micro-scale to the macro-scale for a composite magneto-mechanically coupled polymeric material, an extended Mori–Tanaka semi-analytic homogenization procedure is utilized. The stiffness gaining phenomenon as in the case of a curing process is realized by time-dependent material parameters appearing within the composite piezomagnetic material tensors. Moreover, to compute the volume reduction during curing, a magnetic induction dependent shrinkage model is proposed. Several numerical examples show that the model proposed herein can capture major observable phenomena in the curing process of polymers under magneto-mechanically coupled infinitesimal deformations.
UnivIS-Import:2015-03-09:Pub.2015.tech.FT.FT-TM.amulti
Keywords: Magneto-sensitive polymers; Polymer curing; Shrinkage; Homogenization; Magneto-mechanical coupled problem; Mori–Tanaka model

An adaptive finite element method based on sensitivities for node insertion - Friederich, Jan; Leugering, Günter; Steinmann, Paul (GAMM-Mitteilungen, 2012)
We consider refinement of finite element discretizations by splitting nodes along edges. For this process, we derive asymptotic expansions of Galerkin solutions of linear second-order elliptic equations. Thereby, we calculate a topological derivative w.r.t. node insertion for functionals such as the total potential energy, minimization of which decreases the approxi- mation error in the energy norm. Hence, these sensitivities can be used to define indicators for local h-refinement. Our results suggest that this procedure leads to an efficient adaptive re- finement method. This presentation is concerned with a model problem in 1d. The extension of this concept to higher dimensions will be the subject of forthcoming publications.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.anadap

An adaptive singular finite element in nonlinear fracture mechanics - Denzer, Ralf; Scherer, Michael; Steinmann, Paul (Proceedings of the International Symposium on Defect and Material Mechanics, 2008)
UnivIS-Import:2015-04-16:Pub.2008.tech.FT.FT-TM.anadap

Analysis of the lamination stack influence on the stiffness of stator active component - Luchscheider, Vera; Willner, Kai (PAMM, 2012)
UnivIS-Import:2015-04-16:Pub.2012.tech.FT.FT-TM.analys_5

Analysis of the machining accuracy when dry turning via experiments and finite element simulations - Aurich, Jan C.; Zimmermann, Marco; Schindler, Stefan; Steinmann, Paul (Production Engineering, 2013)
Workpiece and tool are subjected to severe mechanical and thermal loads when turning. These loads cause thermal expansions and mechanically induced deflections of the tool and the workpiece. Such deformations induce deviations from the nominal workpiece geometry. In order to decrease these deviations, the cutting condition needs to be optimized prior to actual machining. In this paper, the accuracy of machining when dry turning aluminum is analyzed via experiments and finite element simulations. For this purpose, seven characteristic values were used: the forces, the deflection of the workpiece, the quantity of heat in the workpiece, the temperature distribution in the workpiece, the temperature of the tool, the temperature of the tool holder, and the actual dimension of the workpiece after turning. These experimentally determined results serve in addition as boundary conditions for a 3D finite element model of the workpiece, which calculates the deformations of the workpiece. The continuous removal of material affecting the temperature distribution in the workpiece is considered. The actual dimensions of the workpiece after turning revealed a remarkable influence of the cutting condition used on the accuracy of machining. Differences of up to 116 μm regarding the deviation from the nominal workpiece diameter of 30 mm were observed. The analysis of the machining accuracy reveals that particularly the use of both high cutting speeds and feeds enhances the accuracy of machining when dry turning aluminum. © 2013 German Academic Society for Production Engineering (WGP).
UnivIS-Import:2015-03-09:Pub.2014.tech.FT.FT-TM.analys
Keywords: Cutting conditions; Deflections; Finite element simulation; Machining accuracy; Thermo-elastic deformations

Analysis of thermo-mechanical effects on the machining accuracy when turning aluminum alloys - Zimmermann, Marco; Schindler, Stefan; Steinmann, Paul; Aurich, Jan C. (Proceedings of the 9th International Conference on High Speed Machining, 2012)
UnivIS-Import:2015-04-16:Pub.2012.tech.FT.FT-TM.analys

ANALYTICAL MECHANICS ALLOWS NOVEL VISTAS ON MATHEMATICAL EPIDEMIC DYNAMICS MODELING - Steinmann, Paul (Mathematics and Mechanics of Complex Systems, 2020)
This contribution aims to shed light on mathematical epidemic dynamics modeling from the viewpoint of analytical mechanics. To set the stage, it recasts the basic SIR model of mathematical epidemic dynamics in an analytical mechanics setting. Thereby, it considers two possible reparametrizations of the basic SIR model: one rescales time, while the other transforms the coordinates, i.e., the independent variables. In both cases, Hamilton's equations in terms of a suited Hamiltonian as well as Hamilton's principle in terms of a suited Lagrangian are considered in minimal and extended phase and state space coordinates, respectively. The corresponding Legendre transformations relating the various options for the Hamiltonians and Lagrangians are detailed. Ultimately, this contribution expands on a multitude of novel vistas on mathematical epidemic dynamics modeling that emerge from the analytical mechanics viewpoint. As a result, it is believed that interesting and relevant new research avenues open up when exploiting in depth the analogies between analytical mechanics and mathematical epidemic dynamics modeling.
CRIS-Team WoS Importer:2021-01-15

An Arlequin-based method to couple molecular dynamics and finite element simulations of amorphous polymers nanocomposites - Pfaller, Sebastian; Rahimi, Mashid; Possart, Gunnar; Steinmann, Paul; Müller-Plathe, Florian; Böhm, Michael C. (Computer Methods in Applied Mechanics and Engineering, 2013)
A new simulation technique is introduced to couple a flexible particle domain as encountered in soft-matter systems and a continuum which is solved by the Finite Element (FE) method. The particle domain is simulated by a molecular dynamics (MD) method in coarse grained (CG) representation. On the basis of computational experiences from a previous study, a staggered coupling procedure has been chosen. The proposed MD-FE coupling approximates the continuum as a static region while the MD particle space is treated as a dynamical ensemble. The information transfer between MD and FE domains is realized by a coupling region which contains, in particular, additional auxiliary particles, so-called anchor points. Each anchor point is harmonically bonded to a standard MD particle in the coupling region. This type of interaction offers a straightforward access to force gradients at the anchor points that are required in the developed hybrid approach. Time-averaged forces and force gradients from the MD domain are transmitted to the continuum. A static coupling procedure, based on the Arlequin framework, between the FE domain and the anchor points provides new anchor point positions in the MD-FE coupling region. The capability of the new simulation procedure has been quantified for an atactic polystyrene (PS) sample and for a PS-silica nanocomposite, both simulated in CG representation. Numerical data are given in the linear elastic regime which is conserved up to 3% strain. The convergence of the MD-FE coupling procedure has been demonstrated for quantities such as reaction forces or the Cauchy stress which have been determined both in the bare FE domain and in the coupled system. Possible applications of the hybrid method are shortly mentioned. © 2013 Elsevier B.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.anarle
Keywords: Bridging domain method; Domain decomposition; Lagrange multipliers; Multiscale modeling; Nanocomposites; Particle-continuum coupling

An atomistic scale analysis of ferroelectric nanodomain interfaces - Endres, Florian; Steinmann, Paul (Proceedings in Applied Mathematics and Mechanics, 2015)
We discuss numerical results of nanodomain interfaces using a new extended molecular statics algorithm for ferroelectric materials. The new algorithm is able to not only calculate the change of the polarization behavior caused by strain but also the influence on the polarization behavior due to mechanical stress. The size effects of 180° head to head and tail to tail nanodomains have already been investigated. This study also considers 90° domain walls and discusses the impact of mechanical stress on polarization patterns and system energies of nanodomain interfaces.

Anatomy matters: The role of the subject-specific respiratory tract on aerosol deposition — A CFD study - Wedel, Jana; Steinmann, Paul; Štrakl, Mitja; Hriberšek, Matjaž; Cui, Yan; Ravnik, Jure (Computer Methods in Applied Mechanics and Engineering, 2022)
The COVID-19 pandemic is one of the greatest challenges to humanity nowadays. COVID-19 virus can replicate in the host's larynx region, which is in contrast to other viruses that replicate in lungs only, i.e. SARS. This is conjectured to support a fast spread of COVID-19. However, there is sparse research in this field about quantitative comparison of virus load in the larynx for varying susceptible individuals. In this regard the lung geometry itself could influence the risk of reproducing more pathogens and consequently exhaling more virus. Disadvantageously, there are only sparse lung geometries available. To still be able to investigate realistic geometrical deviations we employ three different digital replicas of human airways up to the 7th level of bifurcation, representing two realistic lungs (male and female) as well as a more simplified experimental model. Our aim is to investigate the influence of breathing scenarios on aerosol deposition in anatomically different, realistic human airways. In this context, we employ three levels of cardiovascular activity as well as reported experimental particle size distributions by means of Computational Fluid Dynamics (CFD) with special focus on the larynx region to enable new insights into the local virus loads in human respiratory tracts. In addition, the influence of more realistic boundary conditions is investigated by performing transient simulations of a complete respiratory cycle in the upper lung regions of the considered respiratory models, focusing in particular on deposition in the oral cavity, the laryngeal region, and trachea, while simplifying the tracheobronchial tree. The aerosol deposition is modeled via OpenFOAMt4ht=® by employing an Euler-Lagrangian frame including steady and unsteady Reynolds Averaged Navier–Stokes (RANS) resolved turbulent flow using the k-ω-SST and k-ω-SST DES turbulence models. We observed that the respiratory geometry altered the local deposition patterns, especially in the laryngeal region. Despite the larynx region, the effects of varying flow rate for the airway geometries considered were found to be similar in the majority of respiratory tract regions. For all particle size distributions considered, localized particle accumulation occurred in the larynx of all considered lung models, which were more pronounced for larger particle size distributions. Moreover, it was found, that employing transient simulations instead of steady-state analysis, the overall particle deposition pattern is maintained, however with a stronger intensity in the transient cases.
CRIS-Team Scopus Importer:2022-10-07
Keywords: Aerosol; CFD; OpenFOAM; SARS-CoV-2

An efficient procedure for concrete fracture analysis based on mesh refinement ergodicity - Chacón, G.; Rivarola, F. L.; van Huyssteen, Daniel; Steinmann, Paul; Etse, G. (Computational Mechanics, 2024)
In this paper a new procedure for modeling brittle fracture processes in concrete components is proposed in the framework of the so-called discrete crack approach and exploiting ergodic behaviour with respect to the refinement of the mesh. The complexity in controlling localized crack development in quasi-brittle materials like concrete usually necessitates very fine meshes that are associated with a very high computational cost. In this work, a method is proposed that exploits the ergodic behavior with respect to mesh refinement/density observed in simulations performed on randomly generated meshes. The proposed method is framed in the discrete crack concept, which avoids or minimizes mesh dependence. It considers the interaction between elastic solids or aggregates and nonlinear interfaces, where the fractures are described based on the relative displacements at the joints where energy dissipation occurs. To allow significant geometric flexibility in the modeling of elastic aggregates, Voronoi discretizations of virtual elements are used in combination with nonlinear interface elements. Numerical simulations of benchmark problems demonstrate that the proposed procedure accurately predicts failure behavior in brittle materials. Specifically, the peak load, crack path, and load–displacement relationship obtained from the averaged behavior of coarse-mesh simulations closely match those from very fine-mesh simulations. The results demonstrate that by taking advantage of both the well-known mesh flexibility of virtual element method and the observed ergodic behavior with respect to mesh density, the proposed procedure represents an efficient and accurate tool for modeling failure behavior in quasi-brittle materials such as concrete.
CRIS-Team Scopus Importer:2024-06-21
Keywords: Interface element; Mesh refinement ergodicity; Virtual element method

An energetically consistent heat input model for additive manufacturing - Burkhardt, Christian; Soldner, Dominic; Steinmann, Paul; Mergheim, Julia (Proceedings in Applied Mathematics and Mechanics, 2019)
Additive manufacturing offers the ability to design parts more freely and to realize complex geometries that would not have been manufacturable with conventional processes. In powder bed‐based beam melting processes parts are build in a layer‐by‐layer fashion by selectively melting the powder material to generate the part. The energy input of the laser beam and the temperature distribution during the process strongly influence the quality of the produced part and can be studied by means of macroscopic thermal simulations. Due to the non‐linearity of the material behaviour and the diverging time and length scales huge computational costs arise. In the present contribution a temporal integration of the heat input model is used to allow for larger time step sizes. In order to reduce the errors due to the spatial discretization in the heat affected zone, a correction term is introduced, rendering an energetically consistent heat input. A numerical example shows the success of this strategy.<br

An energetically consistent surface correction method for bond-based peridynamics - Ritter, Jonas; Shegufta, Shucheta; Steinmann, Paul; Zaiser, Michael (Forces in Mechanics, 2022)
A novel surface correction method is proposed for bond-based peridynamics which ensures energy consistency with a classical reference body for general affine deformations. This method is validated for simple geometries and then applied to a typical surface-dominated problem, namely the indentation of a surface in the shallow to moderate-depth regime.
CRIS-Team Scopus Importer:2022-11-04
Keywords: Indentation; Peridynamics; Surface effect

A new approach for the FE modelling of cohesive cracks - Mergheim, Julia; Steinmann, Paul; Kuhl, Ellen (Proceedings of 21st International Congress of Theoretical and Applied Mechanics, 2004)
UnivIS-Import:2015-04-16:Pub.2004.tech.FT.FT-TM.anewap_9

A new micro–macro transition for hyperelastic materials - Zhan, Lin; Wang, Siyu; Qu, Shaoxing; Steinmann, Paul; Xiao, Rui (Journal of the Mechanics and Physics of Solids, 2023)
Many classic hyperelastic models fail to predict the stress responses of soft materials in complex loading conditions with parameters calibrated through one simple test. To address this fundamental issue, we propose a new micro–macro transition for the microstructural hyperelasticity modeling, which is further integrated into the full network framework. With a Gaussian chain distribution, this new mapping scheme yields an explicit one-parameter hyperelastic model in terms of principal stretches. This new linear model achieves remarkable success in capturing the stress responses in multi-axial deformation modes for soft materials with an absence of strain stiffening effect, which is beyond the capability of the widely used neo-Hookean model. A new two-parameter hyperelastic model is further developed by combining the new micro–macro transition and non-Gaussian Langevin chain distribution. Compared with other two-parameter hyperelastic models based on Langevin statistics, such as the eight-chain model, affine full network model, and equilibrated microsphere model, our new model exhibits greatly improved predictive ability for complex loading types. The new model is also implemented for finite element analysis, which shows the ability to capture the responses of soft materials with heterogeneous strain distribution. In all cases, the parameters in our models can be determined through the data of uniaxial loading tests, along with the behaviors in other loading modes being well forecast, which is a challenge for various other existing hyperelastic models. This novel micro–macro transition is shown to properly capture the inherent correlations between different deformation modes, which may advance fundamentally modeling hyperelasticity and other constitutive behaviors for soft materials.
CRIS-Team Scopus Importer:2023-01-13
Keywords: Finite element simulation; Hyperelastic model; Micro–macro transition; Multi-axial deformation

An extended molecular statics algorithm simulating the electromechanical continuum response of ferroelectric materials - Endres, Florian; Steinmann, Paul (Computational Mechanics, 2014)
Molecular dynamics (MD) simulations of ferroelectric materials have improved tremendously over the last few decades. Specifically, the core-shell model has been commonly used for the simulation of ferroelectric materials such as barium titanate. However, due to the computational costs of MD, the calculation of ferroelectric hysteresis behaviour, and especially the stress-strain relation, has been a computationally intense task. In this work a molecular statics algorithm, similar to a finite element method for nonlinear trusses, has been implemented. From this, an algorithm to calculate the stress dependent continuum deformation of a discrete particle system, such as a ferroelectric crystal, has been devised. Molecular statics algorithms for the atomistic simulation of ferroelectric materials have been previously described. However, in contrast to the prior literature the algorithm proposed in this work is also capable of effectively computing the macroscopic ferroelectric butterfly hysteresis behaviour. Therefore the advocated algorithm is able to calculate the piezoelectric effect as well as the converse piezoelectric effect simultaneously on atomistic and continuum length scales. Barium titanate has been simulated using the core-shell model to validate the developed algorithm.
UnivIS-Import:2015-03-09:Pub.2014.tech.FT.FT-TM.anexte
Keywords: Barium titanate; Core-shell model; Ferroelectric hysteresis; Ferroelectric material; Molecular statics

An implicitly coupled finite element-electronic circuit simulator method for efficient system simulations of piezoelectric energy harvesters - Hegendörfer, Andreas; Steinmann, Paul; Mergheim, Julia (Journal of Intelligent Material Systems and Structures, 2023)
A piezoelectric vibration-based energy harvester (PVEH) consists of an electromechanical structure and an electric circuit, influencing each other. The finite element method (FEM) allows for the simulation of arbitrarily shaped and nonlinear electromechanical structures, while an electronic circuit simulator (ECS) can be applied to simulate arbitrary electric circuits. We propose a novel implicit FEM-ECS coupling method, which combines the advantages of the FEM and the flexibility of an ECS. The Newton-Raphson method is applied to achieve rapid convergence at the interface between the FEM and ECS simulations, so that arbitrary PVEHs can be efficiently analyzed. The new implicit FEM-ECS coupling is validated against explicitly and monolithically coupled FEM-ECS simulations of PVEHs from literature. Moreover, an application example consisting of a nonlinear electromechanical structure and a self-powered SSHI circuit is considered and a shock-like base excitation is applied. The examples demonstrate the practical applicability of the novel coupling method for realistic simulations of PVEHs.
CRIS-Team Scopus Importer:2023-04-07
Keywords: coupled problem; electronic circuit simulator; finite element method; multiphysics simulation; numerical simulation; Piezoelectric energy harvesting

An integrated approach to shape optimization and mesh adaptivity based on material residual forces - Riehl, Stefan; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2014)
This contribution is concerned with the coupling of finite element based shape optimization to methods of mesh adaptivity. Therein, the nodal points of a finite element mesh serve as design variables in an optimization problem that aims to minimize a cost functional with respect to different constraints. In order to avoid the occurrence of oscillating boundaries in the optimal design trials, we generate the respective design updates through solving a series of fictitious boundary value problems on an updated Lagrangian configuration. The design update process is accompanied by adaptive mesh refinement to obtain more accurate results for the structural analysis and the design sensitivity analysis. For the mesh adaptation process, we consider r-adaptive node relocation, h-adaptive mesh refinement and a combination of both approaches. In each case, the derivations rest upon the notion of material residual forces induced by finite element discretization and the coupling of shape optimization and mesh adaptivity is of intermittent type, i.e. mesh adaptivity is invoked once a certain number of design updates has been generated. We examine the benefits of the proposed method on the basis of some numerical examples in comparison to the same shape optimization method not involving adaptive mesh refinement where we evaluate the corresponding numerical costs, the gain in accuracy and the effects on the optimal shapes being obtained.
UnivIS-Import:2015-03-09:Pub.2014.tech.FT.FT-TM.aninte
Keywords: Adaptive finite elements; Material force method; Shape optimization; Traction method

An internal-variable rod model for stress-induced phase transitions in a slender SMA layer. I. asymptotic equations and a two-phase solution - Wang, Jiong; Dai, Hui-Hui (Mechanics of Materials, 2012)
In part I of this series of two papers, an internal-variable rod model is proposed to study the stress-induced phase transitions in a slender shape memory alloy (SMA) layer. To study the mechanical responses of SMAs, two independent energy functions are adopted: the Helmholtz free energy and the rate of mechanical dissipation. A phase state variable is introduced to describe the phase transition process. Starting from the 2-D governing system and by using the coupled series-asymptotic expansion method, one single equilibrium equation is derived, which involves the leading order term of the axial strain and the phase state functions. Further by using the phase transition criteria, the evolution laws of the phase state functions corresponding to the outer loop of the stress-strain response are derived. As a result, the governing ODEs for the purely loading and purely unloading processes are obtained, which are called the asymptotic rod equations. The two-phase solution of the asymptotic rod equations in an infinitely long layer is then constructed. An explicit solution for the phase volume fraction of the corresponding inhomogeneous deformation is deduced, which appears to be the first analytical expression for this important quantity in stress-induced phase transitions. The key parameters in terms of original material constants for the phase transitions and deformations are also identified. © 2011 Elsevier Ltd. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.aninte

An internal-variable rod model for stress-induced phase transitions in a slender SMA layer. II. analytical solutions for the outer loop and inner loops - Wang, Jiong; Dai, Hui-Hui (Mechanics of Materials, 2011)
In this sequel paper, the analytical solutions to the asymptotic rod equations (derived in part I of this series of papers) are constructed. More specifically, it is considered that the two ends of the layer satisfy the natural boundary conditions. By conducting a phase plane analysis, both a force-controlled problem and a displacement-controlled problem are studied. It is found that under certain conditions, both the constant solutions and the nontrivial solutions exist. The explicit expressions for the possible solutions are derived and the corresponding stress–strain curves are plotted. By comparing the total pseudo-elastic energies, the preferred solution in the displacement-controlled problem is determined. With the preferred solution obtained, the stress–strain curve and the profiles of the layer at the different stages are plotted, which can capture the key experimental features. Some further analysis has been given on the inner loops, where the reverse loading processes start just after the phase transformations are partially completed. By using the WKB method, the asymptotic solutions corresponding to the inner loops are constructed, which appear to provide the first analytical descriptions for the inner loops. The corresponding stress–strain curves and the graphes of the axial strain distribution of the layer are plotted. It is shown that the analytical solutions for the inner loops are also consistent with the experimental results.
UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.aninte_2

An investigation of free vibrations of a strain gradient Timoshenko beams with the method of initial values - Nur, Ceyda; Artan, Reha (Microsystem Technologies-Micro-And Nanosystems-Information Storage and Processing Systems, 2019)
Investigated herein is the free vibrations of beams based on the strain gradient Timoshenko beam theory with the method of initial values. For the vibration of strain-gradient Timoshenko beam (SGTB), the sixth-order ordinary differential equation and three boundary conditions at each end have been obtained by using the Hamilton principle. The effect of the characteristic length on the frequencies of free vibrations is shown. The frequencies of the SGTB are compared to the frequencies of the strain gradient Euler beam (SGEB), classical Timoshenko beam (CTB) and classical Euler beam (CEB). It has been observed that the high-frequency values of conventional and strain-gradient beams are very different. This result can be used to determine the value of the material characteristic length for a nanobeam for which lengthscale effects are believed to be dominant.
CRIS-Team Scopus Importer:2019-10-29

An investigation of static bending of a bi-directional strain-gradient Euler–Bernoulli nano-beams with the method of initial values - Çelik, Murat; Artan, Reha (Microsystem Technologies-Micro-And Nanosystems-Information Storage and Processing Systems, 2020)
Investigated herein is the static bending of Euler–Bernoulli nano-beams made of bi-directional functionally graded material with the method of initial values in the frame of gradient elasticity. To the best of the researchers’ knowledge, in the literature, there is no study carried out into gradient elasticity theory for bending analysis of bi-directional strain-gradient Euler–Bernoulli (BDSGEB) nanostructures with arbitrary functions. Basic equations and boundary conditions are derived by using the principle of minimum potential energy. The transfer matrix for beams is given analytically. For an initial value problem, the transport matrix is unique. The diagrams of the solutions for different end conditions and various values of the parameters are given and the results are discussed.
CRIS-Team Scopus Importer:2020-06-30

An MD-FE coupling simulation method applied to fracture of viscoelastic-viscoplastic glassy polymers. - Zhao, Wuyang; Pfaller, Sebastian (Presentations and videos to 16th International Conference on Computational Plasticity (COMPLAS 2021), 2021)
Fracture of materials is a multiscale process and requires appropriate simulation techniques. In order to obtain fine scale insights into the processes near the crack tip, an atomistic point of view in this region is suitable, but needs to be embedded into macroscopic loading conditions of the surrounding material. In this regard, particle-continuum coupling methods are appropriate for simulations of fracture, which treat the vicinity of the crack at particle resolution while describing the material far away by continuum mechanics. Although there have been various multiscale simulation methods designed to study the fracture of crystalline materials or elastic polymers, multiscale methods for simulations of viscoelastic or viscoplastic polymers are still rare due to the complex mechanical behavior and the material’s amorphous structure. The Capriccio method [1] was proposed for multiscale simulations of glassy polymers within the elastic regime, which couples a particle domain resolved by Molecular Dynamics (MD) simulations with stochastic boundary conditions and a continuum domain solved by the Finite-Element (FE) method. This method has been extended to inelasticity [4] by employing a viscoelastic-viscoplastic constitutive model [3] informed by MD simulations [2] in the continuum domain. In this contribution, we enhance the inelastic Capriccio method [4] to simulations of fracture of glassy polymers. We consider a polystyrene sample with a pre-crack consisting of a cubic MD domain embedded in an FE domain. The sample is loaded in Mode-I and its mechanical behavior is studie
Keywords: Fracture; Polymers; Viscoelasticity; Viscoplasticity; Particle-continuum coupling

A non-invasive form finding approach with application to metal forming - Landkammer, Philipp; Schneider, Thomas; Schulte, Robert Karl; Steinmann, Paul; Merklein, Marion (Production Engineering, 2016)
Inverse form finding aims in determining the optimal material configuration of a workpiece for a specific forming process. A gradient- and parameter-free (nodal-based) form finding approach has recently been developed, which can be coupled non-invasively as a black box to arbitrary finite element software. Additionally the algorithm is independent from the constitutive behavior. Consequently, the user has not to struggle with the underlying optimization theory behind. Benchmark tests showed already that the approach works robustly and efficiently. This contribution demonstrates that the optimization algorithm is also applicable to more sophisticated forming processes including orthotropic large strain plasticity, combined hardening and frictional contact. A cup deep drawing process with solid-shell elements and a combined deep drawing and upsetting process to form a functional component with external teeth are investigated.
LFT Import::2019-08-07 (2148)
Keywords: Inverse form finding; Shape optimization; Cup deep drawing; Sheet-bulk Metal Forming

A non-invasive heuristic approach to shape optimization in forming - Landkammer, Philipp; Steinmann, Paul (Computational Mechanics, 2016)
The aim is to determine - relating to a given forming process - the optimal material (undeformed) configuration of a workpiece when knowing the target spatial (deformed) configuration. Therefore, the nodal positions of a discretized setting based on the finite element method (FEM) are the discrete free parameters of the form finding problem. As a verification, inputting the determined optimal material nodal positions, a subsequent re-computation of the forming process should then result in exactly the target spatial nodal positions. A new, non-invasive iterative algorithm, which is purely based on the nodal data of each iteration, is proposed to determine the discretized optimal material configuration. Specifically, the L2-smoothed deformation gradient at each discretization node is used to update the discretized material configuration by a transformation of the difference vectors between the currently computed and the target spatial nodal positions. The iterative strategy can be easily coupled in a non-invasive fashion via subroutines with arbitrary external FEM software. Since only the computed positions of the discretization nodes are required for an update step within the form finding algorithm, the procedure does not depend on the specific material modelling and is moreover applicable to arbitrary element types, e. g. solid- or solid-shell-elements. Furthermore the convergence rate for solving the form finding problem is nearly linear. This is demonstrated by examples that are realized by a coupling of Matlab (iterative update procedure) and MSC.Marc (external FEM software). Solving the form finding problem to determine an optimum workpiece design is of great interest especially for metal forming application
UnivIS-Import:2015-10-26:Pub.2015.tech.FT.FT-TM.anonin
Keywords: Optimum workpiece design; Shape optimization; Metal forming; Non-invasive approach

A non-invasive node-based form finding approach with discretization-independent target configuration - Caspari, Michael; Landkammer, Philipp; Steinmann, Paul (Advanced Modeling and Simulation in Engineering Sciences, 2018)
Form finding is used to optimize the shape of a semi-finished product, i.e. the material configuration in a forming process. The geometry of the semi-finished product is adapted so that the computed spatial configuration corresponds to a prescribed target spatial configuration. Differences between these two configurations are iteratively minimized. The algorithm works non-invasively, thus there is a strict separation between the form update and the finite element (FE) forming simulation. This separation allows the use of arbitrary commercial FE-solvers. In particular, there is no need for a modification of the FE forming simulation, only the material configuration is iteratively updated. A new method is introduced to calculate the difference between the target and the computed spatial configuration. Thereby the target mesh is separated from the mesh for the FE forming simulation, which enables a more accurate and independent representation of the target configuration. In addition, the possibility of taking into account manufacturing constraints in the optimization process is presented. The procedure is illustrated for the example of the first stage of a novel two-stage sheet-bulk metal forming proces
Keywords: Form finding; Inverse problems; Metal forming; Non-invasive methods; Shape Opitmization

A nonlocal interface approach to peridynamics exemplified by continuum‐kinematics‐inspired peridynamics - Laurien, Marie; Javili, Ali; Steinmann, Paul (International Journal for Numerical Methods in Engineering, 2022)
In this contribution, we present a novel approach on how to treat material interfaces in nonlocal models based on peridynamics (PD) and in particular continuum-kinematics-inspired peridynamics (CPD), a novel variationally consistent peridynamic formulation. Our method relies on a nonlocal interface where the material subdomains overlap. Within this region, a kinematic coupling of the two constituents is enforced. The contact is purely geometrical as interaction forces act only between points of the same material. We provide a detailed description of the computational implementation within the framework of CPD, that is in principle applicable to all formulations of PD. A variety of numerical examples for modeling bimaterial interfaces illustrate the utility of the technique for both two-dimensional and three-dimensional problems, including examples at large deformations. Our model approaches a local model when the nonlocality parameter, the horizon size, is decreased. The proposed methodology offers a viable alternative to previous approaches in PD, which are essentially imposing mixture rules for the interfacial material parameters.<br
Keywords: peridynamics; nonlocality; material interface; continuum mechanics

A Novel Approach to Predict the Process-Induced Mechanical Behavior of Additively Manufactured Materials - Kergaßner, Andreas; Köpf, Johannes; Markl, Matthias; Körner, Carolin; Mergheim, Julia; Steinmann, Paul (Journal of Materials Engineering and Performance, 2021)
The grain structure and texture of additively manufactured materials depend strongly on the local temperature gradients during the solidification of the material. These grain structures and textures influence the mechanical behavior, ranging from isotropy to transversal and orthotropic symmetry. In the present contribution, a cellular automaton is used to model the grain growth during selective electron beam melting. The resulting grain structures and textures serve as input for a mesoscopic mechanical model. The mechanical behavior on the mesoscale is modeled by means of gradient-enhanced crystal plasticity, applying the finite element method. Computational homogenization is applied to determine the resulting macroscopic elastic and plastic properties of the additively manufactured metals. A general orthotropic yield criterion is identified by means of the initial yield loci computed with mesoscopic simulations of representative volume elements. The numerical results are partly validated with experimental data.
CRIS-Team WoS Importer:2021-05-21

A novel continuum approach to gradient plasticity based on the complementing concepts of dislocation and disequilibrium densities - Steinmann, Paul; Kergaßner, Andreas; Landkammer, Philipp; Zbib, Hussein M. (Journal of the Mechanics and Physics of Solids, 2019)
A geometrically linear continuum mechanics framework is proposed for gradient plasticity combining ‘strain gradients’ and, with a novel approach, ‘stress gradients’. Thereby the duality of kinematic and kinetic quantities is exploited in view of the ‘div-grad-curl orthogonality’ in continuum field theories. On the one hand the non-integrability of the plastic distortion results in the well-established dislocation density - often denoted as the geometrically-necessary-dislocation (GND) density - that enters the energy storage function. On the other hand - as entirely novel concept introduced in this contribution - the non-equilibrium of the plastic stress results in the disequilibrium density that parameterizes the dual dissipation potential within the convex analysis setting of plasticity. Consequently both, the dislocation density as well as the disequilibrium density contribute in modelling the size-dependent hardening state of a material in a continuum mechanics setting. The novel approach is eventually elucidated in much detail for the specific case of single crystal plasticity.
CRIS-Team Scopus Importer:2019-08-30

A novel model for the lift force acting on a prolate spheroidal particle in an arbitrary non-uniform flow. Part I. Lift force due to the streamwise flow shear - Cui, Yan; Ravnik, Jure; Hribersek, Matjaz; Steinmann, Paul (International Journal of Multiphase Flow, 2018)
The paper proposes a generic method to extend lift force models that were originally devised for single linear shear flow, to arbitrary flow conditions. The method computes the lift force due to the dominant streamwise flow shear in the Stokes flow regime by implementing a series of coordinate transformations, facilitating the computation of the lift force from dominant streamwise flow shear. The derived numerical algorithm is applied to the computation of a dedicated shear lift force model for prolate spheroidal particles (or axisymmetric ellipsoidal particles) and a novel generalised Saffman-type lift force model for spherical particles in a general shear flow. In order to verify the proposed shear lift force for prolate spheroidal particles, numerical simulations of a particle moving in Poiseuille flow at four different initial positions and two aspect ratios are perfomed. The new generalised Saffman-type lift model is compared with an established generalised Saffman-type lift model by simulating the axial migration of a spherical particle in Poiseuille flow. The computational results confirm the correctness of the proposed shear lift force models. (C) 2018 Elsevier Ltd. All rights reserved.
Keywords: Prolate spheroidal particle; Axisymmetric ellipsoidal particle; Shear lift force; Lagrangian particle tracking

A novel model for the lift force acting on a prolate spheroidal particle in arbitrary non-uniform flow. Part II. Lift force taking into account the non-streamwise flow shear - Cui, Yan; Ravnik, Jure; Verhnjak, Ozbej; Hribersek, Matjaz; Steinmann, Paul (International Journal of Multiphase Flow, 2019)
The present contribution is the second part of a two-part research work presenting a generic method to extend lift force models that were originally devised for single linear shear flow to arbitrary flow conditions. The method can be applied to the computation of lift forces exerted on prolate spheroidal particles (or fibres) in arbitrary non-uniform flows. The method proposed in the Part I calculates the lift force arising from the dominant streamwise flow shear. In Part II the influence of the non-streamwise flow shear on the lift force is also taken into account. The present method assumes that the particle slip velocity is parallel to the fluid velocity along the particle trajectory. The novelty in the presented method is the computation of the shear lift force model for prolate spheroidal particles taking into account also non-streamwise flow shear. The accuracy of the novel shear lift force model for prolate spheroidal particles is verified by comparing it with the lift force model proposed in Part I via simulating the axial migration of a prolate spheroidal particle in the Poiseuille flow. In order to validate the ability of the present method for capturing the lift component arising from non-streamwise flow shear, the lift force model is compared with established generalised Saffman-type lift models by simulating the motion of a particle in lid-driven cavity flow. The computational results demonstrate that the present lift force model for prolate spheroidal particles is applicable in flow cases with streamwise and non-streamwise flow shear, even if some (reasonably small) accuracy for the case of the streamwise-only shear is lost. (C) 2018 Elsevier Ltd. All rights reserved.
CRIS-Team WoS Importer:2019-02-21

A novel particle–particle and particle–wall collision model for superellipsoidal particles - Wedel, Jana; Štrakl, Mitja; Hriberšek, Matjaž; Steinmann, Paul; Ravnik, Jure (Computational Particle Mechanics, 2023)
In the framework of computational studies of particulate multiphase flow systems, either dilute or dense, particle–particle as well as particle–wall collisions need to be considered, which in the case of nonspherical particle shapes still presents a computational challenge. In this study, we present an efficient numerical implementation of a novel superellipsoidal particle collision model that can be used in general fluid flows. The superellipsoid shape formulation can be viewed as an extension of spherical or ellipsoidal shapes and can be used to represent spherical, ellipsoidal, cylindrical, diamond-like and cubic particles by varying solely five shape parameters. In this context, we present a fast, stable Newton–Raphson-based method for modeling frictional collisions of nonspherical superellipsoidal particles, and demonstrate the performance of our algorithms.
CRIS-Team Scopus Importer:2023-10-13
Keywords: Collision; Friction; Lagrangian particle tracking; Multiphase flow; Superellipsoid

A novel spectral formulation for transversely isotropic magneto-elasticity - MHBM, Shariff; Bustamante, Roger A.; Mokarram, Hossain; Steinmann, Paul (Mathematics and Mechanics of Solids, 2015)
UnivIS-Import:2015-03-11:Pub.2015.tech.FT.FT-TM.anovel

A novel strategy to identify the critical conditions for growth-induced instabilities - Javili, Ali; Steinmann, Paul; Kuhl, Ellen (Journal of the Mechanical Behavior of Biomedical Materials, 2014)
Geometric instabilities in living structures can be critical for healthy biological function, and abnormal buckling, folding, or wrinkling patterns are often important indicators of disease. Mathematical models typically attribute these instabilities to differential growth, and characterize them using the concept of fictitious configurations. This kinematic approach toward growth-induced instabilities is based on the multiplicative decomposition of the total deformation gradient into a reversible elastic part and an irreversible growth part. While this generic concept is generally accepted and well established today, the critical conditions for the formation of growth-induced instabilities remain elusive and poorly understood. Here we propose a novel strategy for the stability analysis of growing structures motivated by the idea of replacing growth by prestress. Conceptually speaking, we kinematically map the stress-free grown configuration onto a prestressed initial configuration. This allows us to adopt a classical infinitesimal stability analysis to identify critical material parameter ranges beyond which growth-induced instabilities may occur. We illustrate the proposed concept by a series of numerical examples using the finite element method. Understanding the critical conditions for growth-induced instabilities may have immediate applications in plastic and reconstructive surgery, asthma, obstructive sleep apnoea, and brain development. © 2013 Elsevier Ltd.
UnivIS-Import:2015-03-09:Pub.2014.tech.FT.FT-TM.anovel
Keywords: Growth; Instabilities; Morphogenesis; Prestress; Residual stress; Stability analysis

A novel two-way coupling model for Euler-Lagrange simulations of multiphase flow - Verhnjak, O.; Hriberšek, M.; Steinmann, Paul; Ravnik, J. (Engineering Analysis With Boundary Elements, 2020)
We propose a novel approach for two-way coupled simulations of multiphase flows within an Eulerian-Lagrange framework. Lagrangian particles are commonly approximated as point sources of either energy, mass or momentum. To introduce them into the Eulerian computation of the fluid flow, an approximation of the Dirac delta function has to be made. By resorting to the Boundary Element Method (BEM) based computation of fluid flow, it is possible to implement the point source concept without any numerical approximation by simply taking advantage of the properties of the fundamental solution present in BEM. However, singularity issues occur in the close vicinity of the mesh nodes. To remedy this effect, the particle-in-cell (PIC) method is used. We present a novel hybrid BEM-PIC two-way coupling algorithm and show that the proposed BEM-PIC model gives superior results compared to a standard PIC implementation. We introduce a critical distance to separate the domain, where the BEM model can be used and the domain, where the PIC model should be used. The results show that the BEM model can be used in about 97%−99% of the domain depending on the mesh used. We provide a criterion for estimating the critical distance within the novel hybrid BEM-PIC two-way coupling algorithm.
CRIS-Team Scopus Importer:2020-07-31
Keywords: Boundary element method; Critical distance; Multiphase flows; Particle-in-cell; Point-wise particles

A numerical study of different projection-based model reduction techniques applied to computational homogenisation - Soldner, Dominic; Brands, Benjamin; Zabihyan, Reza; Mergheim, Julia; Steinmann, Paul (Computational Mechanics, 2017)
Keywords: Computational homogenisation; Reduced-order modelling; Hyper-reduction

A numerical study on the visco-plastic regularization of a rate-independent strain gradient crystal plasticity formulation - Lara Hernandez, Jose Aurelio; Steinmann, Paul (Computational Mechanics, 2023)
A common practice in computational investigations of rate-independent plasticity is to approximate the rate-independent behavior by a visco-plastic regularization. As the fidelity of the approximation increases, the numerical solution of the non-linear problem becomes challenging and it can eventually lead to divergence; thus, there is a numerical limit to the regularization parameter. This limit may be exacerbated by complex material models and critical values of material parameters. Due to these constraints, the regularization may be rendered insufficient and the artificially introduced rate-dependency may lead to a behavior that can be mistakenly attributed to the material model and that we thus identify as spurious in a rate-independent context. To study these spurious effects and their onset, here the problem of an infinite strip under shear loading is numerically solved using a visco-plastic regularized gradient crystal plasticity formulation. The required accuracy of the rate-dependent approximation is found to vary with respect to the type of loading. Furthermore, a set of sigmoid functions used for the regularization is investigated and a subset is shown to deliver improved approximation of the rate-independent case.
CRIS-Team Scopus Importer:2023-12-15
Keywords: Gradient crystal plasticity; Rate-independent approximation; Viscoplastic regularization

A particle‐continuum coupling method for amorphous polymers with multiple particle‐based domains - Torres Huamani, David; Zhao, Wuyang; Pfaller, Sebastian (Proceedings in Applied Mathematics and Mechanics, 2023)
This contribution presents a partitioned-domain particle-continuum coupling method for amorphous polymers with multiple particle-based domains. The coupling method treats the particle-based domains with molecular dynamics (MD) simulations and the continuum domain discretized by the Finite Element (FE) method. In the continuum domain, a viscoelastic-viscoplastic (VE-VP) constitutive model derived from MD simulation results of the polymer at molecular resolution is employed. The effects of the minimum distances between the domains, the distribution and the number of the MD domains as well as the strain rates are studied under uniaxial tension. This method is a precursor for multiscale simulations of polymer-based nanocomposites (PNC).<br

A particle‐continuum coupling method for multiscale simulations of viscoelastic‐viscoplastic amorphous glassy polymers - Zhao, Wuyang; Steinmann, Paul; Pfaller, Sebastian (International Journal for Numerical Methods in Engineering, 2021)
In this contribution, we present a partitioned-domain method coupling a particle domain and a continuum domain for multiscale simulations of inelastic amorphous polymers under isothermal conditions. In the continuum domain, a viscoelastic-viscoplastic constitutive model calibrated from previous molecular dynamics (MD) simulations is employed to capture the inelastic properties of the polymer. Due to the material's rate-dependence, a temporal coupling scheme is introduced. The influence of the time-related parameters on the computational cost and accuracy is discussed. With appropriate parameters, multiscale simulations of glassy polystyrene under various loading conditions are implemented to showcase the method's capabilities to capture the mechanical behavior of polymers with different strain rates and with non-affine deformations of the MD domain.

A Penalty Approach for Contact Description by FEM Based on Interface Physics - Willner, Kai; Gaul, L. (Computational Methods in Contact Mechanics II, 1995)
UnivIS-Import:2015-04-16:Pub.1995.tech.FT.FT-TM.apenal

A peridynamic formulation for nonlocal bone remodelling - Schaller, Emely; Javili, A.; Schmidt, Ina; Papastavrou, Areti; Steinmann, Paul (Computer Methods in Biomechanics and Biomedical Engineering, 2022)
Bone remodelling is a complex biomechanical process, which has been studied widely based on the restrictions of local continuum theory. To provide a nonlocal bone remodelling framework, we propose, for the first time, a peridynamic formulation on the macroscale. We illustrate our implementation with a common benchmark test as well as two load cases of the proximal femur. On the one hand, results of our peridynamic model with diminishing nonlocality measure converge to the results of a local finite element model. On the other hand, increasing the neighbourhood size shows to what extent the additional degree of freedom, the nonlocality, can influence the density evolution.
CRIS-Team WoS Importer:2022-04-29
Keywords: Bone remodelling; peridynamics; nonlocal material; density evolution; influence of nonlocality

A Phenomenological Finite Strain Framework for the Simulation of Elastic Curing - Mokarram, Hossain; Possart, Gunnar; Steinmann, Paul (Proceedings of the 6th European Conference on Constitutive Models for Rubber, 2009)
UnivIS-Import:2015-04-16:Pub.2009.tech.FT.FT-TM.apheno_8

Application of a non-invasive form-finding algorithm to the ring compression test with varying friction coefficients - Landkammer, Philipp; Steinmann, Paul (Key Engineering Materials, 2015)
It is a great challenge in the development of functional components to determine the optimal blank design (material configuration) of a workpiece according to a specific forming process, while knowing the desired target geometry (spatial configuration). A new iterative non-invasive algorithm, which is purely based on geometrical considerations, is developed to solve inverse form finding problems. The update-step is performed by mapping the nodal spatial difference vector, between the computed spatial coordinates and the desired spatial target coordinates, with a smoothed deformation gradient to the discretized material configuration. The iterative optimization approach can be easily coupled non-invasively via subroutines to arbitrary finite element codes such that the pre-processing, the solving and the post-processing can be performed by the habitual simulation software. This is exemplary demonstrated by an interacting between Matlab (update procedure) and MSC. MarcMentat (forming simulation). The algorithm succeeds for a parameter study of a ring compression test within nearly linear convergence rates, despite highly deformed elements and tangential contact with varying friction parameter
UnivIS-Import:2015-10-26:Pub.2015.tech.FT.FT-TM.applic_3
Keywords: Friction; Inverse form finding; Plasticity; Tangential contact

Application of Lattice-Boltzmann Method for Analysing Detachment of Micron-Sized Particles from Carrier Particles in Turbulent Flows - Cui, Yan; Sommerfeld, Martin (Flow Turbulence and Combustion, 2018)
Numerical calculations based on the Lattice-Boltzmann method were performed for a particle cluster consisting of a large spherical carrier particle covered with hundreds of small spherical drug particles. This cluster, fixed in space within a cubic computational domain, was exposed to turbulent plug airflow with predefined intensity. Such a situation is found in dry powder inhalers where carrier particles blended with fine drug powder are dispersed in a highly turbulent flow with the objective of detaching the drug powder for pulmonary delivery. Turbulence was generated by a digital filtering technique applied to the inflow velocity boundary condition. This technique was first validated by analysing the turbulence intensity at 15 fluid nodes along the stream-wise direction of the computational domain. The size ratio between the drug and carrier particle was 5 μ m/100 μ m, and the coverage degree of the carrier by the small particles was 50%, which is a typical value for carrier particle blending. The range of carrier particle Reynolds numbers considered was between 80 and 200, typical values found in inhaler devices. Exemplarily, at Re = 200 turbulence intensity was varied from 0.3% to 9.0%. The systematic increase of the mean flow (i.e. 80 < Re <200) resulted in varying turbulence intensities from 20 to 9%. These simulations provided the temporal evolution of the fluid dynamic forces on the drug particles in dependence of their angular position on the carrier in order to estimate the possibility of drug particle detachment. For turbulent conditions (i.e. Re = 200 and I = 9.0%) the maximum fluid forces on the drug particles were found to be about 10-times larger than found in laminar flow. The fluctuations in the forces were found to be higher than the flow velocity fluctuations due to the modification of the boundary layer around the cluster and instabilities triggered by the turbulent flow. There are three possibilities for detaching the drug powder, namely, through lift-off and sliding or rolling. Lift-off was found to be of minor importance due to the observed small normal fluid forces even at Re = 200 and I = 9.0%. The probability of sliding and rolling detachment in dependence of the angular position was estimated based on measured adhesion properties, i.e. van der Waals force, adhesion surface energy and friction coefficient. The remarkable rise of detachment probability for both effects due to the action of turbulence is an important finding of this study. In accordance with laminar flow, rolling detachment occurs before sliding, however in turbulent conditions over the entire carrier particle. The present studies improve the understanding of drug particle detachment from carrier particles in an inhaler device. The results will be the basis for developing Lagrangian detachment models that eventually should allow the optimisation of dry powder inhalators through computational fluid dynamics.<br
Keywords: Turbulent flow; Fully resolved particle cluster; Lattice-Boltzmann method; Drug powder detachment; Detachment probabilities; Fluid dynamic forces; Dry powder inhaler

Application of the fast nonlinear analysis method on a clamped beam with a cubic spring - Akar, Özge; Willner, Kai (Proceedings in Applied Mathematics and Mechanics, 2019)
In civil engineering reduction methods are used for the mechanical design of buildings in order to avoid unnecessary complexity and computational effort especially in the seismic design of structures. The determination of vibration modes by earthquake excitation is carried out by using Ritz vectors instead of eigenvectors. Thus, only the modes of interest are obtained. Furthermore, the Fast Nonlinear Analysis (FNA) method was formulated to easily insert nonlinearities like concentrated damping in a construction model. The main idea is to take the nonlinear forces to the right hand side of the equation of motion. In the context of this work, the FNA method is applied on a finite element model of a clamped beam with a cubic spring that works at the free end of the beam. First, a harmonic excitement is applied and the vibration modes of the system are obtained by using Ritz vectors. Then, a piecewise exact integration method is implemented to iteratively determine the results for displacement, velocity and acceleration of the discretized beam.<br

Applying a generic and fast coarse-grained molecular dynamics model to extensively study the mechanical behavior of polymer nanocomposites - Ries, Maximilian; Seibert, Jakob; Steinmann, Paul; Pfaller, Sebastian (eXPRESS Polymer Letters, 2022)

A Predictor - Corrector Procedure for the Determination of the Shape of 3D Crack Fronts - Kolk, Karsten; Kuhn, Günther (Proceedings of the Fifth World Congress on Computational Mechanics, 2002)
UnivIS-Import:2015-04-16:Pub.2002.tech.FT.FT-TM.apredi
Keywords: 3D crack growth; Dual BEM; stress intensity factor; 3D singularities

A quantitative interphase model for polymer nanocomposites: Verification, validation, and consequences regarding size effects - Ries, Maximilian; Weber, Felix; Possart, Gunnar; Steinmann, Paul; Pfaller, Sebastian (Composites Part A-Applied Science and Manufacturing, 2022)
The enhanced mechanical behavior of polymer nanocomposites with spherical filler particles is attributed to the formation of matrix-filler interphases. The nano-scale leads to particularly high interphase volume fractions while rendering experimental investigations extremely difficult. Previously, we introduced a molecular dynamics-based interphase model capturing the crucial spatial profiles of elastic and inelastic properties inside the interphase. This contribution demonstrates that our model captures polymer nanocomposites’ essential characteristics reported from experiments. To this end, we thoroughly verify and validate the model before discussing the resulting local plastic strain distribution. Furthermore, we obtain a reinforcement in terms of the overall stiffness for smaller particles and higher filler contents, while the influence of particle spacing seems negligible, matching experimental observations in the literature. This paper proposes a methodology to unravel the underlying complex mechanical behavior of polymer nanocomposites and to translate the findings into engineering quantities accessible to a broader audience and technical applications.
CRIS-Team Scopus Importer:2022-08-12
Keywords: Finite element method; Interphase properties; Polymer nanocomposites; Size effect

A Raman technique applicable for the analysis of the working principle of promoters and inhibitors of gas hydrate formation - Will, Stefan; Bräuer, Andreas; Hankel, Robert; Mehnert, Markus; Schuster, Julian (Journal of Raman Spectroscopy, 2015)
We report a Raman technique applicable for the in situ analysis of the development of hydrogen bonds in the liquid water-rich phase just before the onset of gas hydrate formation. Herewith, the phase transition as well as the working principle of hydrate formation inhibitors and promoters can be analyzed. (C) 2015 The Authors. Journal of Raman Spectroscopy published by John Wiley & Sons Ltd.
Keywords: gas hydrate; inhibitor; Raman spectroscopy; hydrogen bond; OH stretch vibration

Arclength Continuation Methods for the Investigation of Non-linear Oscillating Systems with the Concept of Non-linear Normal Modes - Jerschl, Martin; Willner, Kai (Proceedings in Applied Mathematics and Mechanics, 2014)
Non-linear normal modes (NNMs) can be considered as a non-linear analogon to the description of linear systems with linear normal modes (LNMs). The definition of NNMs can be found in [1]. Small systems with a low number of degrees of freedom and non-linear couplings (cubic springs) are investigated here. With increasing energy in the system the progressive non-linearity leads to a hardening effect. One typical dynamical property of non-linear systems is the frequency-energy dependency of the resulting oscillations. A good graphic illustration is to plot such a dependency in a so called frequency-energy plot (FEP). A NNM branch can be calculated by a numerical continuation method with starting at low energy level in a quasi linear regime and increasing the energy and reducing the period of the oscillation iteratively. Thereby a branch is a family of NNM oscillations with qualitatively equal motion properties [2]. In non-linear systems internal resonances and other phenomena can occur. Several tongues can bifurcate from a NNM branch. Therefore ordinary continuation methods may fail at such bifurcation points. Here a predictor-corrector-method is used and different corrector algorithms are discussed for the branch continuation.

A Receding Contact Problem in Elastostatics - Selvadurai, A.P.S.; Willner, Kai; Gaul, L. (Proceedings of the Seventh Pan American Congress of Applied Mechanics, 2002)
UnivIS-Import:2015-04-16:Pub.2002.tech.FT.FT-TM.areced

A Small-Strain Model to Simulate the Curing of Thermosets - Mokarram, Hossain; Possart, Gunnar; Steinmann, Paul (Computational Mechanics, 2009)
This contribution presents a newly developed phenomenological model to describe the curing process of thermosets undergoing small strain deformations. The governing equations are derived from a number of physical and chemical presuppositions and details of the numerical implementation within the finite element method are given. The curing of thermosets is a very complex process involving a series of chemical reactions which result in the conversion of liquid low molecular weight monomer mixtures into highly cross-linked solid macromolecular structures. This phase transition from a viscous fluid to a viscoelastic solid can be modelled by a constitutive relation which is based on a temporal evolution of shear modulus and relaxation time. Some numerical examples demonstrate the capability of the model to correctly represent the evolution of elastic and inelastic material properties as well as the volume shrinkage taking place during the curing process. © 2008 Springer-Verlag.
UnivIS-Import:2015-03-09:Pub.2009.tech.FT.FT-TM.asmall
Keywords: Curing; Stiffness increase; Thermosets; Viscoelasticity; Volume shrinkage

A specific slip length model for the Maxwell slip boundary conditions in the Navier–Stokes solution of flow around a microparticle in the no-slip and slip flow regimes - Wedel, Jana; Strakl, Mitja; Ravnik, Jure; Steinmann, Paul; Hribersek, Matjaz (Theoretical and Computational Fluid Dynamics, 2022)
Abstract: In the case of microscopic particles, the momentum exchange between the particle and the gas flow starts to deviate from the standard macroscopic particle case, i.e. the no-slip case, with slip flow occurring in the case of low to moderate particle Knudsen numbers. In order to derive new drag force models that are valid also in the slip flow regime for the case of non-spherical particles of arbitrary shapes using computational fluid dynamics, the no-slip conditions at the particle surface have to be modified in order to account for the velocity slip at the surface, mostly in the form of the Maxwell’s slip model. To allow a continuous transition in the boundary condition at the wall from the no-slip case to the slip cases for various Knudsen (Kn) number value flow regimes, a novel specific slip length model for the use with the Maxwell boundary conditions is proposed. The model is derived based on the data from the published experimental studies on spherical microparticle drag force correlations and Cunningham-based slip correction factors at standard conditions and uses a detailed CFD study on microparticle fluid dynamics to determine the correct values of the specific slip length at selected Kn number conditions. The obtained data on specific slip length are correlated using a polynomial function, resulting in the specific slip length model for the no-slip and slip flow regimes that can be applied to arbitrary convex particle shapes. Graphic abstract: [Figure not available: see fulltext.]
CRIS-Team Scopus Importer:2022-09-16
Keywords: Computational fluid dynamics; Drag force; Maxwell slip velocity; Slip flow regime; Slip length; Tangential momentum accommodation coefficient

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound - Saeb, Saba; Steinmann, Paul; Javili, Ali (Applied Mechanics Reviews, 2016)
The objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method. The underlying assumption of computational homogenization is separation of length scales, and hence, computing the material response at the macroscopic scale from averaging the microscopic behavior. In doing so, the energetic equivalence between the two scales, the Hill–Mandel condition, is guaranteed via imposing proper boundary conditions such as linear displacement, periodic displacement and antiperiodic traction, and constant traction boundary conditions. Focus is given on the finite element implementation of these boundary conditions and their influence on the overall response of the material. Computational frameworks for all canonical boundary conditions are briefly formulated in order to demonstrate similarities and differences among the various boundary conditions. Furthermore, we detail on the computational aspects of the classical Reuss' and Voigt's bounds and their extensions to finite strains. A concise and clear formulation for computing the macroscopic tangent necessary for FE2 calculations is presented. The performances of the proposed schemes are illustrated via a series of two- and three-dimensional numerical examples. The numerical examples provide enough details to serve as benchmarks.
EAM Import::2019-03-13

Aspects of computational homogenization in magneto-mechanics: Boundary conditions, RVE size and microstructure composition - Zabihyan, Reza; Mergheim, Julia; Javili, Ali; Steinmann, Paul (International Journal of Solids and Structures, 2018)
In the present work, the behavior of heterogeneous magnetorheological composites subjected to large deformations and external magnetic fields is studied. Computational homogenization is used to derive the macroscopic material response from the averaged response of the underlying microstructure. The microstructure consists of two materials and is far smaller than the characteristic length of the macroscopic problem. Different types of boundary conditions based on the primary variables of the magneto-elastic enthalpy and internal energy functionals are applied to solve the problem at the micro-scale. The overall responses of the RVEs with different sizes and particle distributions are studied under different loads and magnetic fields. The results indicate that the application of each set of boundary conditions presents different macroscopic responses. However, increasing the size of the RVE, solutions from different boundary conditions get closer to each other and converge to the response obtained from periodic boundary conditions.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Boundary condition; Homogenization; Magneto-mechanics

Aspects of implementing constant traction boundary conditions in computational homogenization via semi-Dirichlet boundary conditions - Javili, Ali; Saeb, Saba; Steinmann, Paul (Computational Mechanics, 2016)
In the past decades computational homogenization has proven to be a powerful strategy to compute the overall response of continua. Central to computational homogenization is the Hill–Mandel condition. The Hill–Mandel condition is fulfilled via imposing displacement boundary conditions (DBC), periodic boundary conditions (PBC) or traction boundary conditions (TBC) collectively referred to as canonical boundary conditions. While DBC and PBC are widely implemented, TBC remains poorly understood, with a few exceptions. The main issue with TBC is the singularity of the stiffness matrix due to rigid body motions. The objective of this manuscript is to propose a generic strategy to implement TBC in the context of computational homogenization at finite strains. To eliminate rigid body motions, we introduce the concept of semi-Dirichlet boundary conditions. Semi-Dirichlet boundary conditions are non-homogeneous Dirichlet-type constraints that simultaneously satisfy the Neumann-type conditions. A key feature of the proposed methodology is its applicability for both strain-driven as well as stress-driven homogenization. The performance of the proposed scheme is demonstrated via a series of numerical examples.
EAM Import::2019-03-13

Assessment of an isogeometric approach with Catmull–Clark subdivision surfaces using the Laplace–Beltrami problems - Liu, Zhaowei; McBride, Andrew; Saxena, Prashant; Steinmann, Paul (Computational Mechanics, 2020)
An isogeometric approach for solving the Laplace–Beltrami equation on a two-dimensional manifold embedded in three-dimensional space using a Galerkin method based on Catmull–Clark subdivision surfaces is presented and assessed. The scalar-valued Laplace–Beltrami equation requires only C continuity and is adopted to elucidate key features and properties of the isogeometric method using Catmull–Clark subdivision surfaces. Catmull–Clark subdivision bases are used to discretise both the geometry and the physical field. A fitting method generates control meshes to approximate any given geometry with Catmull–Clark subdivision surfaces. The performance of the Catmull–Clark subdivision method is compared to the conventional finite element method. Subdivision surfaces without extraordinary vertices show the optimal convergence rate. However, extraordinary vertices introduce error, which decreases the convergence rate. A comparative study shows the effect of the number and valences of the extraordinary vertices on accuracy and convergence. An adaptive quadrature scheme is shown to reduce the error.
CRIS-Team Scopus Importer:2020-07-24
Keywords: Catmull–Clark subdivision surfaces; Finite element method; Isogeometric analysis; Laplace–Beltrami equation

A staggered approach to shape and topology optimization using the traction method and an evolutionary-type advancing front algorithm - Riehl, Stefan; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2015)
We investigate a novel approach for structural shape optimization on the basis of complementary shape and topological sensitivity analysis. As in early approaches to shape optimization, the domain variation is specified by modification of boundary nodal points, hence leading to an updated Lagrangian description for the course of optimization. To overcome the formation of oscillating boundaries in the optimal design trials, we employ the traction method to establish smooth descent directions for shape variation. Therein, an auxiliary elastic problem is solved in which the shape sensitivity constitutes the external loading and the deformation of the auxiliary elastic body is used as a descent direction for shape variation rather than the shape sensitivity itself. We complement this method through an evolutionary-type element removal procedure that is based on the topological sensitivity such that an advancing front algorithm is gradually removing elements from the design boundary of the domain. Once the minimum topological sensitivity is no longer encountered at the design boundary, we create a hole in the domain, again using the topological sensitivity to specify its exact location, and resume the element removal procedure for the newly established design boundary. Since this approach yields only a vague estimate of the true optimal shape of newly established holes, the traction method is again used for shape variation of the extended design boundary.
UnivIS-Import:2015-03-09:Pub.2015.tech.FT.FT-TM.astagg
Keywords: Parameter-free; Shape optimization; Topological sensitivity; Traction method

A staggered approach to structural shape and topology optimization - Riehl, Stefan; Steinmann, Paul (Proc. Appl. Math. Mech., 2015)

A study on brake squeal using a beam-on-disc model - Allgaier, R.; Gaul, L.; Keiper, W.; Willner, Kai; Hoffmann, N. (IMAC-XX: A Conference on Structural Dynamics, 2002)
In this paper the phenomenon of mode lock-in is investigated, which occurs in structures where vibrations are excited by frictional contact forces, as for example at disc brakes. In general "mode lock-in" denotes the coupling of substructure modes which form the vibratory response of the assembly, leading e.g. to brake squeal. For studying this effect an experimental beam-disk set-up was built and a corresponding FE model was generated. A presented normal and tangential contact law is based on the statistical distribution of contacting asperities derived from measured surface roughness profiles. The time-stepping solutions of the FE model were checked for system resonances and compared to the experimentally observed mode lock-i

A study on brake squeal using a beam-on-disc model - Willner, Kai; Allgaier, R.; Gaul, L.; Keiper, W. (Konstruktion, 2005)
The phenomenon of "mode lock-in" occurs in structures, where vibrations are excited by contact forces, as for example between disc and pads at disc brakes. In general, mode lock-in denotes the coupling of substructure modes which form the vibratory response of the assembly, leading to brake squeal.

A Study on Brake Squeal Using a Beam-On-Disk Model - Allgaier, R.; Gaul, L.; Willner, Kai; Hoffmann, N. (Proceedings of IMAC-XX, 2002)
UnivIS-Import:2015-04-16:Pub.2002.tech.FT.FT-TM.astudy

A theory of finite deformation magneto-viscoelasticity - Saxena, Prashant; Mokarram, Hossain; Steinmann, Paul (International Journal of Solids and Structures, 2013)
This paper deals with the mathematical modelling of large strain magneto-viscoelastic deformations. Energy dissipation is assumed to occur both due to the mechanical viscoelastic effects as well as the resistance offered by the material to magnetisation. Existence of internal damping mechanisms in the body is considered by decomposing the deformation gradient and the magnetic induction into 'elastic' and 'viscous' parts. Constitutive laws for material behaviour and evolution equations for the non-equilibrium fields are derived that agree with the laws of thermodynamics. To illustrate the theory the problems of stress relaxation, magnetic field relaxation, time dependent magnetic induction and strain are formulated and solved for a specific form of the constitutive law. The results, that show the effect of several modelling parameters on the deformation and magnetisation process, are illustrated graphically.© 2013 Elsevier Ltd. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.atheor
Keywords: Magneto-viscoelasticity; Nonlinear elasticity; Viscoelasticity

A thermodynamically consistent theory of stress-gradient plasticity - Reddy, B. D.; Steinmann, Paul; Kergaßner, Andreas (Journal of the Mechanics and Physics of Solids, 2021)
As an extension to strain-gradient models of size-dependent plastic behaviour, this work proposes a model for a stress-gradient theory. The model is distinguished from earlier works on the topic by its being embedded in a thermodynamically consistent framework. The development is carried out in the context of single-crystal plasticity, and draws on thermodynamically consistent models for single-crystal conventional and strain-gradient plasticity. The model is explored numerically using the example of torsion of a thin wire comprising a face centred cubic crystal, and its behaviour compared with that based on a recent disequilibrium density model of size-dependent plasticity.<br

A thermoelastoplastic theory for special Cosserat rods - Smriti,; Kumar, Ajeet; Großmann, Alexander; Steinmann, Paul (Mathematics and Mechanics of Solids, 2019)
A general framework is presented to model coupled thermoelastoplastic deformations in the theory of special Cosserat rods. The use of the one-dimensional form of the energy balance in conjunction with the one-dimensional entropy balance allows us to obtain an additional equation for the evolution of a temperature-like one-dimensional field variable, together with constitutive relations for this theory. Reduction to the case of thermoelasticity leads us to the well-known nonlinear theory of thermoelasticity for special Cosserat rods. Later on, additive decomposition is used to separate the thermoelastic part of the strain measures of the rod from their plastic counterparts. We then present the most general quadratic form of the Helmholtz energy per unit undeformed length for both hemitropic and transversely isotropic rods. We also propose a prototype yield criterion in terms of forces, moments, and hardening stress resultants, as well as associative flow rules for the evolution of plastic strain measures and hardening variables.
CRIS-Team WoS Importer:2019-04-18

A thermo-mechanical cohesive zone model accounting for mechanically energetic Kapitza interfaces - Esmaeili, Ali; Javili, Ali; Steinmann, Paul (International Journal of Solids and Structures, 2016)
Interfaces can play a dominant role in the thermo-mechanical response of a body. The importance of interfaces is more pronounced as the problem scale decreases since the interface area to the bulk volume ratio grows. The objective of this contribution is to study computational aspects of modeling thermo-mechanical solids containing mechanically energetic, geometrically non-coherent Kapitza interfaces under cyclic loading. The interface is termed energetic in the sense that it possesses its own energy, entropy, constitutive relations and dissipation. To date, classical thermomechanical cohesive zone models do not account for elastic interfaces. Therefore we propose a novel interface model that couples the classical cohesive zone formulation to the interface elasticity theory under the Kapitza assumption within a thermo-mechanical framework. In other words, such an interface model allows for discontinuities in geometry, temperature and normal stress fields, while not permitting a jump in the normal heat flux across the interface. The equations governing a fully non-linear transient problem are given. They are solved using the finite element method. The results are illustrated through a series of three-dimensional numerical examples for various interfacial parameters. In particular, a comparison is made between the results of the classical thermo-mechanical cohesive zone model and our novel (cohesive + energetic Kapitza) interface formulation.

A thermo-viscoplastic constitutive law for isotropic hardening of metals - Schindler, Stefan; Steinmann, Paul; Aurich, Jan C.; Zimmermann, Marco (Archive of Applied Mechanics, 2016)
A novel empirical constitutive law for thermo-viscoplasticity is proposed, which considers isotropic strain and strain rate hardening as well as thermal softening. The yield stress considers strain rate and thermal effects independently for the initial yield stress and the (strain) hardening stress. To date, most plasticity models consider strain rate and temperature effects only combined for the initial and hardening stress, which is not sufficient for several materials. Seidt and Gilat (Int J Solids Struct 50(2):1781–1790, 2013) presented comprehensive experimental measurements for the aluminum alloy Al2024 including isothermal compression tests at low strain rates and various constant temperatures from room temperature to almost melting temperature as well as adiabatic compression tests at high strain rates (up to 10,900 s-1). In contrast to established thermo-viscoplastic material models, the proposed model is suitable to describe the material behavior of Al2024 accurately over a large range of loading conditions, i.e. from small to large plastic strains, low and high strain rates, and from room temperature to melting temperature, which is validated by the experimental data of Seidt and Gilat (2013). Consequently, with the use of the proposed constitutive law a variety of applications can be modeled, e.g. bulk forming, hot working, chip formation during cutting processes, or crash simulations. It is in particular promising for applications where combined loading conditions occur, like high strain rates and high temperatures at the chip formation.
Keywords: Strain hardening; Strain rate hardening; Thermal softening; Al2024

Atomistic configurational forces in crystalline fracture - Birang Oskouei, Seyedehelmira; Park, Harold S.; Smith, Ana-Suncana; Steinmann, Paul (Forces in Mechanics, 2021)
Configurational atomistic forces contribute to the configurational mechanics (i.e. non-equilibrium) problem that determines the release of total potential energy of an atomistic system upon variation of the atomistic positions relative to the initial atomic configuration. These forces drive energetically favorable irreversible re-organizations of the material body, and thus characterize the tendency of crystalline defects to propagate. In this work, we provide new expressions for the atomistic configurational forces for two realistic interatomic potentials, i.e. the embedded atom potential (EAM) for metals, and second generation reactive bond order (REBO-II) potential for hydrocarbons. We present a range of numerical examples involving quasistatic fracture for both FCC metals and mono and bi-layer graphene at zero Kelvin that demonstrate the ability to predict defect nucleation and evolution using the proposed atomistic configurational mechanics approach. Furthermore, we provide the contributions for each potential including two-body stretching, three-body mixed-mode stretching-bending, and four-body mixed-mode stretching-bending-twisting terms that make towards defect nucleation and propagation.
Keywords: Atomistic configurational mechanics; Configurational forces; Many-body potentials; Fracture mechanics

Atomistic two-, three- and four-body potentials. Spatial and material settings - Steinmann, Paul; Smith, Ana-Suncana; Birang Oskouei, Seyedehelmira; Birang, E.; McBride, A.; Javili, A. (Journal of the Mechanics and Physics of Solids, 2021)
In molecular dynamics or molecular statics (MD/MS) multi-body potentials empirically capture the energetic interactions in atomistic systems enabling the computation of the corresponding atomistic forces as energetic conjugates to the atomistic positions. We distinguish here between spatial and material atomistic positions and consequently between the corresponding spatial and material atomistic forces. In quasi-statics, i.e. MS, the former, also denoted as deformational atomistic forces, contribute to the classical deformational mechanics (i.e., equilibrium) problem that seeks to minimise the total potential energy of an atomistic system with respect to the atomistic positions relative to the ambient space. The latter, also denoted as configurational atomistic forces, contribute to the configurational mechanics (i.e., non-equilibrium) problem that determines the release of total potential energy of an atomistic system upon variation of the atomistic positions relative to the ambient material, i.e., due to perturbations of the material (initial) atomistic configuration. The importance of material atomistic forces is that they drive energetically favourable re-organisations of the material atomistic configuration, thereby characterising the tendency of generic atomistic defects to propagate. In this contribution we focus on two-, three-, and four-body potentials, whereby we distinguish between novel stretch- and classical angle-based potentials for the two latter cases. Taken together, as the main contribution, we derive expressions for the corresponding spatial and, for the first time, material atomistic forces and highlight their striking formal similarity. The derivations are detailed but the final expression compact and well-suited for numerical implementation.
CRIS-Team Scopus Importer:2021-06-25

A two-field computational model couples cellular brain development with cortical folding - Zarzor, Mohammad Saeed; Käßmair, Stefan; Steinmann, Paul; Blümcke, Ingmar; Budday, Silvia (Brain Multiphysics, 2021)
The convoluted macroscopic shape of the mammalian brain plays an important role for brain function. To date, the link between the cellular processes during brain development and normal or abnormal cortical folding on the macroscopic scale remains insufficiently understood. Disruption of cellular division, migration, or connectivity may lead to malformations of cortical development associated with neurological disorders like schizophrenia, autism, or epilepsy. Here, we use a computational model, which couples an advection-diffusion model with finite growth, to assess the link between cellular division and migration on the cell scale and growth and cortical folding on the tissue or organ scale. It introduces the cell density as independent field controlling volumetric growth. This allows us to numerically study the influence of cell migration velocity, cell diffusivity, and the temporally changing local stiffness of brain tissue on the cortical folding process during normal brain development. We show that the model is capable of capturing the local distribution of cells through the comparison with histologically stained sections of the developing human brain. Our results further demonstrate that it is important to take temporal changes in tissue stiffness into account, which naturally occur during brain development. The present study constitutes an important step towards a computational model that could help to better understand, diagnose, and, eventually, treat neurological disorders arising from abnormal cellular development and cortical malformations.<br
Keywords: Brain development; Cortical folding; Neurogenesis; Finite growth; Multifield modeling; Mechanical instability

A two-scale simulation method accounting for thermal effects during turning - Schindler, Stefan; Zimmermann, Marco; Aurich, Jan C.; Steinmann, Paul (PAMM 2014, 2014)
During chip formation in turning processes, mechanical work is dissipated into thermal energy by plastic deformations and frictional processes. In case of dry cutting, the generated heat is in part removed with the chips while the rest flows into the tool and the workpiece. Within the latter, the temperature increases due to this heat flow, which in turn causes thermal expansions that increase the  cutting depth and thus induced eviations from the nominal workpiece geometry. These effects are treated separately by a local model for the chip formation and a global model for the whole workpiece in order to determine the temperature distribution inside the workpiece and the dependent thermal expansion
UnivIS-Import:2015-04-16:Pub.2014.tech.FT.FT-TM.atwosc_8

A unified computational framework for bulk and surface elasticity theory: A curvilinear-coordinate-based finite element methodology - Javili, Ali; Mcbride, Andrew; Steinmann, Paul; Reddy, B. D. (Computational Mechanics, 2014)
A curvilinear-coordinate-based finite element methodology is presented as a basis for a straightforward computational implementation of the theory of surface elasticity that mimics the underlying mathematical and geometrical concepts. An efficient formulation is obtained by adopting the same methodology for both the bulk and the surface. The key steps to evaluate the hyperelastic constitutive relations at the level of the quadrature point in a finite element scheme using this unified approach are provided. The methodology is illustrated through selected numerical examples. © 2014 Springer-Verlag Berlin Heidelberg.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Curvilinear coordinates; Finite element; Surface elasticity

A unifying finite strain modeling framework for anisotropic mixed-mode fracture in soft materials - Pranavi, D.; Steinmann, Paul; Rajagopal, A. (Computational Mechanics, 2023)
Elastomers and composites made thereof have wide applications, e.g., in automobile, aerospace, and civil engineering. Predicting fracture in such materials is crucial for efficient design and optimum utilization. These materials are oftentimes hyperelastic and anisotropic in nature and in general subjected to mixed mode loading rather than merely pure modes. Soft biological tissues can also be considered anisotropic hyperelastic materials. Computational modeling helps in studying the role of different sources influencing mixed-mode fracture. A unifying thermodynamically consistent anisotropic phase field formulation for modeling the mixed-mode fracture of hyperelastic soft materials like elastomers, elastomeric fiber-reinforced composites, and soft biological tissues at finite strains is proposed and formulated. To model the mechanical response of anisotropic hyperelastic materials subjected to mixed-mode loading, a coupled Neo-Hookean model with orthotropic anisotropy is adopted considering volumetric-deviatoric and a tension-compression decomposition. For modeling the complex crack initiation and propagation, a phase field method based on a power law criterion is adopted by considering a single order parameter as the damage variable. This model is suitable for capturing the overall response of soft fiber-reinforced elastomeric composites as well as soft biological tissues. The proposed model is validated by conducting fracture tests on (a) silicone elastomers, (b) unidirectional fiber-reinforced elastomeric composites, (c) natural rubber reinforced with black carbon, and (d) brain tissue reinforced with axons. The results obtained are compared with experimental and numerical investigations from literature.
Created from Fastlane, Scopus look-up
Keywords: Anisotropic; Elastomers; Fiber reinforced; Finite element; Soft tissue

Automated discovery of interpretable hyperelastic material models for human brain tissue with EUCLID - Flaschel, Moritz; Yu, Huitian; Reiter, Nina; Hinrichsen, Jan; Budday, Silvia; Steinmann, Paul; Kumar, Siddhant; De Lorenzis, Laura (Journal of the Mechanics and Physics of Solids, 2023)
We propose an automated computational algorithm for simultaneous model selection and parameter identification for the hyperelastic mechanical characterization of biological tissue and validate it on experimental data stemming from human brain tissue specimens. Following the motive of the recently proposed computational framework EUCLID (Efficient Unsupervised Constitutive Law Identification and Discovery) and in contrast to conventional parameter calibration methods, we construct an extensive set of candidate hyperelastic models, i.e., a model library including popular models known from the literature, and develop a computational strategy for automatically selecting a model from the library that conforms to the available experimental data while being represented as an interpretable symbolic mathematical expression. This computational strategy comprises sparse regression, i.e., a regression problem that is regularized by a sparsity promoting penalty term that filters out irrelevant models from the model library, and a clustering method for grouping together highly correlated and thus redundant features in the model library. The model selection procedure is driven by data stemming from mechanical tests under different deformation modes, i.e., uniaxial compression/tension and simple torsion. The data is acquired through conventional mechanical tests that deliver labeled one-dimensional data pairs, and thus the method can be interpreted as a supervised counterpart to the originally proposed EUCLID that is informed by full-field displacement data and global reaction forces. The proposed method is verified on synthetical data with artificial noise. In addition, we present for the first time an experimental investigation of the EUCLID framework by validating the proposed method on experimental data acquired through mechanical tests of human brain specimens, proving that the method is capable of discovering hyperelastic models that exhibit both high fitting accuracy to the data as well as concise and thus interpretable mathematical representations.
CRIS-Team Scopus Importer:2023-09-08
Keywords: Brain tissue; Constitutive models; Hyperelasticity; Interpretable models; Sparse regression

A versatile implicit computational framework for continuum-kinematics-inspired peridynamics - Firooz, Soheil; Javili, Ali; Steinmann, Paul (Computational Mechanics, 2023)
Continuum-kinematics-inspired peridynamics (CPD) has been recently proposed as a novel reformulation of peridynamics that is characterized by one-, two- and three-neighbor interactions. CPD is geometrically exact and thermodynamically consistent and does not suffer from zero-energy modes, displacement oscillations or material interpenetration. In this manuscript, for the first time, we develop a computational framework furnished with automatic differentiation for the implementation of CPD. Thereby, otherwise tedious analytical differentiation is automatized by employing hyper-dual numbers (HDN). This differentiation method does not suffer from round-off errors, subtractive cancellation errors or truncation errors and is thereby highly stable with superb accuracy being insensitive to perturbation values. The computational framework provided here is compact and model-independent, thus once the framework is implemented, any other material model can be incorporated via modifying the potential energy solely. Finally, to illustrate the versatility of our proposed framework, various potential energies are considered and the corresponding material response is examined for different scenarios.<br
Keywords: Nonlocal elasticity; Peridynamics; Automatic differentiation; Hyper-dual numbers

A viscoelastic Mooney-Rivlin model for adhesive curing and first steps toward its calibration based on photoelasticity measurements - Lengger, Michael; Possart, Gunnar; Steinmann, Paul (Archive of Applied Mechanics, 2022)
The transition of polymer adhesives from an initially liquid to a fully cured viscoelastic state is accompanied by three phenomenological effects, namely an increase in stiffness and viscosity in conjunction with a decrease in volume (curing shrinkage). Under consideration of these phenomena, some of us (Hossain et al. in Computational Mechanics 46:363-375, 2010) have devised a generic, viscoelastic finite strain framework for the simulation of the curing process of adhesives, which renders a thermodynamically consistent model regardless of the selected free energy density. In the present work, this generic curing framework is modified by means of more precise integration schemes and is applied to a hyperelastic Mooney-Rivlin material based on an additive volumetric-isochoric split of the strain energy density. The benefit of this decomposition is directly related to the distinct material responses of various polymers to volumetric and isochoric deformations [4]. The resulting Mooney-Rivlin curing model provides the foundation for implementing a user-defined material subroutine (UMAT) in Abaqus requiring the Cauchy stress and a non-standard formulation of the tangent operator. To this end, the corresponding transformations are presented. Additionally, a first attempt to determine the evolution of the curing-dependent material parameters through optimization with respect to a photoelasticity measurement is presented. A subset of the material properties, which reflect the emergence of shrinkage stresses inside a ceramic-epoxy composite after its fabrication, is determined via inverse parameter identification. However, due to a lack of experimental data and some rather strong assumptions made on the physics involved, this demonstration can currently be considered only as a proof-of-concept.
CRIS-Team WoS Importer:2022-11-04

A viscoelastic-viscoplastic constitutive model for glassy polymers informed by molecular dynamics simulations - Zhao, Wuyang; Ries, Maximilian; Steinmann, Paul; Pfaller, Sebastian (International Journal of Solids and Structures, 2021)
This contribution presents a phenomenological viscoelastic-viscoplastic constitutive model informed by coarse-grained (CG) molecular dynamics (MD) simulations of pure glassy polystyrene (PS). In contrast to experiments, where viscoplasticity is caused by various effects simultaneously, these effects can be decomposed in MD simulations by adjusting the MD system. In the MD simulations considered here, neither bond breakage nor cross-links are introduced; instead, we focus on the intermolecular interaction of polymer chains. We employ a thermo-dynamically consistent generalized Maxwell framework parallelly comprising an elastic, a viscoelastic, and several elasto-viscoplastic modules with different yield stress to capture the viscoelastic and the viscoplastic mechanical behavior simultaneously. The yield stresses decrease with the maximum deformation the MD system has experienced. The constitutive model presented here is based on 10 material parameters, which can be identified by a few data sets and fits well the CG MD simulations of PS under uniaxial and biaxial deformation with time-proportional and cyclic loading conditions in a wide range of strain rates.<br
Keywords: Constitutive model; Glassy polymers; Viscoelasticity; Viscoplasticity; Molecular dynamics

A web-based tool for the interactive visualization of stresses in an infinite plate with an elliptical hole under simple tension: www.ltm.fau.de/plate . - Friederich, Jan; Pfaller, Sebastian; Steinmann, Paul (Archive of Applied Mechanics, 2015)

A Week Ahead Water Demand Forecasting using Convolutional Neural Network on Multi-Channel Wavelet Scalogram - Ramachandran, Adithya; Mousa, Hatem; Maier, Andreas; Bayer, Siming (WDSA CCWI 2024 - 3rd International Joint Conference on Water Distribution Systems Analysis & Computing and Control for the Water Industry, 2024)

Basic considerations for determining the amount of press fit in acetabular cup endoprostheses as a function of the elastic bone behavior - Winter, Werner; Karl, Matthias (Biomedizinische Technik, 2014)
Acetabular cup endoprostheses are frequently placed in pelvic bone, employing the mechanical principle of press fit. While a sufficiently stable bone-implant connection is desirable, deformation of the cup and fracture of the pelvis should be avoided. The goal of this work is to demonstrate the importance of the elastic properties of bone on the amount of press fit achievable in a specific situation. On the basis of previous work describing the relation between relative bone mineral density and relative elastic modulus for cortical and trabecular bone, mechanical equations were used for analyzing the press-fit loading situation of an acetabular cup. Additionally, a two-dimensional finite element model was used for visualizing the stress and strain situation in the host bone occurring as a consequence of implant insertion, as well as the effect of moment loads acting on the acetabular cup. Given the fact that oversizing the implant for a specific recipient site is the only clinical means of optimizing press fit, knowledge of the elastic properties of the host bone before implant selection would be beneficial. Such information could, for instance, be derived from intraoperative compressive testing of the host bone.
EVALuna2:24819

Behavior of vibration energy harvesters composed of polymer fibers and piezoelectric ceramic particles - Hasegawa, R.; Mehnert, Markus; Mergheim, Julia; Steinmann, Paul; Kakimoto, K. (Sensors and Actuators A-Physical, 2020)
Flexible piezoelectric composites of polymer fiber and ceramic particles are promising candidates for ambient vibration energy harvesters. However, observations of stress transfer behavior between polymer fiber and ceramic particle have not been clarified. In this study, the output from two types of composite with ceramic particles inside and outside of the fiber was measured, where the output for ceramic particles inside the fiber was 209 mV and 91 mV for fibers outside. Experimental results were confirmed using a microstructure-based finite element method. A simplified microstructure model that consists of one piezoelectric particle and two polymer fibers was created and loaded with the prescribed strain. Ceramic particle strain inside the fiber was higher than one outside the fiber, which was quantitatively consistent with experimental results. Analysis indicates that stress transfer between the polymer fiber and ceramic particles occurs on the interface and is important for electrical output. This is the first study to clarify the relation between stress transfer and output. Study results will lead to the material design of flexible piezoelectric composites and their application to ambient vibration energy harvesters.
CRIS-Team Scopus Importer:2020-02-18
Keywords: Energy harvester; Fiber composite; Finite element method; Piezoelectric

Berücksichtigung von produktionsspezifischen Abweichungen im interdisziplinären Toleranzmanagement - Heling, Björn; Oberleiter, Thomas; Rohrmoser, Andreas; Kiener, Christoph; Schleich, Benjamin; Hagenah, Hinnerk; Merklein, Marion; Willner, Kai; Wartzack, Sandro (Industriekolloquium der Forschergruppe FOR 2271, 2019)
LFT Import::2019-08-05 (2353)

Biomechanical analysis of the cervical spine segment as a method for studying the functional and dynamic anatomy of the human neck - Ovsepyan, A. L.; Smirnov, A. A.; Pustozerov, E. A.; Mokhov, D. E.; Mokhova, E. S.; Trunin, E. M.; Dydykin, S. S.; Vasil'Ev, Yu. L.; Yakovlev, E. V.; Budday, Silvia; Paulsen, Friedrich; Zhivolupov, S. A.; et al. (Annals of Anatomy-Anatomischer Anzeiger, 2022)
Background: Traditionally, dynamic and functional anatomy, in particular the dynamic anatomy of the neck, is studied on cadaveric material. However, the development of in vivo visualization technologies and in silico modeling has made it possible to expand these possibilities. Despite significant progress in the study of dynamic and functional anatomy of the neck by means of in silico methods, the issues of validating the developed models and taking into account the pronounced nonlinearity of soft tissues as well as local anisotropy remain open. The aim of this study was to develop a virtual dynamic anatomical model of the human neck and reproduce the dynamic processes in the cervical spine from this model using the finite element method. Materials and methods: Reverse engineering was used to generate a dynamic anatomical model of the neck from CT data (both male, 24 and 22 years old). Two segments of the cervical spine (C3-C5, C2-T1) were isolated from the resulting model for finite element analysis. Finite element mesh generation and contact interactions were performed using the HyperMesh software (Altair Engineering Inc, Troy, Michigan, USA). The anisotropic hyperelastic Holzapfel-Gasser-Ogden model was used to describe the material behavior of the fibrous rings of the disc. Material modeling and finite element analysis were performed using Abaqus CAE 6.14 software (Simulia, Johnston, Rhode Island, USA). Results: A technique for creating a virtual dynamic anatomical model of the neck was elaborated and implemented. The model includes 79 major anatomical structures of the neck segmented from radiological data. A finite element analysis of the cervical spine was performed. The results of finite element analysis of the C3-C5 segment under axial load were compared with in vitro data. The proposed model shows nonlinear deformation of the disc under static loading; the model predicted displacement values agree well with the experimental ones. The displacement of the С3-С5 central vertebra with an axial load of 800 N reaches a value of 0.65 mm. For the segment C2-T1, data on intradiscal pressure, stress plots and displacements during flexion were obtained. The maximum stress value of 10.036 MPa is observed in the C3-C4 disc. Conclusion: Simulation results using the proposed methodology are in good agreement with experimental data. The generated biomechanical models allow describing dynamic phenomena in the cervical spine and obtaining a wide range of quantitative properties of anatomical objects, which are otherwise inaccessible to classical methods for studying dynamic and functional anatomy.
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Keywords: Abaqus CAE; Finite element method (FEM); Functional anatomy of the neck; Holzapfel-Gasser-Ogden material model; Intervertebral disc; Neck biomechanics

Bone fracture healing within a continuum bone remodelling framework - Schmidt, Ina; Albert, Jacob; Ritthaler, Marina; Papastavrou, Areti; Steinmann, Paul (Computer Methods in Biomechanics and Biomedical Engineering, 2021)
Bone fracture healing is a complex process which is still under research. Computer-aided patient-specific prediction of bone development, fracture risk, prevention and treatment approaches promises a significant milestone in clinical practice. With this long-term goal in mind, a novel model is presented and examined in this work in the context of continuum bone remodelling. Therein, a clear distinction is made between external mechanical stimulation and the biological healing process of an injured bone tissue. The model is implemented within a finite element framework and investigated for the example of a fractured proximal femur head. The results show promising perspectives for further application. Besides, the model offers the possibility of easily integrating other factors like age-dependency and the availability of nutrition. For the future, further studies with large clinical datasets are essential for validation.
CRIS-Team Scopus Importer:2021-11-12
Keywords: bone fracture; Bone remodelling; femur head; finite element method; healing

Bounds on size-dependent behavior of composites - Saeb, Saba; Steinmann, Paul; Javili, A. (Philosophical Magazine, 2017)
Computational homogenisation is a powerful strategy to predict the effective behaviour of heterogeneous materials. While computational homogenisation cannot exactly compute the effective parameters, it can provide bounds on the overall material response. Thus, central to computational homogenisation is the existence of bounds. Classical first-order computational homogenisation cannot capture size effects. Recently, it has been shown that size effects can be retrieved via accounting for elastic coherent interfaces in the microstructure. The primary objective of this contribution is to present a systematic study to attain computational bounds on the size-dependent response of composites. We show rigorously that interface-enhanced computational homogenisation introduces two relative length scales into the problem and investigate the interplay between them. To enforce the equivalence of the virtual power between the scales, a generalised version of the Hill–Mandel condition is employed, and accordingly, suitable boundary conditions are derived. Macroscopic quantities are related to their microscopic counterparts via extended average theorems. Periodic boundary conditions provide an effective behaviour bounded by traction and displacement boundary conditions. Apart from the bounds due to boundary conditions for a given size, the size-dependent response of a composite is bounded, too. The lower bound coincides with that of a composite with no interface. Surprisingly, there also exists an upper bound on the size-dependent response beyond which the expected `smaller is stronger' trend is no longer observed. Finally, we show an excellent agreement between our numerical results and the corresponding analytical solution for linear isotropic materials which highlights the accuracy and broad applicability of the presented scheme.
EAM Import::2019-03-13

Brain stiffness increases with myelin content - Weickenmeier, Johannes; de Rooij, Rijk; Budday, Silvia; Steinmann, Paul; Ovaert, Timothy; Kuhl, Ellen (Acta Biomaterialia, 2016)
Brain stiffness plays an important role in neuronal development and disease, but reported stiffness values vary significantly for different species, for different brains, and even for different regions within the same brain. Despite extensive research throughout the past decade, the mechanistic origin of these stiffness variations remains elusive. Here we show that brain tissue stiffness is correlated to the underlying tissue microstructure and directly proportional to the local myelin content. In 116 indentation tests of six freshly harvested bovine brains, we found that the cerebral stiffnesses of 1.33 ± 0.63 kPa in white matter and 0.68 ± 0.20 kPa in gray matter were significantly different (p < 0.01). Strikingly, while the inter- specimen variation was rather moderate, the minimum and maximum cerebral white matter stiffnesses of 0.59 ± 0.19 kPa and 2.36 ± 0.64 kPa in each brain varied by a factor of four on average. To provide a mechanistic interpretation for this variation, we performed a histological characterization of the tested brain regions. We stained the samples with hematoxylin and eosin and luxol fast blue and quantified the local myelin content using image analysis. Interestingly, we found that the cerebral white matter stiffness increased with increasing myelin content, from 0.72kPa at a myelin content of 64–2.45kPa at a myelin content of 89%, with a Pearson correlation coefficient of 0.91 (p < 0.01). This direct correla- tion could have significant neurological implications. During development, our results could help explain why immature, incompletely myelinated brains are softer than mature, myelinated brains and more vul- nerable to mechanical insult as evident, for example, in shaken baby syndrome. During demyelinating disease, our findings suggest to use stiffness alterations as clinical markers for demyelination to quantify the onset of disease progression, for example, in multiple sclerosis. Taken together, our study indicates that myelin might play a more important function than previously thought: It not only insulates signal propagation and improves electrical function of single axons, it also provides structural support and mechanical stiffness to the brain as a whole.
Keywords: Brain; Mechanical testing; Indentation; Soft matter; Stiffness; Myelin

Buckling analysis of a bi-directional strain-gradient Euler–Bernoulli nano-beams - Çelik, Murat; Artan, Reha (International Journal of Structural Stability and Dynamics, 2020)
Investigated herein is the buckling of Euler–Bernoulli nano-beams made of bi-directional functionally graded material with the method of initial values in the frame of gradient elasticity. Since the transport matrix cannot be calculated analytically, the problem was examined with the help of an approximate transport matrix (matricant). This method can be easily applied with buckling analysis of arbitrary two-directional functionally graded Euler–Bernoulli nano-beams based on gradient elasticity theory. Basic equations and boundary conditions are derived by using the principle of minimum potential energy. The diagrams and tables of the solutions for different end conditions and various values of the parameters are given and the results are discussed.
CRIS-Team Scopus Importer:2020-10-23
Keywords: Bi-directional functionally graded materials; Buckling; Euler–Bernoulli nanobeams; Method of initial values; Stability of beams; Theory of gradient elasticity; Transfer matrix

Buckling Analysis of Nanobeams Based on Nonlocal Timoshenko Beam Model by the Method of Initial Values - Demirkan, Erol; Artan, Reha (International Journal of Structural Stability and Dynamics, 2019)
Investigated herein is the buckling of .nanobeams based on a nonlocal Timoshenko beam model by the method of initial values within the framework of nonlocal elasticity. Since the nonlocal Timoshenko beam theory is of higher order than the nonlocal Euler-Bernoulli beam theory, it is known to be superior in predicting the small-scale effect. The buckling determinants and critical loads for bars with various kinds of supports are presented. The Carry-Over matrix (Transverse Matrix) is presented and the priorities of the method of initial values are depicted. To the best of the researchers' knowledge, this is the first work that investigates the buckling of nonlocal Timoshenko beam with the method of initial values.
CRIS-Team WoS Importer:2019-04-23

Buckling optimization of additively manufactured cellular structures using numerical homogenization based on beam models - Hübner, Daniel; Herrnböck, Ludwig; Wein, Fabian; Mergheim, Julia; Steinmann, Paul; Stingl, Michael (Archive of Applied Mechanics, 2023)
Interest in components with detailed structures increased with the progress in advanced manufacturing techniques. Parts with lattice elements can provide improved global buckling stability compared to solid structures of the same weight. However, thin features are prone to local buckling. We present a two-scale optimization approach that simultaneously improves the local and global stability of parametrized graded lattice structures. Elastic properties and local buckling behavior are upscaled via homogenization based on geometric exact beam theory. To reduce computational effort, we construct a worst-case model for the homogenized buckling load factor, which acts as a safeguard against local buckling. We briefly discuss advantages and limitations by means of numerical examples.
CRIS-Team Scopus Importer:2023-11-03
Keywords: Beam theory; Buckling; Numerical homogenization; Two-scale optimization

Calculating the Dynamic Response of Jointed Structures in the Frequency Domain Using Contact Interface Elements - Süß, Dominik; Jerschl, Martin; Willner, Kai (The Mechanics of Jointed Structures, 2018)
This chapter focuses on the presentation of zero thickness elements as a method to discretize the contact plane of a bolted joint in the framework of the finite element method (FEM). A constitutive law based on a Jenkins element is used to describe the dry friction within the zero thickness elements. The harmonic balance method (HBM) is applied to calculate the dynamic response of the system in the frequency domain. In this chapter, a three-dimensional constitutive law based on Jenkins elements is used in order to simulate the dynamic behavior of a jointed friction resonator. The calculation is performed in the frequency domain utilizing the adaptive harmonic balance method (AHBM). This new, adaptive tool combines the advantages of classical HBM and multi-harmonic balance method (MHBM). Two different approaches for the application of the adaptive harmonic balance are shown with both delivering different results. The combination of the general modeling approach via zero thickness elements and the efficient computation using the AHBM brings out a powerful methodology for the calculation of the dynamics of jointed structures in the framework of the FEM.

Can CFD establish a connection to a milder COVID-19 disease in younger people? Aerosol deposition in lungs of different age groups based on Lagrangian particle tracking in turbulent flow - Wedel, Jana; Steinmann, Paul; Strakl, Mitja; Hribersek, Matjaz; Ravnik, Jure (Computational Mechanics, 2021)
To respond to the ongoing pandemic of SARS-CoV-2, this contribution deals with recently highlighted COVID-19 transmission through respiratory droplets in form of aerosols. Unlike other recent studies that focused on airborne transmission routes, this work addresses aerosol transport and deposition in a human respiratory tract. The contribution therefore conducts a computational study of aerosol deposition in digital replicas of human airways, which include the oral cavity, larynx and tracheobronchial airways down to the 12th generation of branching. Breathing through the oral cavity allows the air with aerosols to directly impact the larynx and tracheobronchial airways and can be viewed as one of the worst cases in terms of inhalation rate and aerosol load. The implemented computational model is based on Lagrangian particle tracking in Reynolds-Averaged Navier-Stokes resolved turbulent flow. Within this framework, the effects of different flow rates, particle diameters and lung sizes are investigated to enable new insights into local particle deposition behavior and therefore virus loads among selected age groups. We identify a signicant increase of aerosol deposition in the upper airways and thus a strong reduction of virus load in the lower airways for younger individuals. Based on our findings, we propose a possible relation between the younger age related fluid mechanical protection of the lower lung regions due to the airway size and a reduced risk of developing a severe respiratory illness originating from COVID-19 airborne transmission.
CRIS-Team WoS Importer:2021-04-02

Case study on the influence of kinematic hardening within a parameter-free and non-invasive form finding approach - Landkammer, Philipp; Steinmann, Paul (MATEC Web of Conferences, 2016)
Inverse form finding – as a type of shape optimization – aims in determining the optimal preform design of a workpiece for a specific forming process, whereby the desired target geometry is known. Recently, a novel parameter-free and heuristic approach was developed to tackle this nonlinear optimization problem. Benchmark tests already delivered promising results. As a particular note-worthy feature of the approach, a coupling to an arbitrary finite element software is feasible in a non-invasive fashion. The aim of this contribution is to investigate the effect of kinematic hardening and cyclic loading on the convergence behavior of the algorithm.

Challenges and perspectives in brain tissue testing and modeling - Budday, Silvia; Holzapfel, Gerhard A.; Steinmann, Paul; Kuhl, Ellen (Proceedings in Applied Mathematics and Mechanics, 2019)
While long underestimated, more and more evidence confirms that mechanics play a critical role for brain function and dysfunction. Therefore, computational simulations based on the field equations of nonlinear continuum mechanics can provide important insights into the underlying mechanisms of brain injury and disease. Realistic numerical predictions, however, require models capable of capturing the complex and unique mechanical behavior of this ultrasoft, highly heterogeneous and adaptive tissue. In recent years, contradictory experimental results have retarded progress in this field. Here, we summarize the key characteristics of brain tissue behavior on different length and time scales and propose application-specific modeling approaches, which are as complex as necessary but as simple as possible. The presented considerations will, on the one hand, facilitate well-designed future experiments and, on the other hand, help to choose the appropriate constitutive law for a specific application.

Challenges of order reduction techniques for problems involving polymorphic uncertainty - Pivovarov, Dmytro; Willner, Kai; Steinmann, Paul; Brumme, Stephan; Müller, Michael; Srisupattarawanit, Tarin; Ostermeyer, Georg Peter; Henning, Carla; Ricken, Tim; Kastian, Steffen; Reese, Stefanie; Moser, Dieter; et al. (GAMM-Mitteilungen, 2019)
Modeling of mechanical systems with uncertainties is extremely challenging and requires a careful analysis of a huge amount of data. Both, probabilistic modeling and nonprobabilistic modeling require either an extremely large ensemble of samples or the introduction of additional dimensions to the problem, thus, resulting also in an enormous computational cost growth. No matter whether the Monte-Carlo sampling or Smolyak's sparse grids are used, which may theoretically overcome the curse of dimensionality, the system evaluation must be performed at least hundreds of times. This becomes possible only by using reduced order modeling and surrogate modeling. Moreover, special approximation techniques are needed to analyze the input data and to produce a parametric model of the system's uncertainties. In this paper, we describe the main challenges of approximation of uncertain data, order reduction, and surrogate modeling specifically for problems involving polymorphic uncertainty. Thereby some examples are presented to illustrate the challenges and solution methods.
CRIS-Team Scopus Importer:2019-05-02
Keywords: approximation of uncertain data; model order reduction; sensitivity analysis; surrogate modeling; uncertainty quantification

Chapter two-neuromechanics: From neurons to brain - Goriely, Alain; Budday, Silvia; Kuhl, Ellen (Advances in Applied Mechanics, 2015)
Arguably, the brain is the most complex organ in the human body, and, at the same time, the least well understood. Today, more than ever before, the human brain has become a subject of narcissistic study and fascination. The fields of neuroscience, neu- rology, neurosurgery, and neuroradiology have seen tremendous progress over the past two decades; yet, the field of neuromechanics remains underappreciated and poorly understood. Here, we show that mechanical stretch, strain, stress, and force play a critical role in modulating the structure and function of the brain. We discuss the role of neuromechanics across the scales, from individual neurons via neuronal tissue to the whole brain. We review current research highlights and discuss challenges and potential future directions. Using the nonlinear field theories of mechanics, we illustrate three phenomena which are tightly regulated by mechanical factors: neuroelasticity, the extremely soft behavior of the brain independent of time; neurodevelopment, the evo- lution of the brain at extremely long time scales; and neurodamage, the degradation of the brain at extremely short time scales. We hope that this review will become a starting point for a multidisciplinary approach to the mechanics of the brain with potential impact in preventing, diagnosing, and treating neurological disorders.

Characterisation of Magneto-Sensitive Elastomers; Material Model meets Experimental Results - Walter, Bastian; Saxena, Prashant; Kaschta, Joachim; Schubert, Dirk W.; Steinmann, Paul (13th Bayreuth Polymer Symposium, Bayreuth, 2013)

Characterization and modeling of polymer nanocomposites across the scales - A comprehensive approach covering the mechanical behavior of matrix, filler, and interphase - Ries, Maximilian (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2023)
Polymers represent a highly versatile material class and can be further enhanced to meet the requirements of highly demanding applications by adding filler particles. Particularly with nano-sized fillers, remarkable improvements in polymer nanocomposites’ (PNCs’) mechanical performance could be achieved experimentally. The outstanding mechanical properties of PNCs are mainly attributed to the matrix-filler interphase, which has a major impact, especially for nano-sized fillers. Therefore, a detailed understanding of the interphase and its impact on the overall behavior is necessary to exploit the full potential of PNCs. For this purpose, precise numerical models are required, to complement the challenging experimental investigation at the nano-scale. Particle-based methods such as molecular dynamics (MD) provide a detailed resolution of the microstructure, but are too expensive to solve problems at the engineering scale. To this end, computationally more efficient continuum approaches like the finite element (FE) method are commonly employed. However, these methods require accurate constitutive laws that capture the impact of the interphase and are usually not available. To this end, the present work introduces a methodology to derive continuum mechanical models for PNCs based on molecular dynamics and thus combines the advantages of particle-based and continuum approaches. Although we use nano-silica-reinforced polystyrene as an example for our investigations, the methods can be easily transferred to other material pairings. First, we present a strategy to characterize the mechanical behavior of neat polymer and filler based on MD simulations. These insights enable us to subsequently calibrate appropriate continuum mechanical constitutive laws for the viscoplastic polymer and the anisotropic, elastic filler. Since the interphase cannot be investigated separately, we consider polystyrene-silica samples with two nanofillers at different filler distances. In order to realize comparable simulation setups, we employ an MD-FE coupling method to perform uniaxial tension simulations. The resulting overall force response and interparticle strain facilitate the identification of the inelastic property profiles within the interphase. This continuum mechanical interphase model reproduces the characteristic size effect of PNCs. Furthermore, the obtained constitutive descriptions for matrix, filler, and interphase form the prerequisite for analyzing representative volume elements (RVEs). Using these RVEs, we evaluate the influence of filler content and distribution on the nanocomposite’s overall stiffness. Consequently, this interdisciplinary work contributes significantly to understanding polymer nanocomposites, especially the crucial matrix-filler interphase, and thus complements experimental insights. Moreover, the transfer of molecular-scale insights into continuum mechanical models forms an essential link between the chemistry and engineering communities for the numerical modeling of polymer nanocomposite
Keywords: finite elements; interphase properties; molecular dynamics; particle-to-continuum coupling; polymer nanocomposites; size effect

Characterization of Polystyrene Under Shear Deformation Using Molecular Dynamics - Ries, Maximilian; Steinmann, Paul; Pfaller, Sebastian (Developments and Novel Approaches in Nonlinear Solid Body Mechanics, 2020)
Nano-filled polymers are becoming more and more important to meet the continuously growing requirements of modern engineering problems. The investigation of these composite materials at the molecular level, however, is either prohibitively expensive or just impossible. Multiscale approaches offer an elegant way to analyze such nanocomposites by significantly reducing computational costs compared to fully molecular simulations. When coupling different time and length scales, however, it is in particular important to ensure that the same material description is applied at each level of resolution. The Capriccio method (Pfaller et al, 2012, 2013), for instance, couples a particle domain modeled with molecular dynamics (MD) with a finite element based continuum description and has been used i.a. to investigate the effects of nano-sized silica additives embedded in atactic polystyrene (PS), cf. Pfaller et al (2016); Liu et al (2017). However, a simple hyperelastic constitutive law is used so far for the continuum description which is not capable to fully match the behavior of the particle domain. To overcome this issue and to enable further optimization of the coupling scheme, the material model used for the continuum should be derived directly from pure MD simulations under thermodynamic conditions identical to those used by the Capriccio method. To this end, we analyze the material response of pure PS under uniaxial deformation using strain-controlled MD simulations (Ries et al, 2019). Analogously, we perform simulations under pure shear deformation to obtain a comprehensive understanding of the material behavior. As a result, the present PS shows viscoelastic characteristics for small strains, whereas viscoplasticity is observed for larger deformations. The insights gained and data generated are used to select a suitable material model whose parameters have to be identified in a subsequent parameter optimization.<br
Keywords: Molecular dynamics; Simulation of polymers; Mechanical properties of polymers; Material characterization

Characterization of the material behavior and identification of effective elastic moduli based on molecular dynamics simulations of coarse-grained silica - Ries, Maximilian; Bauer, Christof; Weber, Felix; Steinmann, Paul; Pfaller, Sebastian (Mathematics and Mechanics of Solids, 2022)
The addition of fillers can significantly improve the mechanical behavior of polymers. The responsible mechanisms at the molecular level can be well assessed by particle-based simulation techniques, such as molecular dynamics. However, the high computational cost of these simulations prevents the study of macroscopic samples. Continuum-based approaches, particularly micromechanics, offer a more efficient alternative but require precise constitutive models for all constituents, which are usually unavailable at these small length scales. In this contribution, we derive a molecular-dynamics-informed constitutive law by employing a characterization strategy introduced in a previous publication. We choose silicon dioxide (silica) as an exemplary filler material used in polymer composites and perform uniaxial and shear deformation tests with molecular dynamics. The material exhibits elastoplastic behavior with a pronounced anisotropy. Based on the pseudo-experimental data, we calibrate an anisotropic elastic constitutive law and reproduce the material response for small strains accurately. The study validates the characterization strategy that facilitates the calibration of constitutive laws from molecular dynamics simulations. Furthermore, the obtained material model for coarse-grained silica forms the basis for future continuum-based investigations of polymer nanocomposites. In general, the presented transition from a fine-scale particle model to a coarse and computationally efficient continuum description adds to the body of knowledge of molecular science as well as the engineering community.
CRIS-Team WoS Importer:2022-08-19

Chemical and structural characterisation of DGEBA-based expocies by Time of Flight Secondary Ion Mass Spectroscopy (ToF-SIMS) as a preliminary to polymer interphase characterisation - Possart, Gunnar; Steinmann, Paul; Passlack, Sven; Brodyanski, Alexander; Kopnarski, Michael; Presser, Melanie; Geiß, Paul L.; Bock, Wolfgang (Analytical and Bioanalytical Chemistry, 2009)
UnivIS-Import:2015-03-09:Pub.2009.tech.FT.FT-TM.chemic

Coefficient of tangential restitution for non-spherical particles - Wedel, Jana; Hriberšek, Matjaž; Steinmann, Paul; Ravnik, Jure (Powder Technology, 2024)
In various industrial and naturally occurring multiphase flows, whether dilute or dense, particle interaction plays a crucial role. In most cases, the particles are non-spherical, which poses a computational challenge in terms of particle motion and particle interaction, i.e. both particle–particle and particle–wall collisions. In this study, we present a novel frictional particle collision model to be used in general fluid flows. The model is derived for superellipsoidal particle shapes and thus allows consideration of frictional collisions of a wide variety of particle geometries. In this context, we derive an expression for the tangential coefficient of restitution applicable to arbitrarily shaped particles. Furthermore, we present the performance of the novel model by applying it to demonstrative examples ranging from two- to multi-particle systems.
CRIS-Team Scopus Importer:2024-03-01
Keywords: Non-spherical particles; Particle collision; Superellipsoids; Tangential restitution coefficient

Coherent energetic interfaces accounting for in-plane degradation - Esmaeili, Ali; Javili, Ali; Steinmann, Paul (International Journal of Fracture, 2016)

Combined continuum mechanics and molecular dynamics approach for uniaxial deformation of a thermoplastic polymer - Bauer, Christof; Pfaller, Sebastian (Proceedings in Applied Mathematics and Mechanics, 2021)
A hybrid molecular dynamics (MD)‐continuum mechanics (CM) method for calculating a molecular system of an amorphous polymer under uniaxial tensile load was developed. In this contribution, the operating principle of this method is introduced and applied to a sample system. Furthermore, the practicability of the hybrid MD‐CM approach is examined.<br

Comparative computational analysis of the Cahn–Hilliard equation with emphasis on C1-continuous methods - Käßmair, Stefan; Steinmann, Paul (Journal of Computational Physics, 2016)
The numerical treatment of the fourth-order Cahn–Hilliard equation is nonstandard. Using a Galerkin -method necessitates, for instance, piecewise smooth and globally C1-continuous basis functions or a mixed formulation. The latter is obtained introducing an auxiliary field which allows to rephrase the Cahn–Hilliard equation as a set of two coupled second-order equations. In view of this, the formulation in terms of the primal unknown appears to be a more intuitive and natural choice but requires a C1-continuous interpolation. Therefore, isogeometric analysis, using a spline basis, and natural element analysis are addressed in the present contribution. Mixed second-order finite element methods introducing the chemical potential or alternatively a nonlocal concentration as auxiliary field serve as references to which both higher-order methods are compared in terms of accuracy and efficiency.
EAM Import::2019-03-13

Comparison of different biaxial tests for the inverse identification of sheet steel material parameters - Schmaltz, Stefan; Willner, Kai (Strain, 2014)
The aim of this work is to compare different biaxial specimen geometries and loading conditions concerning their applicability as experimental database for an inverse finite element model updating procedure to identify the material parameters of sheet steel. Therefore, the deformation of the specimens is recorded with an optical, three-dimensional full-field deformation measurement system, and the utilised displacement data at the surface of the specimens are calculated via digital image correlation. The numerical material model for the simulations is based on a three-dimensional, anisotropic elasto-plastic ansatz and is implemented into a commercial finite element software code. The material parameters that are identified with the different specimen geometries are the hardening variables and the anisotropic plastic values. Based on the identification results, a selection criterion for the evaluation of specimen geometries for the inverse parameter identification is presented.
Keywords: Anisotropy; Computational plasticity; FEMU; Parameter identification; Sheet steel

Comparison of Different Sensitivity Analysis Methods in the Context of Dimensional Management - Heling, Björn; Oberleiter, Thomas; Schleich, Benjamin; Willner, Kai; Wartzack, Sandro (ASME 2017 International Mechanical Engineering Congress and Exposition, Volume 2: Advanced Manufacturing, 2017)
Although mass production parts look the same, every manufactured part is unique, at least on a closer inspection. The reason for this is that every manufactured part is inevitable subjected to different scattering influencing factors and variation in the manufacturing process, such as varying temperatures or tool wear. All these factors inevitably lead to parts, which deviate from their ideal shape. Products, which are built from these deviation-afflicted parts consequently show deviations from their ideal properties. To ensure that every single product nevertheless meets its technical requirements, it is necessary to specify the permitted deviations. Furthermore it is necessary to estimate the consequences of the permitted deviations, which is done via tolerance analysis. During this process the imperfect parts are assembled virtually and the effects of the geometric deviations can be calculated during a variation simulation. Since the tolerance analysis is to enable engineers to identify weak points in an early design stage it is important to know which contribution every single tolerance has on a certain quality-relevant characteristic, to restrict or increase the correct tolerances. In this paper two different approaches are shown and compared to represent the statistical behavior and the strongly connected sensitivity analyses. In particular a newly developed approach, which is based on fuzzy arithmetic, is compared to the established EFAST-method. The exemplary application of both methods and the comparison of the results are illustrated on a case stud

Comparison of several staggered atomistic-to-continuum concurrent coupling strategies - Davydov, Denis; Pelteret, Jean-Paul; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2014)
In this contribution several staggered schemes used to couple continuum mechanics (CM) and molecular mechanics (MM) are proposed. The described approaches are based on the atomistic-to-continuum correspondence, obtained by spatial averaging in the spirit of Irving and Kirkwood, and Noll. Similarities between this and other concurrent coupling schemes are indicated, thus providing a broad overview of different approaches in the field. The schemes considered here are decomposed into the surface-type (displacement or traction boundary conditions) and the volume-type. The latter restricts the continuum displacement field (and possibly its gradient) in some sense to the atomistic (discrete) displacements using Lagrange multipliers. A large-strain CM formulation incorporating Lagrange multipliers and a strategy to solve the resulting coupled linear system using an iterative solver is presented. Finally, the described coupling methods are numerically examined using two examples: uniaxial deformation and a plate with a hole relaxed under surface tension. Accuracy and convergence rates of each method are reported. It was found that the displacement (surface) coupling scheme and the Lagrangian (volume) scheme based on either discrete displacements or the H1 norm derived from continuous displacement fields provide the best performance. © 2014 Elsevier B.V.
UnivIS-Import:2015-03-09:Pub.2014.tech.FT.FT-TM.compar
Keywords: Atomic-to-continuum coupling methods; Concurrent multiscale methods; Finite elements; Irving-Kirkwood-Noll procedure; Large strain; Molecular mechanics

Compilation of Fatigue Data for Austenitic Stainless Steels - Wilhelm, Paul; Steinmann, Paul; Rudolph, Jürgen (Compacts of the 45th AMNT, 2014)

Complex mechanical behavior of human articular cartilage and hydrogels for cartilage repair - Weizel, A.; Distler, Thomas; Schneidereit, Dominik; Friedrich, Oliver; Bräuer, Lars; Paulsen, Friedrich; Detsch, Rainer; Boccaccini, Aldo R.; Budday, Silvia; Seitz, H. (Acta Biomaterialia, 2020)
The mechanical behavior of cartilage tissue plays a crucial role in physiological mechanotransduction processes of chondrocytes and pathological changes like osteoarthritis. Therefore, intensive research activities focus on the identification of implant substitute materials that mechanically mimic the cartilage extracellular matrix. This, however, requires a thorough understanding of the complex mechanical behavior of both native cartilage and potential substitute materials to treat cartilage lesions. Here, we perform complex multi-modal mechanical analyses of human articular cartilage and two surrogate materials, commercially available ChondroFillerliquid, and oxidized alginate-gelatin (ADA-GEL) hydrogels. We show that all materials exhibit nonlinearity and compression-tension asymmetry. However, while hyaline cartilage yields higher stresses in tension than in compression, ChondroFillerliquid and ADA-GEL exhibit the opposite trend. These characteristics can be attributed to the materials’ underlying microstructure: Both cartilage and ChondroFillerliquid contain fibrillar components, but the latter constitutes a bi-phasic structure, where the 60% nonfibrillar hydrogel proportion dominates the mechanical response. Of all materials, ChondroFillerliquid shows the most pronounced viscous effects. The present study provides important insights into the microstructure-property relationship of cartilage substitute materials, with vital implications for mechanically-driven material design in cartilage engineering. In addition, we provide a data set to create mechanical simulation models in the future.
CRIS-Team Scopus Importer:2020-11-06
Keywords: Human articular cartilage; Hydrogels; Mechanical testing; Microstructure; Tissue engineering

Component residual stress control in forward rod extrusion by material flow and tribology—experiments and modeling - Jobst, Andreas; Floros, Dimosthenis; Steinmann, Paul; Merklein, Marion (Forschung Im Ingenieurwesen-Engineering Research, 2021)
The forward rod extrusion of ferritic stainless steel X6Cr17 (DIN 1.4016) is here investigated with the objectives to experimentally identify and numerically verify the effect of the lubrication system and die opening angle on residual stresses. Three lubricants – MoS2, soap and polymer – are considered whose tribological properties are characterized via double cup extrusion tests. The effect of material flow is also studied by forming in conical dies featuring three different opening angles. The extrusion experiments revealed a decrease in the near-surface tensile stresses with decreasing friction for all the considered opening angles. An opening angle of 2α = 90° led to the highest tensile residual stresses. Both an increase to 2α = 120° and a decrease to 60° resulted in reduced tensile stresses and even a shift to compressive stresses. Furthermore, a previously developed numerical model of forward rod extrusion is optimized and validated against the experimentally measured residual stresses. The effect of the spatial and temporal discretizations of the model on the predicted residual stresses is investigated. Based on the experimental and numerically verified results, the recommendation to reduce friction in forward rod extrusion is derived as a means to obtain a less detrimental to the lifecycle of extruded parts residual stress state.

Computational aeroacoustic simulations of small vertical axis wind turbine - Weber, Johannes; Regensburger, Christoph; Tautz, Matthias; Becker, Stefan; Hüppe, Andreas; Kaltenbacher, Manfred (45th International Congress and Exposition on Noise Control Engineering: Towards a Quieter Future, INTER-NOISE 2016, 2016)
Reducing the noise of wind turbines, which are installed in the vicinity of urban areas, is one major issue for social acceptance. In general, horizontal wind turbines are the most common configuration for using wind energy. However, the interest of small wind turbines are grown in the last years because of the future demand for decentralized power generation. The present work deals with two different numerical schemes of noise prediction of small vertical axis wind turbines using hybrid methods. For both schemes the time-dependent turbulent flow field is solved with Scale-Adaptive Simulation. The two schemes then differ in how the location of the acoustic sources and their propagation is calculated. In the first scheme the Ffowcs-Williams Hawkings method is used which is based on a free field Green's function. The far field acoustic radiation is calculated by extrapolation of the acoustic waves. In the second scheme the acoustic source terms are computed according to Perturbed Convective Wave Equations, which gives source terms located on the original CFD grid. These source terms are projected onto a coarser acoustic grid on which the propagation is calculated by solving the wave equation. Both methodologies are compared with each other and validated with experimental data.
Keywords: Noise; Simulation; Wind turbines

Computational aspects of thermomechanical solids with Kapitza interfaces - Javili, Ali; McBride, Andrew; Steinmann, Paul (Computational Materials Science, 2012)
UnivIS-Import:2015-03-09:Pub.2012.tech.FT.FT-TM.comput_6

Computational electro- and magneto-elasticity for quasi-incompressible media immersed in free space - Pelteret, Jean-Paul; Davydov, Denis; McBride, Andrew; Vu, Duc Khoi; Steinmann, Paul (International Journal for Numerical Methods in Engineering, 2016)
In this work, a mixed variational formulation to simulate quasi-incompressible electro-active or magneto-active polymers immersed in the surrounding free space is presented. A novel domain decomposition is used to disconnect the primary coupled problem and the arbitrary free-space mesh update problem. Exploiting this decomposition, we describe a block-iterative approach to solving the linearised multiphysics problem, and a physically and geometrically based, three-parameter method to update the free space mesh. Several application-driven example problems are implemented to demonstrate the robustness of the mixed formulation for both electro-elastic and magneto-elastic problems involving both finite deformations and quasi-incompressible media

Computational Failure Mechanics : State-of-the Art and Future Trends - Willam, Kaspar; Steinmann, Paul (Proceedings of FEM' 90 Congress, 1990)
UnivIS-Import:2015-04-16:Pub.1990.tech.FT.FT-TM.comput

Computational first-order homogenization in chemo-mechanics - Käßmair, Stefan; Steinmann, Paul (Archive of Applied Mechanics, 2018)
In the present contribution, we consider species diffusion coupled to finite deformations in strongly heterogeneous microstructures. A semi-dual energy formulation parameterized in terms of the chemical potential is obtained by Legendre transformation of the free energy. Doing so avoids the presence of higher gradients of the deformation field. The constitutive response at the macroscopic level is obtained using variationally consistent homogenization (Larson et al. in Int J Numer Method Eng 81(13):1659–1686, 2010. doi:10.1002/nme.2747). This approach allows to treat transient microscale problems on a representative volume element which has a finite size, i.e., the scales are not clearly separated. Full details of the implementation are provided. A series of numerical examples compares the homogenization results to single-scale formulations which fully resolve all microstructural features.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Coupled problem; First-order homogenization; Transient microscale

Computational Fracture Modeling in Heterogeneous Materials - Recent Advances and Future Challenges - Kumar, Paras; Phansalkar, Dhananjay; Mergheim, Julia; Leyendecker, Sigrid; Steinmann, Paul (conference, WCCM-APCOM 15th World Congress on Computational Mechanics & 8th Asian Pacific Congress on Computational Mechanics, 2022)

Computational Homogenisation of Material Layers with Micromorphic Mesostructure - Hirschberger, C. B.; Sukumar, N; Steinmann, Paul (Philosophical Magazine, 2008)
In this paper, a multiscale approach to capture the behavior of material layers that possess a micromorphic mesostructure is presented. To this end, we seek to obtain a macroscopic traction-separation law based on the underlying meso and microstructure. At the macro level, a cohesive interface description is used, whereas the underlying mesostructure is resolved as a micromorphic representative volume element. The micromorphic continuum theory is particularly well-suited to account for higher-order and size-dependent effects in the material layer. On considering the height of the material layer, quantities at different scales are related through averaging theorems and the Hill condition. An admissible scale-transition is guaranteed via the adoption of customized boundary conditions, which account for the deformation modes in the interface. On the basis of this theoretical framework, computational homogenization is embedded within a finite-element approach, and the capabilities of the model are demonstrated through numerical example
UnivIS-Import:2015-03-09:Pub.2008.tech.FT.FT-TM.comput_7
Keywords: Cohesive interface; Computational homogenization; Multiscale mechanics; Size effect; Thin layer

Computational Homogenisation using Reduced-Order Modelling applied to Hyperelasticity - Soldner, Dominic; Brands, Benjamin; Zabihyan, Reza; Steinmann, Paul; Mergheim, Julia (Proceedings in Applied Mathematics and Mechanics, 2016)
Within this study nonlinear reduced-order modelling for hyperelastic material is applied for the boundary value problem on the micro-scale which arises in the context of computational homogenisation. This involves the Proper Orthogonal Decomposition and the Discrete Empirical Interpolation Method for the nonlinear term. Considered error measures are the errors of the displacement field, the averaged stresses and the effective elasticity tensor.
Keywords: Model Reduction; Computational Homogenisation; Discrete Empirical Interpolation Method

Computational Homogenization and Parameter-Identification for Heterogeneous Inelastic Materials - Schmidt, Ulrike; Mergheim, Julia; Steinmann, Paul (Proceedings of Applied Mathematics and Mechanics (PAMM), 2011)
The aim of this paper is to describe a method for identifying micro material parameters using only macroscopic experimental data. The FE2 method is used to model the behavior of the complex materials with heterogeneous micro-structure. The resulting least squares problem is minimized using gradient-based optimization algorithms, where the gradient information is derived analytically within the discretized scheme.
UnivIS-Import:2015-04-16:Pub.2011.tech.FT.FT-TM.comput_8

Computational Homogenization in Magneto-Mechanical Composites - Zabihyan, Reza; Mergheim, Julia; Javili, Ali; Steinmann, Paul (Proceedings in Applied Mathematics and Mechanics, 2016)
In the present work, the behavior of heterogeneous magnetorheological elastomers undergoing large deformations under the action of magnetic fields is studied. First-order computational homogenization is used to derive the homogenized stresses and magnetic inductions of the macro-structure from the response of the underlying micro-structure. Different types of boundary conditions are applied to solve the micro problem where the constitutive law is assumed to be known.
Keywords: Magneto-elasticity; homogenization; boundary condition

Computational homogenization in magneto-mechanics - Javili, Ali; Chatzigeorgiou, Georgios; Steinmann, Paul (International Journal of Solids and Structures, 2013)
This work presents a geometrically nonlinear homogenization framework for composites with magneto-mechanical behavior whereby the composite can be subject to large deformation processes. The magneto-mechanical governing equations in the material description for both the overall body and its microstructure are presented, and the connections between micro- and macro-scale field variables are identified. Considering periodic boundary conditions for the microscopic unit cell, a finite element framework for computing the macroscopic field variables and the effective tangent moduli is developed. The proposed methodology is utilized to study a variety of two- and three-dimensional numerical examples. In particular, the behavior of fiber and particle reinforced composites with magneto-mechanical constitutive laws are illustrated. Finally, a specific physically motivated problem of a magnetorheological elastomer, consisting of a polymer matrix and iron particles, under finite deformation and applied magnetic field is analyzed and the results are given for several combinations of deformation modes and applied magnetic fields. © 2013 Elsevier Ltd. All rights reserved.
UnivIS-Import:2015-04-14:Pub.2013.tech.FT.FT-TM.comput_5
Keywords: Computational homogenization; Finite element formulation; Hill-Mandel condition; Magnetorheological elastomers; Micro-to-macro transition

Computational Homogenization of Defect Driving Forces - Ricker, Sarah; Mergheim, Julia; Steinmann, Paul (Proceedings of the IUTAM Symposium on Progress in the Theory and Numerics of Configuration Mechanics (peer reviewed), 2009)
Due to the fact that many engineeringmaterials and also biological tissues possess an underlying (heterogeneous)micro-structure it is not sufficient to simulate these materials by pre-assumed overall constitutive assumptions. Therefore, we apply a homogenization scheme, which determines the macroscopicmaterial behavior based on analysis of the underlying micro-structure. In the work at hand focus is put on the extension of the classical computational homogenization scheme towards the homogenization of material forces. Therefore, volume forces have to incorporated which may emerge due to inhomogeneities in the material. With assistance of this material formulation and the equivalence of the J-integral and the material force at a crack tip, studies on the influence of the micro-structure onto the macroscopic crack-propagation are carried out. © Springer Science+Business Media B.V. 2009.
UnivIS-Import:2015-04-16:Pub.2009.tech.FT.FT-TM.comput

Computational Homogenization of Micromechanically Resolved Textile Materials - Mehnert, Markus; Fillep, Sebastian; Mergheim, Julia; Steinmann, Paul (2015)

Computational homogenization of nano-materials accounting for size effects via surface elasticity - Javili, Ali; Chatzigeorgiou, George; McBride, Andrew T.; Steinmann, Paul; Linder, Christian (GAMM-Mitteilungen, 2015)
The objective of this contribution is to establish a first-order computational homogenization framework for micro-to-macro transitions of porous media that accounts for the size effects through the consideration of surface elasticity at the microscale. Although the classical (firstorder) homogenization schemes are well established, they are not capable of capturing the well-known size effects in nano-porous materials. In this contribution we introduce surface elasticity as a remedy to account for size effects within a first-order homogenization scheme. This proposition is based on the fact that surfaces are no longer negligible at small scales. Following a standard first-order homogenization ansatz on the microscopic motion in terms of the macroscopic motion, a Hill-type averaging condition is used to link the two scales. The averaging theorems are revisited and generalized to account for surfaces. In the absence of surface energy this generalized framework reduces to classical homogenization. The influence of the length scale is elucidated via a series of numerical examples performed using the finite element method. The numerical results are compared against the analytical ones at small strains for tetragonal and hexagonal microstructures. Furthermore, numerical results at small strains are compared with those at finite strains for both microstructures. Finally, it is shown that there exists an upper bound for the material response of nano-porous media. This finding surprisingly restricts the notion of "smaller is stronger".
CRIS-Team Scopus Importer:2022-08-05
Keywords: Homogenization; Nano-materials; Size effects; Surface elasticity

Computational homogenization of one-dimensional textile structures - Fillep, Sebastian; Mergheim, Julia; Steinmann, Paul (Proceedings of the 7th International Conference on Textile Composites and Inflatable Structures, STRUCTURAL MEMBRANES 2015, 2015)
In this contribution a computational homogenization method for one-dimensional technical textiles, i.e. ropes or cables, is developed. Regarding the large length-tothickness ratio that characterizes rope-like textiles on the macro level, a discretization with beam elements is numerically efficient. The homogeneous macro level is influenced by the heterogeneous micro structure involving contact between the fibers. Therefore, the fibers are modeled explicitly a representative volume element to capture the contact within interactions. For the connection of the two scales a specific homogenization method is introduced involving theoretical aspects and numerical examples for periodic rope-like structures.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Beam; Computational homogenization; Contact; Technical textiles

Computational homogenization of rope-like technical textiles - Fillep, Sebastian; Mergheim, Julia; Steinmann, Paul (Computational Mechanics, 2015)
This contribution investigates a computational homogenization method for one-dimensional technical textiles i.e. ropes or cables. On the macroscopic level rope-like textiles are characterized by a large length-to-thickness ratio, such that a discretization with structural elements, i.e. beam elements, is numerically efficient. The material behavior is, however, strongly influenced by the heterogeneous micro structure. Here, the fibers at the micro structure are modeled explicitly via a representative volume element whereby the contact interactions between fibers are captured. To transfer the microscopic response to the macro level a beam specific homogenization scheme is introduced. Theoretical aspects are discussed, e.g. the advocated beam specific power averaging theorem and the corresponding scale transition, and numerical examples for periodic rope-like structures are given.
UnivIS-Import:2015-10-26:Pub.2015.tech.FT.FT-TM.comput
Keywords: Beam kinematics; Computational homogenization; Contact; Ropes; Technical textiles

Computational modeling of case II diffusion in polymeric materials - Bargmann, Swantje; McBride, Andrew; Steinmann, Paul (Proceedings of the 24th Nordic Seminar on Computational Mechanics, 2011)
UnivIS-Import:2015-04-16:Pub.2011.tech.FT.FT-TM.comput_9

Computational modelling and homogenization of technical textiles - Fillep, Sebastian; Mergheim, Julia; Steinmann, Paul (Engineering Structures, 2013)
This contribution presents a multiscale homogenization method to model technical textiles. On the macroscopic level textiles are characterized by a large area-to-thickness ratio, such that a discretization with shell elements is numerically efficient. The material behavior is strongly influenced by the heterogeneous (e.g. woven) microstructure. This is explicitly modelled by means of a volumetric microsample, and a homogenization scheme is applied to transfer the microscopic response to the macrolevel. Theoretical aspects are discussed and a numerical example for periodic textile structures is given. © 2013 Elsevier Ltd.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.comput
Keywords: Homogenization; Multi scale; Shell kinematic; Technical textiles

Computational Modelling of Failure with the Discontinuous Galerkin Method - Mergheim, Julia; Steinmann, Paul; Kuhl, Ellen (Proceedings of the 1st International LUXFEM Conference, 2003)
UnivIS-Import:2015-04-16:Pub.2003.tech.FT.FT-TM.comput_4

Computational Multiscale Modelling of Heterogeneous Material Layers - Hirschberger, C. B.; Ricker, S.; Steinmann, Paul; Sukumar, N (Engineering Fracture Mechanics, 2009)
A computational homogenization procedure for a material layer that possesses an underlying heterogeneous microstructure is introduced within the framework of finite deformations. The macroscopic material properties of the material layer are obtained from multiscale considerations. At the macro level, the layer is resolved as a cohesive interface situated within a continuum, and its underlying microstructure along the interface is treated as a continuous representative volume element of given height. The scales are linked via homogenization with customized hybrid boundary conditions on this representative volume element, which account for the deformation modes along the interface. A nested numerical solution scheme is adopted to link the macro and micro scales. Numerical examples successfully display the capability of the proposed approach to solve macroscopic boundary value problems with an evaluation of the constitutive properties of the material layer based on its micro-constitution.
UnivIS-Import:2015-03-09:Pub.2009.tech.FT.FT-TM.comput_6

Computational thermomechanics with boundary structures - Steinmann, Paul; Javili, Ali (IUTAM Bookseries, 2013)
This contribution is concerned with the numerical implementation of boundary potential energies and the study of their impact on the deformations of thermomechanical solids. Although boundary effects can play a dominant role in material behavior, the common modelling in continuum mechanics takes exclusively the bulk into account, nevertheless, neglecting possible contributions from the boundary. In the approach of this contribution the boundary is equipped with its own thermodynamic life, i.e. we assume separate boundary energy, entropy and the like. Furthermore, the generalized local balance laws are given according to Javili and Steinmann (Int J Solids Struct, 47:3245-3253,2010). Afterwards, derivations of a generalized weak formulation which is employed for the discretization and finite element implementation, including boundary potentials, are carried out completely based on a tensorial representation. Finally, numerical examples are presented to demonstrate the boundary effects due to the proposed thermohyperelastic material model.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Finite element method; Nanoscale materials; Surface thermoelasticity

Computation of the effective lamination stack's behavior considering the contact simulation with a multi-scale homogenization - Luchscheider, Vera; Maidorn, Mischa; Willner, Kai (Joint 11th World Congress on Computational Mechanics, WCCM 2014, the 5th European Conference on Computational Mechanics, ECCM 2014 and the 6th European Conference on Computational Fluid Dynamics, ECFD 2014, 2014)
The influence of the lamination stack on the mechanical behavior of an electrical machine is significant, especially for lightweight designs. Information about the stack's behavior is relevant for a proper calculation of the whole motor. This behavior is dependent on the contact between the single sheets. This paper aims to show that the normal contact behavior can be simulated with the elastic model of Bush, Gibson and Thomas, a plastic term depending on deformation of the highest peaks and a viscous term. The tangential slip is described through a micro-macro model. These models can be used in a representative volume element and consequently for a multi-scale homoge-nization. A material model of the whole lamination stack can be identified by loading the representative volume element with different deformations.
Keywords: Contact mechanics; Homogenization; Lamination stack

Concurrent consideration of cortical and cancellous bone within continuum bone remodelling - Schmidt, Ina; Papastavrou, Areti; Steinmann, Paul (Computer Methods in Biomechanics and Biomedical Engineering, 2021)
Continuum bone remodelling is an important tool for predicting the effects of mechanical stimuli on bone density evolution. While the modelling of only cancellous bone is considered in many studies based on continuum bone remodelling, this work presents an approach of modelling also cortical bone and the interaction of both bone types. The distinction between bone types is made by introducing an initial volume fraction. A simple point-wise example is used to study the behaviour of novel model options, as well as a proximal femur example, where the interaction of both bone types is demonstrated using initial density distributions. The results of the proposed model options indicate that the consideration of cortical bone remarkably changes the density evolution of cancellous bone, and should therefore not be neglected.
CRIS-Team WoS Importer:2021-03-12

Configurational force method enables fracture assessment in soft materials - Moreno Mateos, Miguel Angel; Steinmann, Paul (Journal of the Mechanics and Physics of Solids, 2024)
Configurational mechanics offers a framework for quantifying the tendency of defects to alter the material configuration. When applied to fracture mechanics, configurational forces can be used to quantify the propensity of cracks to propagate. An alternative, well-established approach involves analytical solutions for crack tip displacement fields. However, these solutions typically apply to a limited range of constitutive behaviors and oftentimes to the linear small strain regime. The ease of calculating configurational forces in a numerical Finite Element implementation, along with their applicability to soft fracture at large strains, motivates the study of their performance as a standalone fracture framework. In contrast to the majority of works that remain theoretical and numerical, our study includes a robust experimental approach to configurational forces at finite strains. We report tensile experiments on a soft elastomer with pre-cuts ante fracture initiation. In a first attempt to approach the -integral via configurational forces, we explore the performance of the linear elastic fracture mechanics solutions on Pacman-shaped domains that reproduce the crack tip vicinity. Then, we implement the entire boundary value problem with three-dimensional simulations that replicate the empirical tensile deformation of the soft elastomer samples. Subsequently, the results are benchmarked against estimations of the -integral obtained through a bespoke finite strain analytical crack tip solution. With the successful validation of the configurational force method at finite strains, we aim to establish a pipeline for the calculation of configurational forces in a standalone manner and circumventing the need for close-form analytical solution
Keywords: Configurational mechanicsMaterial forcesSoft fractureFinite strainsNumerical methodsExperimental mechanics

Configurational Forces in Bond Order Potentials - Birang Oskouei, Seyedehelmira; Smith, Ana-Suncana; Steinmann, Paul (Proceedings in Applied Mathematics and Mechanics, 2021)
In this contribution, a configurational mechanics framework is elaborated to assess the applicability of atomistic configurational forces in fracture of crystalline lattices. To this end, an analytical interatomic potential is reformulated in terms of the material positions occupied by the atoms participating in two- and three-body interactions. It is demonstrated that such a potential satisfies the requirements of invariances i.e., translational, rotational and parity. The focus of this work is developing the configurational setting for the bond order Tersoff potential. Two-dimensional pre-cracked mono-layer graphene modelled with the Tersoff potential is chosen to study the configurational force approach in determining energy release during crack propagation into the lattice.<br

Consequences of Thermodynamical Balances - Steinmann, Paul (Spatial and Material Forces in Nonlinear Continuum Mechanics, 2022)
This chapter exploits the consequences of the thermodynamical balances and the resulting formats of the dissipation power inequalities by identifying the forces driving material (configurational) changes on the boundary and at singular surfaces as the appropriate contributions to the balance of material momentum. It is the here advocated thermodynamical derivation of material forces that qualifies the current approach as being dissipation-consistent.
CRIS-Team Scopus Importer:2022-04-15

Constitutive Contact Laws in Structural Dynamics - Willner, Kai (Cmes-Computer Modeling in Engineering & Sciences, 2009)
The dynamic behavior of structures with joints is strongly influenced by the constitutive behavior within the contact areas. In this paper the influence of an elaborate constitutive contact model based on a rough surface model is investigated. The contact model is able to describe several effects like pressure dependent contact stiffness in normal and tangential direction as well as microslip effects. The corresponding constitutive contact laws are implemented in a finite element code. Numerical simulations are compared to experimental results of a clamped double-beam experiment. Copyright © 2009 Tech Science Press.
UnivIS-Import:2015-03-09:Pub.2009.tech.FT.FT-TM.consti
Keywords: Damping; Friction; Joints; Structural dynamics

Constitutive Friction Law for the Description and Optimization of Tailored Surfaces - Henneberg, Johannes; Beyer, Florian; Löffler, Maria; Willner, Kai; Merklein, Marion (Sheet Bulk Metal Forming, 2021)

Constitutive modelling of sheet-layered lamination stacks - Baloglu, Maximilian Volkan; Willner, Kai (Proceedings in Applied Mathematics and Mechanics, 2018)
Sheet‐layered lamination stacks found in electric motors as rotor and stator are a challenging task in structural mechanics due to their special design. The manufacturing process determines the nature of the microstructure resulting in the presence of bonding varnish or frictional contact between the individual metal sheets. For the latter case, a penalty method in normal and tangential direction can be used to capture the contact interactions of single plates. In combination with homogenization techniques, a transversely isotropic surrogate material model with a corresponding strain energy density can be identified. In this paper, the focus lies on the influence of the penalty parameters on the elastic quantities of the constitutive equation.<br

Construction of a Finite Element Damping Matrix from Measured Modal Data - Willner, Kai; Gaul, L. (Proceedings of the International Conference on Structural Dynamics Modelling, 2002)
UnivIS-Import:2015-04-16:Pub.2002.tech.FT.FT-TM.constr

Contact Description by FEM Based on Interface Physics - Willner, Kai; Gaul, L. (Proceedings of COMPLAS V, 1997)
UnivIS-Import:2015-04-16:Pub.1997.tech.FT.FT-TM.contac

Contact Laws for Rough Surfaces - Willner, Kai (Zeitschrift für angewandte Mathematik und Mechanik, 2000)
Contact laws for rough surfaces are used to obtain e.g. contact stiffness or contact conductivity. Usually contact laws are derived on the basis of asperity deformation models in conjunction with a stochastic roughness model. As the stochastic parameters depend strongly on the measurement procedure, the obtained contact laws have to be used carefully. Fractal surface parameters can be obtained, which are independent of sampling interval or length, but the resulting contact laws are still dependent on these values.
UnivIS-Import:2015-04-16:Pub.2000.tech.FT.FT-TM.contac

Contact of fractal surfaces - Experimental and numerical results - Willner, Kai; Görke, Daniel (Proceedings of GAMM Annual Conference, 2006)
UnivIS-Import:2015-04-16:Pub.2006.tech.FT.FT-TM.contac_2

Contact of rough surfaces - A comparison between experimental and numerical results - Willner, Kai; Görke, Daniel (Proceedings of the III. European Conference on Computational Mechanics, 2006)
UnivIS-Import:2015-04-16:Pub.2006.tech.FT.FT-TM.contac

Continuum-Atomistic Coupling based on Computational Homogenization - Mergheim, Julia; Steinmann, Paul; Menzel, Andreas; Ricker, Sarah (Proceedings of the 79th Annual Meeting of the International Association of Applied Mathematics and Mechanics, 2008)
UnivIS-Import:2015-04-16:Pub.2008.tech.FT.FT-TM.contin

Continuum-kinematics-inspired peridynamics. Mechanical problems - Javili, A.; McBride, A. T.; Steinmann, Paul (Journal of the Mechanics and Physics of Solids, 2019)
The main objective of this contribution is to develop a novel continuum-kinematics-inspired approach for peridynamics (PD), and to revisit PD's thermodynamic foundations. We distinguish between three types of interactions, namely, one-neighbour interactions, two-neighbour interactions and three-neighbour interactions. While one-neighbour interactions are equivalent to the bond-based interactions of the original PD formalism, two- and three-neighbour interactions are fundamentally different to state-based interactions in that the basic elements of continuum kinematics are preserved exactly. In addition, we propose that an externally prescribed traction on the boundary of the continuum body emerges naturally and need not vanish. This is in contrast to, but does not necessarily violate, standard PD. We investigate the consequences of the angular momentum balance and provide a set of appropriate arguments for the interactions accordingly. Furthermore, we elaborate on thermodynamic restrictions on the interaction energies and derive thermodynamically-consistent constitutive laws through a Coleman–Noll-like procedure.
CRIS-Team Scopus Importer:2019-07-16
Keywords: Continuum kinematics; Peridynamics; Thermodynamic consistency

Continuum-kinematics-inspired peridynamics: Thermo-mechanical problems - Javili, A.; Ekiz, E.; McBride, A. T.; Steinmann, Paul (Continuum Mechanics and Thermodynamics, 2021)
The recently proposed continuum-kinematics-inspired peridynamics (CPD) is extended to account for thermo-mechanical coupling at large deformations. The key features of CPD are that it is geometrically exact and is built upon multi-neighbour interactions. The bond-based interactions of the original PD formalism are equivalent to one-neighbour interactions of CPD. Two- and three-neighbour interactions, however, are fundamentally different from state-based PD in that the basic elements of continuum kinematics are preserved exactly. We elaborate on thermodynamic restrictions on the interaction energies and derive thermodynamically consistent constitutive laws through a Coleman–Noll-like procedure. Notably, we show that various choices for temperature, or coldness, satisfy the dissipation inequality and provide meaningful temperature, or coldness, evolution equations together with Fourier-like conduction relations.
CRIS-Team Scopus Importer:2021-04-09
Keywords: Continuum kinematics; Peridynamics; Thermo-mechanical CPD; Thermodynamic consistency

Continuum physics of materials with time dependent properties: Reviewing the case of polymer curing - Mokarram, Hossain; Steinmann, Paul (Advances in Applied Mechanics, 2015)
UnivIS-Import:2015-07-08:Pub.2015.tech.FT.FT-TM.contin

Control of minimum member size in parameter-free structural shape optimization by a medial axis approximation - Schmitt, Oliver; Steinmann, Paul (Computational Mechanics, 2018)
We introduce a manufacturing constraint for controlling the minimum member size in structural shape optimization problems, which is for example of interest for components fabricated in a molding process. In a parameter-free approach, whereby the coordinates of the FE boundary nodes are used as design variables, the challenging task is to find a generally valid definition for the thickness of non-parametric geometries in terms of their boundary nodes. Therefore we use the medial axis, which is the union of all points with at least two closest points on the boundary of the domain. Since the effort for the exact computation of the medial axis of geometries given by their FE discretization highly increases with the number of surface elements we use the distance function instead to approximate the medial axis by a cloud of points. The approximation is demonstrated on three 2D examples. Moreover, the formulation of a minimum thickness constraint is applied to a sensitivity-based shape optimization problem of one 2D and one 3D model.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Manufacturing constraint; Medial axis approximation; Minimum member size; Shape optimization

Convergence study of the h-adaptive PUM and the hp-adaptive FEM applied to eigenvalue problems in quantum mechanics - Davydov, Denis; Gerasimov, Tymofiy; Pelteret, Jean-Paul; Steinmann, Paul (Advanced Modeling and Simulation in Engineering Sciences, 2017)
In this paper the h-adaptive partition-of-unity method and the h- and hp-adaptive finite element method are applied to eigenvalue problems arising in quantum mechanics, namely, the Schrödinger equation with Coulomb and harmonic potentials, and the all-electron Kohn–Sham density functional theory. The partition-of-unity method is equipped with an a posteriori error estimator, thus enabling implementation of error-controlled adaptive mesh refinement strategies. To that end, local interpolation error estimates are derived for the partition-of-unity method enriched with a class of exponential functions. The efficiency of the h-adaptive partition-of-unity method is compared to the h- and hp-adaptive finite element method. The latter is implemented by adopting the analyticity estimate from Legendre coefficients. An extension of this approach to multiple solution vectors is proposed. Numerical results confirm the theoretically predicted convergence rates and remarkable accuracy of the h-adaptive partition-of-unity approach. Implementational details of the partition-of-unity method related to enforcing continuity with hanging nodes are discussed.

Correction to: Risk Assessment of Infection by Airborne Droplets and Aerosols at Different Levels of Cardiovascular Activity (Archives of Computational Methods in Engineering, (2021), 28, 6, (4297-4316), 10.1007/s11831-021-09613-7) - Wedel, Jana; Steinmann, Paul; Strakl, Mitja; Hribersek, Matjaz; Ravnik, Jure (Archives of Computational Methods in Engineering, 2022)
Incorrect versions of Figs. 8, 11, 12, 13 and 14 were published due to wrong version of file used by typesetter. Original article has been corrected with the correct version.
CRIS-Team Scopus Importer:2022-08-05

Coupled electro-elastic deformation and instabilities of a toroidal membrane - Liu, Zhaowei; Mcbride, Andrew; Sharma, Basant Lal; Steinmann, Paul; Saxena, Prashant (Journal of the Mechanics and Physics of Solids, 2021)
We analyse here the problem of large deformation of dielectric elastomeric membranes under coupled electromechanical loading. Extremely large deformations (enclosed volume changes of 100 times and greater) of a toroidal membrane are studied by the use of a variational formulation that accounts for the total energy due to mechanical and electrical fields. A modified shooting method is adopted to solve the resulting system of coupled and highly nonlinear ordinary differential equations. We demonstrate the occurrence of limit point, wrinkling, and symmetry-breaking buckling instabilities in the solution of this problem. Onset of each of these ?reversible?instabilities depends significantly on the ratio of the mechanical load to the electric load, thereby providing a control mechanism for state switching.
CRIS-Team WoS Importer:2021-05-28

Coupled modeling and simulation of electro-elastic materials at large strains - Possart, Gunnar; Steinmann, Paul; Vu, Duc Khoi; et al. (Conference of the SPIE Symposium on Smart Structures and Materials 2006, 2006)
Keywords: continuum mechanics; electro-elastic materials; constitutive modeling; finite elements

COUPLED THERMALLY GENERAL IMPERFECT AND MECHANICALLY COHERENT ENERGETIC INTERFACES SUBJECT TO IN-PLANE DEGRADATION - Esmaeili, Ali; Steinmann, Paul; Javili, Ali (Journal of Mechanics of Materials and Structures, 2017)
To date, the effects of interface in-plane damage on the thermomechanical response of a thermally general imperfect (GI) and mechanically coherent energetic interface are not taken into account. A thermally GI interface allows for a discontinuity in temperature as well as in the normal heat flux across the interface. A mechanically coherent energetic interface permits a discontinuity in the normal traction but not in the displacement field across the interface. The temperature of a thermally GI interface is a degree of freedom and is computed using a material parameter known as the sensitivity. The current work is the continuation of the model developed by Esmaeili et al. (2016a) where a degrading highly conductive (HC) and mechanically coherent energetic interface is considered. An HC interface only allows for the jump in normal heat flux and not the jump in temperature across the interface. In this contribution, a thermodynamically consistent theory for thermally GI and mechanically coherent energetic interfaces subject to in-plane degradation is developed. A computational framework to model this class of interfaces using the finite element method is established. In particular, the influence of the interface in-plane degradation on the sensitivity is captured. To this end, the equations governing a fully nonlinear transient problem are given. They are solved using the finite element method. The results are illustrated through a series of three-dimensional numerical examples for various interfacial parameters. In particular, a comparison is made between the results of the intact and the degraded thermally GI interface formulation.

Coupled topology and shape optimization using an embedding domain discretization method - Stankiewicz, Gabriel; Dev, Chaitanya; Steinmann, Paul (Structural and Multidisciplinary Optimization, 2021)
Density-based topology optimization and node-based shape optimization are often used sequentially to generate production-ready designs. In this work, we address the challenge to couple density-based topology optimization and node-based shape optimization into a single optimization problem by using an embedding domain discretization technique. In our approach, a variable shape is explicitly represented by the boundary of an embedded body. Furthermore, the embedding domain in form of a structured mesh allows us to introduce a variable, pseudo-density field. In this way, we attempt to bring the advantages of both topology and shape optimization methods together and to provide an efficient way to design fine-tuned structures without predefined topological features.
CRIS-Team Scopus Importer:2021-08-27
Keywords: Coupled topology and shape optimization; Embedding domain discretization; Structural optimization

Coupling of 3D Boundary Elements with Curved Finite Shell Elements - Kuhn, Günther; Helldörfer, Bastian (GAMM 2006, 2006)
UnivIS-Import:2015-03-09:Pub.2006.tech.FT.FT-TM.coupli_5

Cutoff-Based Modeling of Coulomb Interactions for Atomistic-to-Continuum Multiscale Methods - Boddu, Vishal; Davydov, Denis; Eidel, Bernhard; Steinmann, Paul (Multiscale Science and Engineering, 2019)
Atomic interactions in a large class of functional materials, essentially—all dielectrics, polarizable solids and ionic solids, involve long-range Coulomb interactions. Yet atomistic-to-continuum multiscale methods, such as the quasicontinuum method, are currently applicable only in cases where the atomic interactions are short-ranged. This restriction on the nature of atomic-level interactions for multiscale methods excludes numerous materials that are central to various scientific and industrial applications. A number of studies have pointed out unphysical artifacts in molecular simulations upon using the direct cutoff-based truncated sum to evaluate Coulomb interactions in ionic solids. However, recently it is understood that the artifacts of the direct cutoff-based truncated sum can be significantly minimized if a suitable correction term is added. In this work we examine whether the Wolf summation method, one of the prominent cutoff-based methods, is suitable to carry out the accumulation of the Coulomb interactions within the context of atomistic-to-continuum multiscale methods. In this regard, we choose the quasicontinuum method from the existing collection of multiscale methods for demonstration. It is found that the Wolf summation method can be applied if the atomistic system has charge ordering; otherwise, the error in the accumulation of the Coulomb interactions could be large.<br

Degree of cure-dependent modelling for polymer curing processes at small-strain. Part I: Consistent reformulation - Mokarram, Hossain; Steinmann, Paul (Computational Mechanics, 2014)
A physically-based small strain curing model has been developed and discussed in our previous contribution (Hossain et al. in Comput Mech 43:769-779, 2009a) which was extended later for finite strain elasticity and viscoelasticity including shrinkage in Hossain et al. (Comput Mech 44(5):621-630, 2009b) and in Hossain et al. (Comput Mech 46(3):363-375, 2010), respectively. The previously proposed constitutive models for curing processes are based on the temporal evolution of the material parameters, namely the shear modulus and the relaxation time (in the case of viscoelasticity). In the current paper, a thermodynamically consistent small strain constitutive model is formulated that is directly based on the degree of cure, a key parameter in the curing (reaction) kinetics. The new formulation is also in line with the earlier proposed hypoelastic approach. The curing process of polymers is a complex phenomenon involving a series of chemical reactions which transform a viscoelastic fluid into a viscoelastic solid during which the temperature, the chemistry and the mechanics are coupled. Part I of this work will deal with an isothermal viscoelastic formulation including shrinkage effects whereas the following Part II will give emphasis on the thermomechanical coupled approach. Some representative numerical examples conclude the paper and show the capability of the newly proposed constitutive formulation to capture major phenomena observed during the curing processes of polymers. © 2013 Springer-Verlag Berlin Heidelberg.
UnivIS-Import:2015-03-09:Pub.2014.tech.FT.FT-TM.degree
Keywords: Cure-dependent model; Curing; Degree of cure; Stiffness increase; Viscoelasticity; Volume shrinkage

Dehydration-induced shrinkage of dentin as a potential cause of vertical root fractures - Winter, Werner; Karl, Matthias (Journal of the Mechanical Behavior of Biomedical Materials, 2012)
Vertical root fractures (VRF) of endodontically treated teeth constitute a severe clinical condition frequently requiring removal of the affected tooth. Numerous attempts have been made to find the cause for VRF without reaching definitive conclusions. As changes in moisture content have been reported to appear as a consequence of root canal therapy, it is the goal of this paper to evaluate associated volume changes as a possible cause for VRF.Considering disk shaped horizontal cross sections of endodontically treated teeth with a moisture content of dentin decreasing from the root surface towards the root canal, both relative circumferential and relative radial stresses resulting from volume changes of dentin were calculated.It could be shown that the presence of a root canal itself increases radial and circumferential stresses acting on root dentin by a factor of two. Reduction in moisture content of dentin at the wall of the root canal results in shrinkage of the tooth structure and tensile stress. On the outer surface of the root, compressive stresses occur. Thus, VRF would start at the canal wall and propagate to the root surface.The theory presented appears to be consistent with previous reports on stress development as a consequence of dehydration of dentin and finite element analysis on root fractures. It may be concluded that dehydration of dentin induces cracks at the walls of a root canal which subsequently grow as a result of cyclic loading or traumatic overload. © 2012 Elsevier Ltd.
UnivIS-Import:2015-03-09:Pub.2012.tech.FT.FT-TM.dehydr

Design and validation of a new fixture for the shear testing of cellular solids - Diel, Sergej; Huber, Otto; Steinmann, Paul; Winter, Werner (Archive of Applied Mechanics, 2013)
The design and validation of a new fixture for the shear testing of cellular solids are presented. The fixture is an extended version of a picture-frame shear fixture (EPF) and is suited for comparatively thick rectangular block specimens. The stress state in the specimen is analyzed using a detailed finite element model. The finite element model is based on a 3D CAD model and incorporates friction in the revolute joints. Using specimens with low stiffness, a nearly pure and uniform shear stress state is induced in the specimen. A correction factor for the shear stress is derived which takes into account the friction in the joints and the nonuniformity of the shear stress distribution in the gauge section. The shear response of the polymer foam Rohacell® 200 WF is determined in order to demonstrate the capabilities of the EPF. The strain state is analyzed by means of digital image correlation and is detected to be very pure and uniform on the specimen’s surface, as predicted by the numerical analysis. The shear modulus obtained with the EPF is in good agreement with the calculated shear modulus derived from tensile tests on the same material. In addition, there is only little scatter of the strength values over the tested specimens which further confirms the accuracy of the new fixture.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.design
Keywords: Shear test fixture Shear modulus Shear strength Cellular solids Digital image correlation FEM Archive of Applied Mechanics Archive of Applied Mechanics Look Inside Other actions Export citation Register for Journal Updates About This Journal Reprints and Permissions Add to Papers Share Shear test fixture Shear modulus Shear strength Cellular solids Digital image correlation FEM Archive of Applied Mechanics Archive of Applied Mechanics Look Inside Other actions Export citation Register for Journal Updates About This Journal Reprints and Permissions Add to Papers Shear test fixture; Shear modulus; Shear strength; Cellular solids; Digital image correlation; FEM

Designing tunable composites with general interfaces - Saeb, Saba; Steinmann, Paul; Javili, A. (International Journal of Solids and Structures, 2019)
In this manuscript, we employ interface enhanced computational homogenization to explore and detail on a number of unfamiliar characteristics that composites can exhibit at different length scales. Here, the interface between the constituents is general in the sense that both displacement and traction jumps across the interface are admissible. We carry out numerous computational investigations using the finite element method for a broad range of various material parameters. Our numerical results reveal that the effective response of a microstructure embedding general interfaces is intuitively unpredictable and highly complex. In particular, for certain ranges of material parameters the overall response shows insensitivity with respect to either microstructure size or stiffness-ratio between inclusion and matrix. This unique behavior is observed likewise for two- and three-dimensional unit-cells. Our findings provide a valuable guideline to design tunable composites utilizing interfaces.
CRIS-Team Scopus Importer:2019-05-02
Keywords: Composites; Computational modeling; Interface/interphase; Micro-mechanics; Size-effect; Smart materials

Design of a frequency-energy independent nonlinear oscillator - Jerschl, Martin; Willner, Kai (35th IMAC Conference and Exposition on Structural Dynamics, 2017, 2017)
A method for the design of a frequency-energy independent nonlinear oscillator, for example a jointed system, is presented. Usually, nonlinear dynamic systems are energy dependent. For a geometrically nonlinear system the eigenfrequency increases with rising energy in the system. For a friction damped system the opposite is the case. These two contrary behaviours of nonlinear system types are used to design a frequency-energy-independent system. The HILBERT-transform is used as a design tool in combination with the Multi-Harmonic-Balance-Method (MHBM). An approach for automated design is introduced.
Keywords: Friction; Hilbert transform; Nonlinear dynamics; Nonlinear normal modes (NNMs); Optimal system design

Determination of a Constitutive Friction Law Using an Elastic-Plastic Half-Space Model - Beyer, Florian; Willner, Kai (Proceedings in Applied Mathematics and Mechanics, 2015)
Friction influences metal forming processes both in economic and technical terms. A precise understanding of friction is inevitable as friction restricts the potential of the product design. Friction depends on the occurring contact loads which is especially true for sheet-bulk metal forming (SBMF) as the incorporated contact loads appear in a very broad range. Numerical simulations, which are verified experimentally, are carried out to analyse contact interactions which typically appear in SBMF. On the one hand the multi-scale character of rough surfaces requires a very fine resolution of the contact area, on the other hand a large contact area is necessary to be representative. A half-space model is chosen for the contact analysis, because it only depends on the two-dimensional surface boundary which consumes less computing capacity than the finite element method (FEM) with its three-dimensional volume approach for the same surface resolution and area. The outcome is a constitutive friction law (CFL) consisting of two equations. The law is implemented into the framework of FEM to see the impact in a typical SBMF-process which aims to form metal sheet into cups with integrated gearing teeth. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinhei

Determination of equivalent transversely isotropic material parameters for sheet-layered lamination stacks - Baloglu, Maximilian Volkan; Ziegler, Marco; Franke, Jörg; Willner, Kai (Mechanical Systems and Signal Processing, 2020)
This paper covers the accurate prediction of equivalent homogenized material parameters for sheet-layered lamination stacks, which are located in rotors and stators of electric motors. Modeling the structural and dynamic behavior of these parts is a challenging task due to the special layered design of these stacks, with a huge influence of the applied joining technology, here a full-surface bonding. For the derivation of equivalent transversely isotropic material parameters, three procedures, namely the rule of mixture, an analytical and numerical homogenization, are compared eventuating in only minor differences between them. The investigations show that rather the input parameters for these averaging methods, i.e. the individual material parameters of each layer, are crucial for an accurate modeling. Experimental tests are carried out on coated sheet laminations to determine the initially unknown bonding varnish thickness with two different measurement methods, the 3D laser scanning microscopy and instrumented indentation testing, resulting in almost equivalent and reasonable values. The capability of the ab initio deduced material parameters is demonstrated by comparing an experimental and numerical modal analysis of a sample lamination stack showing an almost perfect agreement. By this, it is also revealed that a varnish Young's modulus measured by nanoindentation is overestimated from a macroscopic point of view. Damping parameters of a bonded lamination stack are determined with the help of the experimental modal analysis showing a relatively low damped system.
CRIS-Team Scopus Importer:2020-05-12
Keywords: Homogenization; Lamination stack; Laser scanning microscopy; Material modeling; Modal analysis; Nanoindentation

Determination of material parameters for a sheet‐layered lamination stack - Baloglu, Maximilian Volkan; Willner, Kai (Proceedings in Applied Mathematics and Mechanics, 2017)
The numerical simulation of sheet‐layered lamination stacks is a challenging task in structural mechanics due to the layout of these components. Depending on the manufacturing process, these sheets are either linked together with the help of a bonding varnish or are just packed up and basically free to slip inside of the stack, which can result in a nonlinear deformation behavior. To avoid a full FE‐simulation incorporating every layer, homogenization can be applied to identify a surrogate material model to achieve the desired accuracy by gaining performance. In this paper, a transversely isotropic material model is analytically formulated for a lamination stack with isotropic sheets in contact, which is captured with the help of a linear penalty method. The resulting stress‐strain relation is compared to results obtained by a numerical homogenization.
Keywords: lamination stack; homogenization; material modelling; contact mechanics

Determination of Material Properties of Plates from Modal ESPI Measurements - Gaul, L.; Willner, Kai; Hurlebaus, S. (Proceedings of the International Modal Analysis Conference, 1999)
Fiber reinforced composites may have unknown non-isotropic properties due to the manufacturing process. Especially injection molded members tend to have orthotropic properties due to alignment of short fibers along streamlines. To obtain the stiffness parameters of such materials, a non-destructive testing method is developed. Electronic-Speckle-Pattern-Interferometry is used to determine the eigenfrequencies and eigenmodes of square sample plates and a simple analytical model of the free vibrating plate is used to identify dynamic stiffness parameters. The method is verified by testing plates with known orthotropy and by static bending tests.
UnivIS-Import:2015-04-16:Pub.1999.tech.FT.FT-TM.determ

Development of a Constitutive Friction Law based on the Frictional Interaction of Rough Surfaces - Beyer, Florian; Hauer, Franz; Willner, Kai (Tribology in Industry, 2015)
Friction has a considerable impact in metal forming. This is in particular true for sheet-bulk metal-forming (SBMF) in which local highly varying contact loads occur. A constitutive friction law suited to the needs of SBMF is necessary, if numerical investigations in SBMF are performed. The identification of the friction due to adhesion and ploughing is carried out with an elasto-plastic half-space model. The normal contact is verified for a broad range of normal loads. In addition, the model is used for the characterization of the occurring shear stress. Ploughing is determined by the work which is necessary to plastically deform the surface asperities of the new area that gets into contact during sliding. Furthermore, the surface patches of common half-space models are aligned orthogonally to the direction in which the surfaces approach when normal contact occurs. For a better reflection of the original surfaces, the element patches become inclined. This leads to a geometric share of lateral forces which also contribute to friction. Based on these effects, a friction law is derived which is able to predict the contact conditions especially for SBMF.
Keywords: half-space; elasto-plastic contact; simulation; constitutive friction law; sheet-bulk metal forming

Development of a contact and a material model of laminated stacks - Luchscheider, Vera; Willner, Kai; Maidorn, Mischa (Proceeding 3rd International Electric Drives Production Conferenz, 2013)
The paper presents measurements and simulations of the stiffness of lamination stacks, which is a relevant parameter for the construction of electric machines. Since the progressive stiffness behavior of a lamination stack is dominated by the contact between the single sheets, different contact models are presented, where the selection and combination of the contact models is based on experimental tests on simple stacks of typical sheet material. With the help of the contact models, a material model will be created using the method of multiscales. © 2013 IEEE.
UnivIS-Import:2015-04-16:Pub.2013.tech.FT.FT-TM.develo_5
Keywords: contact behavior; hysteresis; lamination stack

Development of a contact model for an electric motor lamination stack - Luchscheider, Vera; Willner, Kai (ECCOMAS 2012 – European Congress on Computational Methods in Applied Sciences and Engineering, e–Book Full Papers, 2012)
For electric motors light weight construction is becoming increasingly important, therefore the dynamical behavior of the lamination stack has to be known. The stacking of a lot of sheets has a relevant influence onto the behavior of the whole motor due to significant contact characteristics between the sheets. In this paper quasi-static tests are performed to identify this characteristic. At first a load representing the packaging process is applied onto the stack. Thereafter a cyclic load is superposed to show the forces during the motors life. With these quasi-static tests elastic and plastic effects and a hysteretic behavior are detected. These nonlinearities are referring to the sheet's roughness, the surface waviness and the existence of a coreplate varnish. In the modeling of the stiffness the roughness parameters are used. Based on the quasi-static model and with dynamic tests it is possible to identify the dynamic characteristic of the lamination stack.
UnivIS-Import:2015-04-16:Pub.2012.tech.FT.FT-TM.develo_8
Keywords: Contact mechanics; Lamination stack; Roughness

Development of a feature adapted measurement evaluation strategy - Loderer, Andreas; Hausotte, Tino; Steinmann, Paul; Merklein, Marion; Landkammer, Philipp; Hildenbrand, Philipp; Schneider, Thomas (MacroScale 2014 - Recent developments in traceable dimensional measurements, 2015)
This article describes a methodical approach for developing a feature adapted measurement evaluation strategy using the example of a multi-scale multi-sensor fringe projection system. In a first step calibrated standard features were selected and measured in the next step by different fringe projection sensors with varying measuring range and resolution. For selecting which sensor is most appropriate for which feature the standard deviation as well as the deviation between calibrated values and measured values were considered. Finally the results were summarized in a decision matrix, which helps to select a feature adapted measurement strategy.

Development of a friction law respecting plastic surface smoothing - Hauer, Franz; Willner, Kai (Key Engineering Materials, 2013)
Friction has a significant effect on the metal forming. This is in particular true for the emerging sheet-bulk metal forming process. Therefore an adequate friction law is necessary for the accurate Finite-Element modelling of the process. This friction law has to incorporate a smooth transition from the Coulomb friction law for low contact pressures to a Tresca friction law for high contact pressures. Furthermore the plastic smoothing of surface roughness has to be taken into account. A friction law fulfilling these requirements is developed based on the results of an elastic-plastic halfspace contact model. This model is verified and calibrated experimentally. Its ability to model the changes in the roughness parameters as well as the Abbott curves in normal contact is demonstrated. Copyright © 2013 Trans Tech Publications Ltd.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.develo
Keywords: Contact; Friction; Halfspace; Sheet-bulk metal forming; Simulation

Development of a model to describe the stiffness of an electric motor lamination stack - Luchscheider, Vera; Willner, Kai; Maidorn, Mischa (Proceedings, 2nd International Electric Drives Production Conference (EDPC 2012), 2012)
A light-weight design is becoming increasingly important for electric motors. As a consequence, adequate knowledge of the mechanical behavior of the lamination stack is of prime importance, since the lamination stack has a significant influence onto the behavior of the complete motor due to the significant contact characteristics between the single sheets. Quasi-static tests are performed to identify this stiffness behavior. A load representing the packaging process is first applied onto the stack. A cyclic load is then superposed to simulate the forces during the motor lifetime. With these quasi-static tests a progressive stiffness behavior with elastic and plastic effects is identified. This non-linearity can be attributed to the sheet's roughness and surface waviness. Based on the identified contact stiffness, an improved simulation of the quasi-static behavior of an electrical motor is possible. © 2012 IEEE.
UnivIS-Import:2015-04-16:Pub.2012.tech.FT.FT-TM.develo_3
Keywords: contact mechanics; lamination stack; roughness

DFT-FE – A massively parallel adaptive finite-element code for large-scale density functional theory calculations - Motamarri, Phani; Das, Sambit; Rudraraju, Shiva; Ghosh, Krishnendu; Davydov, Denis; Gavini, Vikram (Computer Physics Communications, 2019)
We present an accurate, efficient and massively parallel finite-element code, DFT-FE, for large-scale ab-initio calculations (reaching ∼100,000 electrons) using Kohn–Sham density functional theory (DFT). DFT-FE is based on a local real-space variational formulation of the Kohn–Sham DFT energy functional that is discretized using a higher-order adaptive spectral finite-element (FE) basis, and treats pseudopotential and all-electron calculations in the same framework, while accommodating non-periodic, semi-periodic and periodic boundary conditions. We discuss the main aspects of the code, which include, the various strategies of adaptive FE basis generation, and the different approaches employed in the numerical implementation of the solution of the discrete Kohn–Sham problem that are focused on significantly reducing the floating point operations, communication costs and latency. We demonstrate the accuracy of DFT-FE by comparing the energies, ionic forces and periodic cell stresses on a wide range of problems with popularly used DFT codes. Further, we demonstrate that DFT-FE significantly outperforms widely used plane-wave codes—both in CPU-times and wall-times, and on both non-periodic and periodic systems—at systems sizes beyond a few thousand electrons, with over 5−10 fold speedups in systems with more than 10,000 electrons. The benchmark studies also highlight the excellent parallel scalability of DFT-FE, with strong scaling demonstrated up to 192,000 MPI tasks. Program summary: Program Title: DFT-FE Program Files doi: http://dx.doi.org/10.17632/tgdmgvmfft.1 Licensing provisions: LGPL v3 Programming language: C/C++ External routines/libraries: p4est (http://www.p4est.org/), deal.II (https://www.dealii.org/), BLAS (http://www.netlib.org/blas/), LAPACK (http://www.netlib.org/lapack/), ELPA (https://elpa.mpcdf.mpg.de/), ScaLAPACK (http://www.netlib.org/scalapack/), Spglib (https://atztogo.github.io/spglib/), ALGLIB (http://www.alglib.net/), LIBXC (http://www.tddft.org/programs/libxc/), PETSc (https://www.mcs.anl.gov/petsc), SLEPc (http://slepc.upv.es). Nature of problem: Density functional theory calculations. Solution method: We employ a local real-space variational formulation of Kohn–Sham density functional theory that is applicable for both pseudopotential and all-electron calculations with arbitrary boundary conditions. Higher-order adaptive spectral finite-element basis is used to discretize the Kohn–Sham equations. Chebyshev polynomial filtered subspace iteration procedure (ChFSI) is employed to solve the nonlinear Kohn–Sham eigenvalue problem self-consistently. ChFSI in DFT-FE employs Cholesky factorization based orthonormalization, and spectrum splitting based Rayleigh–Ritz procedure in conjunction with mixed precision arithmetic. Configurational force approach is used to compute ionic forces and periodic cell stresses for geometry optimization. Restrictions: Exchange–correlation functionals are restricted to Local Density Approximation (LDA) and Generalized Gradient Approximation (GGA), with and without spin. The pseudopotentials available are optimized norm conserving Vanderbilt (ONCV) pseudopotentials and Troullier–Martins (TM) pseudopotentials. Calculations are non-relativistic. Unusual features: DFT-FE handles all-electron and pseudopotential calculations in the same framework, while accommodating periodic, non-periodic and semi-periodic boundary conditions. Additional comments: DFT-FE github https://github.com/dftfeDevelopers/dftfe
CRIS-Team Scopus Importer:2019-10-01
Keywords: Ab-initio molecular dynamics; All-electron; Electronic structure; Ionic forces; Mixed-precision arithmetic; Pseudopotential; Real-space; Spectral finite-elements

Discrete and Continuous Methods for Modelling and Simulation of Polymer Materials - Pfaller, Sebastian (2021)
The present thesis subsumes recent research activities of the "Capriccio" group, which has been established by the author at the Institute of Applied Mechanics of the Friedrich-Alexander-Universität Erlangen-Nürnberg in 2018. It focuses on multiscale modelling and simulation of polymers and is interested, among others, in particle-based material descriptions and molecular dynamics pseudo experiments, constitutive modelling of polymers, material characterization and model calibration, polymer nanocomposites and fracture of polymers. To this end, the group further advances the Capriccio method, which is a domain-decomposition multiscale technique specifically designed for amorphous materials and which has proven to be a suitable simulation tool to couple a continuum with a particle domain treated by molecular dynamics (MD). This approach subdivides the entire domain of interest into sub-domains of different resolution and thus confines the computationally expensive particle-based treatment to regions of specific interest: Typically, these are located in the vicinity of interfaces, crack tips, or other types of discontinuities. In contrast, the remaining regions are modelled as a continuum requiring significantly less computational effort. Such an approach, however, requires a careful consideration of the transition region between the different domains involved, but is a powerful tool for material modelling and simulation. With such a technique at hand, the system sizes which molecular dynamics is usually capable of can be significantly enlarged. Hence, representative volume elements of, e.g., heterogeneous materials like polymer nanocomposites, come within reach and form the basis for further upscaling techniques. The first part of this theses concentrates on an enhanced version of the Capriccio method in a purely elastic setting. The second part provides a profound data basis by MD pseudo experiments of a polymer model system at coarse-grained resolution. It turns out that the material behaviour is by far too complex to be captured by simple elastic descriptions and even available inelastic models are not able to adequately reproduce the MD simulation data. Hence, another part of this thesis focuses on the development of a viscoelastic-viscoplastic constitutive law which is able to appropriately model the material behaviour. With this novel constitutive description at hand, the Capriccio method is extended to inelasticity and yields promising results. Finally, the present thesis applies the multiscale framework introduced here to polymer nancomposites and detects material parameter profiles in the interphase between the filler particles and the bulk polymer. The approach presented here is rather unconventional and uses goal data obtained from coupled simulations using the Capriccio method. There, the interphase regions are described at particle resolution and base exclusively on the interactions between the particles. By means of an appropriate, purely continuum surrogate model, the material property profiles in the interphase are eventually detected. This procedure enables insights into regions which are not accessible by experiments and thus is a promising, novel methodology to identify the material behaviour informed by molecular dynamics simulations. Based on these findings, this thesis closes with an outlook to future research activities of the Capriccio group and embeds them into a larger scientific context. There, envisioned studies in the fields of multiscale treatment of nanocomposites and fracture, integration of modelling, simulation, and experiments as well as of advanced design of polymer materials are addresse
Keywords: continuum mechanics; domain decomposition coupling; molecular dynamics; multiscale simulation; particle-continuum coupling; polymer simulation

Discrete configurational mechanics for the computational study of atomistic fracture mechanics - Birang Oskouei, Seyedehelmira; Steinmann, Paul (Forces in Mechanics, 2021)
We formulate discrete configurational mechanics in an atomistic setting, discuss the corresponding computational details, and demonstrate its utility via computational analyses of atomistic fracture mechanics problems. To this end, we first propose a novel Configurational-Force-Criterion (CFC) to predict crack propagation into an atomic crystalline lattice. Thereby, specifically, the CFC relies on comparing discrete configurational forces with a corresponding Crack-Propagation-Threshold (CPT) in the quasi-static approximation of atomistic systems at zero Kelvin. Next, based on the CFC, we introduce a quasi-static computational atomistic crack propagation algorithm. Therein, whenever an atomic pair meets the CFC, we modify the lattice connectivity by deleting the corresponding interatomic bond, thus resulting in true irreversibility, i.e. dissipation upon crack extension. Finally, based on different choices for the magnitude of the CPT employed in the CFC, we demonstrate suitability and versatility of discrete configurational mechanics in analyzing atomistic fracture mechanics.<br
Keywords: Atomistic configurational mechanics; Fracture criterion; Crack propagation

Discrete data-adaptive approximation of hyperelastic energy functions - Wiesheier, Simon; Mergheim, Julia; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2023)
Phenomenological constitutive modeling is prone to uncertainty and results in loss of information as data coming from experiments are not used directly in calculations. Data-driven approaches are a promising alternative to constitutive modeling. We present a new data-adaptive approach to model hyperelastic rubber-like materials at finite strains. Our proposed modeling procedure combines the advantages of phenomenological hyperelasticity with the data-driven paradigm of directly including experimental data in calculations. We suggest formulating a finite-element-like approximation of the strain energy function as a sum of basis functions expanded over a set of invariants multiplied by unknown parameters. The parameters are determined by an optimization algorithm to match measured experimental data (full-field displacements and global reaction forces) in a least-squares sense. We verify our approach and show that computation times are similar compared to those of phenomenological models. By numerical examples, we demonstrate the ability of our approach to re-identify O(10) parameters.
CRIS-Team Scopus Importer:2023-09-15
Keywords: Data-adaptive modeling; Finite-element-method; Hyperelasticity; Parameter identification

Discussion of Fatigue Data for Austenitic Stainless Steels - Wilhelm, Paul; Steinmann, Paul; Rudolph, Jürgen (Proceedings of the ASME 2014 Pressure Vessels & Piping Conference, 2014)

Dissipation-consistent modelling and classification of extended plasticity formulations - Mcbride, A. T.; Reddy, B. D.; Steinmann, Paul (Journal of the Mechanics and Physics of Solids, 2018)
A unified classification framework for models of extended plasticity is presented. The models include well known micromorphic and strain-gradient plasticity formulations. A unified treatment is possible due to the representation of strain-gradient plasticity within an Eringen-type micromorphic framework. The classification is based on the form of the energetic and dissipative model structures and exploits the framework of dissipation-consistent modelling to elucidate the flow relation and yield condition. Models are identified as either serial or parallel. This designation is also applicable to familiar models of classical plasticity. Particular attention is paid to the rate-dependent problem arising from the choice of a smooth dissipation potential. The inability to locally determine the region of admissible stresses for the non-smooth (rate-independent) parallel models of plasticity is made clear.
CRIS-Team Scopus Importer:2022-08-05
Keywords: B elastic plastic material; B viscoplastic material; Extended plasticity

Distributed Coalgebraic Partition Refinement - Birkmann, Fabian; Deifel, Hans-Peter; Milius, Stefan (TOOLS AND ALGORITHMS FOR THE CONSTRUCTION AND ANALYSIS OF SYSTEMS, TACAS 2022, PT II, 2022)
CRIS-Team WoS Importer:2022-04-29

Drehen metallischer Verbundwerkstoffe - Zimmermann, Marco; Schindler, Stefan; Steinmann, Paul; Aurich, Jan C. (wt Werkstattstechnik - Online, 2014)
Werkstück und Werkzeug unterliegen während der Zerspanung einer thermischen Belastung. Diese bewirkt in Abhängigkeit zur Höhe der Belastung eine Abweichung zwischen nomineller und realer Schnitttiefe, wodurch die Fertigungsgenauigkeit negativ beeinflusst wird. In diesem Beitrag wird der Einfluss der Prozessparameter und der Verstärkungsphase metallischer Verbundwerkstoffe auf die thermischen Belastungen und die resultierenden Fertigungsgenauigkeiten analysiert.
UnivIS-Import:2015-03-09:Pub.2014.tech.FT.FT-TM.drehen

Dried Vegetables as Potential Clean-Label Phosphate Substitutes in Cooked Sausage Meat - Weigel, Ingrid; Nistler, Sarah; Pichner, Rohtraud; Budday, Silvia; Gensberger-Reigl, Sabrina (Foods, 2023)
While phosphates are key additives in sausage production, their use conflicts with consumer preferences for “natural” foods. In this study, we investigated the potential of using vegetables as “clean-label” phosphate substitutes and their effects on water holding capacity, consumer acceptance, color, softness, and tenderness. Six freeze-dried vegetables with a pH above 6.0 were added to sausage meat on a laboratory scale. Adding 1.6% freeze-dried Brussels sprouts or Red Kuri squash resulted in a similar weight gain (7.0%) as the positive control of 0.6% commercial phosphate additive. Higher vegetable concentrations (2.2–4.0%) caused a significant increase in weight (p ≤ 0.05, 10.4–18.4% weight gain). Similar stress was needed to compress sausages containing 1.6/4.0% Brussels sprouts (14.2/11.2 kPa) and the positive control (13.2 kPa). Indentation tests also led to similar softness results for the sausages prepared with 1.6/4.0% Brussels sprouts (15.5 kPa/16.6 kPa) and the positive control (16.5 kPa). A force of 1.25 N was needed to shear the positive control, while 1.60 N/1.30 N was needed for the samples (1.6/4% Brussels sprouts). In summary, the present study indicates that freeze-dried vegetables have the potential to effectively replace phosphate in meat products.
CRIS-Team Scopus Importer:2023-06-09
Keywords: clean-label; freeze-dried vegetables; meat products; phosphate; phosphate substitutes; sausages

Dynamic performance of dielectric elastomers utilized as acoustic actuators - Hochradel, Klaus; Rupitsch, Stefan; Sutor, Alexander; Lerch, Reinhard; Vu, Duc Khoi; Steinmann, Paul (Applied Physics A-Materials Science & Processing, 2012)
We report on the frequency dependent behavior of dielectric elastomer actuators (DEA). The introduced smart material actuators consist of 3M™'s elastomer VHB™4905 (9469) and a compliant, sputtered copper electrode on each side. The presented experiments on these compounds contain the active tuning of their resonance frequency and their application as acoustic actuators.We are able to decrease the membranes' eigenfrequency by 30% with an electrical offset potential. Alternatively, if an alternating signal is applied, sound pressure levels up to 130 dB in an enclosed volume of 28 ccm are achieved. In order to verify the results, a numerical simulation is introduced incorporating the two physical fields involved: electrical and mechanical. © 2012 Springer-Verlag.
UnivIS-Import:2015-04-14:Pub.2012.tech.FT.FT-TM.dynami

Editorial: Advances in Brain Mechanics - Budday, Silvia; Bayly, Philip V.; Holzapfel, Gerhard A. (Frontiers in Mechanical Engineering, 2021)
CRIS-Team WoS Importer:2022-01-14

Effect of model parameters on finite element analysis of micromotions in implant dentistry - Winter, Werner; Klein, Daniel; Karl, Matthias (The Journal of oral implantology, 2013)
Micromotion between dental implant and bony socket may occur in immediate-loading scenarios. Excessive micromotion surpassing an estimated threshold of approximately 150 μm may result in fibrous encapsulation instead of osseointegration of the implant. As finite element analysis (FEA) has been applied in this field, it was the aim of this study to evaluate the effect of implant-related variables and modeling parameters on simulating micromotion phenomena. Three-dimensional FEA models representing a dental implant within a bony socket were constructed and used for evaluating micromotion (global displacement) and stress transfer (von Mises equivalent stress) at the implant-bone interface when static loads were applied. A parametric study was conducted altering implant geometry (cylinder, screw), direction of loading (axial, horizontal), healing status (immediate implant, osseointegrated implant), and contact type between implant and bone (friction free, friction, rigid). Adding threads to a cylindrically shaped implant as well as changing the contact type between implant and bone from friction free to rigid led to a reduction of implant displacement. On the other hand, reducing the elastic modulus of bone for simulating an immediate implant caused a substantial increase in displacement of the implant. Altering the direction of loading from axial to horizontal caused a change in loading patterns from uniform loading surrounding the whole implant to localized loading in the cervical area. Implant-related and bone-related factors determine the degree of micromotion of a dental implant during the healing phase, which should be considered when choosing a loading protocol.
UnivIS-Import:2015-03-09:Pub.2012.tech.FT.FT-TM.effect
Keywords: Simulation; Implantologie

Effect of the cutting condition and the reinforcement of the MMC on the machining accuracy Drehen metallischer Verbundwerkstoffe: Einfluss von Prozessparametern und Verstärkungsphase auf die Fertigungsgenauigkeit - Zimmermann, M.; Schindler, Stefan; Steinmann, Paul; Aurich, J. C. (wt Werkstattstechnik - Online, 2014)
Workpiece and tool are subjected to thermal loads when turning. These loads that deform workpiece and tool cause a difference between the actual and the nominal depth of cut. The accuracy of machining is thus decreased. In this paper, the accuracy of machining is analyzed with regard to both the cutting condition (and hence the thermal loads) used for turning and the reinforcement of the metal matrix composite (MMC) in order to enhance the accuracy of machining in dry turning.
CRIS-Team Scopus Importer:2022-08-05

Effect of the cutting condition and the reinforcement phase on the thermal load of the workpiece when dry turning aluminum metal matrix composites - Aurich, Jan C.; Zimmermann, Marco; Schindler, Stefan; Steinmann, Paul (International Journal of Advanced Manufacturing Technology, 2015)
Aluminum metal matrix composites (Al-MMCs) are two-phase high-performance materials. The reinforcement of aluminum alloys enhances the properties of the composite material but leads to poor machinability. The required mechanical work for machining is mostly dissipated into heat. Considerable generated quantities of heat are therefore expected when machining Al-MMCs due to the poor machinability of these composite materials. The machine tool, the tool, and the workpiece are thus subjected to a thermal load, which decreases the accuracy of machining. The thermal load increases moreover when dry turning due to the missing heat convection through the cutting fluid. It is therefore necessary to investigate the effect of the reinforcement phase and the cutting condition used on the thermal load of the workpiece in dry turning. Therefore, composites with different reinforcement phases and the non-reinforced aluminum matrix were used as the workpiece materials. The reinforcement differs regarding the volume percent and the average size of the silicon carbide particulate reinforcements. The results revealed that the thermal load and the thermal expansion of the workpiece are significantly affected by the cutting condition used and the reinforcement phase. High cutting speeds and feeds and moderate depths of cut need to be used in order to decrease the thermal load of the workpiece. The Al-MMC workpieces are subjected to greater thermal loads than the workpieces of the non-reinforced alloy. However, better machining accuracies were achieved in dry turning the Al-MMCs.
UnivIS-Import:2015-07-08:Pub.2015.tech.FT.FT-TM.effect
Keywords: Aluminum metal matrix composite; Dry turning; Thermal load of the workpiece; Thermally induced deformation of the workpiece

Effects of Boiling Water Reactor Medium on the Fatigue Life of Austenitic Stainless Steels - Wilhelm, Paul; Steinmann, Paul; Rudolph, Jürgen (Journal of Pressure Vessel Technology-Transactions of the Asme, 2016)

Effects of Pressurized Water Reactor Medium on the Fatigue Life of Austenitic Stainless Steels - Wilhelm, Paul; Steinmann, Paul; Rudolph, Jürgen (Journal of Pressure Vessel Technology-Transactions of the Asme, 2015)

Effects of soft and hard magnetic particles on the mechanical performance of ultra-soft magnetorheological elastomers - Moreno Mateos, Miguel Angel; Lopez-Donaire, Maria Luisa; Mokarram, Hossain; Garcia-Gonzalez, Daniel (Smart Materials and Structures, 2022)
Magnetorheological elastomers (MREs) mechanically respond to external magnetic stimuli by changing their mechanical properties and/or changing their shape. Recent studies have shown the great potential of MREs when manufactured with an extremely soft matrix and soft-magnetic particles. Under the application of an external magnetic field, such MREs present significant mechanical stiffening, and when the magnetic field is off, they show a softer response, being these alternative states fully reversible. Although soft-magnetic particles are suitable for their high magnetic susceptibility, they require the magnetic actuation to remain constant in order to achieve the magneto-mechanical stiffening. Here, we present an alternative solution based on hard-magnetic MREs to provide stiffening responses that can be sustained along time without the need of keeping the external magnetic field on. To this end, we manufacture novel extremely soft hard-magnetic MREs (stiffness in the order of 1 kPa) and characterise them under magneto-mechanical shear and confined magnetic expansion deformation modes, providing a comparison framework with the soft-magnetic counterparts. The extremely soft nature of the matrix allows for easily activating the magneto-mechanical couplings under external magnetic actuation. In this regard, we provide a novel approach by setting the magnetic actuation below the fully magnetic saturating field. In addition, free deformation tests provide hints on the microstructural transmission of torques from the hard-magnetic particles to the viscoelastic matrix, resulting in macroscopic geometrical effects and intricate shape-morphing phenomena.
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Keywords: experimental characterisation; hard-magnetics MRE; magnetic properties; magneto-mechanics; magnetorheological elastomers (MREs); multifunctional materials

Efficient crack growth analyzes by combining fast methods for BEM - Weber, Wilhelm; Kolk, Karsten; Kuhn, Günther (Proceedings of the 77th Annual Meeting of the International Association of Applied Mathematics and Mechanics, 2006)
UnivIS-Import:2015-04-16:Pub.2006.tech.FT.FT-TM.effici

Efficient gradient enhancements for plasticity with ductile damage in the logarithmic strain space - Friedlein, Johannes; Mergheim, Julia; Steinmann, Paul (European Journal of Mechanics A-Solids, 2023)
We contrast different gradient-enhancements for plasticity-damage material models in the logarithmic strain space and compare them to reference models based on multiplicative plasticity. The models being compared include plasticity - gradient-damage, where the gradient-enhancement is applied on the local damage variable, and gradient-plasticity - damage with a gradient-enhanced plastic hardening variable. Thereby, gradient-plasticity proved to be able to simultaneously regularise plastic and ductile (plasticity-driven) damage localisation as confirmed by numerical localisation analyses. This appears to be especially advantageous for logarithmic strain space plasticity-damage, because of the observed plastic localisation even for the case of plasticity with hardening. Even though gradient-plasticity appears to be numerically more demanding, two numerical examples indicate a good robustness and mesh objectivity in the softening regime. Moreover, the internal length for plasticity is able to adjust the damage zone width, similarly to gradient-damage, however ensuring a priori that damage takes place exclusively inside the plastic zone.
CRIS-Team Scopus Importer:2023-03-17
Keywords: Ductile damage; Finite plasticity; Gradient-damage; Gradient-enhancement; Gradient-plasticity; Logarithmic strain space; Loss of ellipticity

Eigenpath analysis of rotating mechanical systems based on ALE formulation - Weidauer, Tim; Willner, Kai (PAMM, Volume 16, Issue 1, 2016)
When bodies rotate they are subjected to velocity-dependent gyroscopic and inertia effects, which alter the dynamic behaviour of the structure. Analysing its eigenpairs consisting of eigenvalues and eigenvectors, these parameter-dependent changes can be tracked as eigenpaths by means of a continuation algorithm as in [1]. For rotationally symmetric structures an ALE approach (ALE = Arbitrary LAGRANGIAN-EULERIAN) for the finite element method as described in [2] can be employed. It allows simulating rotational influences on the body without actually having to rotate the mesh of the structure itself. This still-standing mesh facilitates further steps like coupling of other, static components with the rotating body. The combination of ALE with eigenpath analysis including an example is described in the following. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
Keywords: eigenpath; continuation; rotation; ALE

Eight-chain and full-network models and their modified versions for rubber hyperelasticity : A comparative study - Mokarram, Hossain; Amin, A.F.M.S.; Nomani Kabir, Muhammad (Journal of the Mechanical Behavior of Materials, 2015)
The eight-chain model, also known as Arruda-Boyce model, is widely used to capture the rate-independent hyperelastic response of rubber-like materials. The parameters of this model are physically based and explained from micromechanics of chain molecules. Despite its excellent performance with only two material parameters to capture bench measurements in uniaxial and pure shear regime, the model is known to be significantly deficient in predicting the equibiaxial data. To ameliorate such drawback, over the years, several modified versions of this successful model have been proposed in the literature. The so-called full-network model is another micromechanically motivated chain model, which has also few modified versions in the literature. For this study, two modified versions of the full-network model have been selected. In this contribution, five modified versions of the Arruda-Boyce model and two modified versions of full-network model are critically compared with the classical eight-chain model for their adequacy in representing equibiaxial data. To do a comparison of all selected models in reproducing the well-known Treloar data, the analytical expressions for the three homogeneous deformation modes, that is, uniaxial tension, equibiaxial tension, and pure shear have been derived and the performances of the selected models are analysed. The comparative study demonstrates that modified Flory-Erman model, Gornet-Desmorat (GD) model, Meissner-Matějka model, and bootstrapped eight-chain model predict well the three deformation modes compare to the classical eight-chain model.
UnivIS-Import:2015-03-09:Pub.2015.tech.FT.FT-TM.eightc
Keywords: eight-chain model; full-network model; micromechanical model; phenomenological model; rubber-like material

Eilenberg's variety theorem without Boolean operations - Birkmann, Fabian; Milius, Stefan; Urbat, Henning (Information and Computation, 2022)
Eilenberg's variety theorem marked a milestone in the algebraic theory of regular languages by establishing a formal correspondence between properties of regular languages and properties of finite monoids recognizing them. Motivated by classes of languages accepted by quantum finite automata, we introduce basic varieties of regular languages, a weakening of Eilenberg's original concept that does not require closure under any boolean operations, and prove a variety theorem for them. To do so, we investigate the algebraic recognition of languages by lattice bimodules, generalizing Klíma and Polák's lattice algebras, and we utilize the duality between algebraic completely distributive lattices and posets.
CRIS-Team Scopus Importer:2022-05-20
Keywords: Eilenberg's theorem; Pseudovariety; Quantum finite automata; Variety of regular languages

Einbindung der neuen Regelwerksanforderungen in lokale Fatigue-Monitoring Lösungen - Wilhelm, Paul; Steinmann, Paul; Rudolph, Jürgen (MPA Workshop 2014: Ermüdungsverhalten, 2014)

Eine Geschichte des Versagens - der PIP Skandal - Schubert, Dirk W.; Kaschta, Joachim; Horch, Raymund E.; Walter, Bastian; Daenicke, Jonas; Wichert, Franziska (Würzburger Tage 2014, 2014)

Ein statistisches Modell für den Kontakt metallischer Körper - Willner, Kai (Friedrich-Alexander-Universität Erlangen-Nürnberg, 1995)
UnivIS-Import:2016-07-26:Pub.1995.tech.FT.FT-TM.einsta_6

Elastic-plastic behaviour of perforated aluminium under tension and compression - Öchsner, Andreas; Winter, Werner; Kuhn, Günther (Technische Mechanik, 2001)
UnivIS-Import:2015-03-09:Pub.2001.tech.FT.FT-TM.elasti

Elastic-plastic halfspace simulation - Hauer, Franz; Willner, Kai (PAMM 2011, 2011)
Due to the roughness of technical surfaces only the surface peaks are in   contact for moderate contact pressures. Thus, the real contact area is smaller than the apparent contact area. Contact forces can only occur in the real contact area. Consequently it is necessary to determine the deformation of surface  asperities in order to analyse the tribological properties of surfaces. The real  contact area is usually small in initial contact. This leads to large contact  pressures which in turn lead to the plastic deformation of surface roughness  peaks. Therefore an elastic-plastic model is necessary. The halfspace model  seems to be beneficial because there is only a system of equations on a surface mesh to be solved and not on a volume mesh like in the Finite-Element-Method. This leads to a much smaller system of equations which should allow  reasonable calculation times even for large contact surfaces.
UnivIS-Import:2015-07-08:Pub.2011.tech.FT.FT-TM.elasti_5

Elasto-plastic contact of fractal surfaces - Willner, Kai (Analysis and Simulation of Contact Problems, 2006)
The elasto-plastic normal contact of fractal surfaces is numerically investigated using a halfspace model. Artificial surface data are generated using the structure function, to study the influence of different surface parameters with respect to the load-area relationship and the load-gap relationship. The simulations show that for realistic surface parameters the deformation is always in the plastic range. © Springer 2006.
UnivIS-Import:2015-04-16:Pub.2006.tech.FT.FT-TM.elasto

Elasto-Plastic Contact of Rough Surfaces - Willner, Kai (Computational Methods in Contact Mechanics III, 1997)
If two rough surfaces are brought into contact, asperities will deform either elastically or plastically. While the mode of initial deformation will depend on geometrical and material properties at any single asperity, the deformation upon unloading and reloading will be in the elastic regime. As it is not feasible to model the behaviour of each single asperity in a structural mechanics application, global contact laws are needed. In the present paper such contact laws are derived for several deformation models.
UnivIS-Import:2015-04-16:Pub.1997.tech.FT.FT-TM.elasto

Elasto-Plastic Normal Contact of Three-Dimensional Fractal Surfaces Using Halfspace Theory - Willner, Kai (Journal of Tribology, 2004)
The elasto-plastic normal contact of fractal surfaces is investigated. To study the influence of several surface parameters like fractal dimension and resolution, the surfaces are numerically generated using a special form of the structure function which is motivated by measurements of real rough surfaces. The contact simulation uses an iterative elastic halfspace solution based on a variational principle. A simple modification allows also the approximative solution of elasto-plastic contact problems. The influence of different surface parameters is studied with respect to the load-area relationship and the load-gap relationship. The simulations show that for realistic surface parameters the deformation is always in the plastic range. © 2004 by ASME.
UnivIS-Import:2015-03-09:Pub.2004.tech.FT.FT-TM.elstop

Electro-mechanical actuation modulates fracture performance of soft dielectric elastomers - Moreno Mateos, Miguel Angel; Mehnert, Markus; Steinmann, Paul (International Journal of Engineering Science, 2024)
Soft dielectric elastomers respond to electric stimuli by undergoing large deformations and changes in their material properties. The actuation with deformable electrodes attached to the material originates Coulomb and dipole forces that convert the electric field into a mechanical response. Applications at large deformations can entail crack onset and propagation. Within this context, the response of a soft polymer to an applied electric field may serve to influence the fracture behavior of such materials, potentially enhancing it. Here we explore the fracture performance of an ultra-soft dielectric elastomer. To do so, we conduct tensile tests while applying electrical actuation on samples with pre-cuts. Additionally, we examine the elastomer filled with piezoelectric BaTiO3 particles to ameliorate the fracture performance beyond the limits observed in the unfilled material. In conjunction with the experiments, we employ a bespoke fracture phase-field model to analyze the stress triaxiality near the crack tip. The results indicate that the electric actuation induces beneficial crack tip blunting and stress de-concentration, enhancing the fracture toughness up to a 125 % and delaying crack propagation. Our work provides a route for applications of soft dielectric elastomers that require improved fracture properties or, more broadly, the modulation of fracture behavior.
CRIS-Team Scopus Importer:2024-01-12
Keywords: Configurational forces; Dielectric elastomers; Filled elastomers; Multifunctional materials; Phase-field modeling; Soft fracture

Energy Corrected Finite Elements for Elliptic PDEs and Linear Elasticity - Kumar, Paras (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2018)

Enhanced computational homogenization techniques for modelling size effects in polymer composites - Kumar, Paras; Steinmann, Paul; Mergheim, Julia (Computational Mechanics, 2021)
Several experimental investigations corroborate nanosized inclusions as being much more efficient reinforcements for strengthening polymers as compared to their microsized counterparts. The inadequacy of the standard first-order computational homogenization scheme, by virtue of lack of the requisite length scale to model such size effects, necessitates enhancements to the standard scheme. In this work, a thorough assessment of one such extension based on the idea of interface energetics is conducted. Systematic numerical experimentation and analysis demonstrate the limitation of the aforementioned approach in modeling mechanical behavior of composite materials where the filler material is much stiffer than the matrix. An alternative approach based on the idea of continuously graded interphases is introduced. Comprehensive evaluation of this technique by means of representative numerical examples reveals it to be the appropriate one for modeling nano-composite materials with different filler-matrix stiffness combinations.
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Keywords: Computational Homogenization; Interface; Interphase; Nano-Composite; Size Effect

Enhancement of a Constitutive Friction Law by Considering Plastic Smoothing of Rough Surfaces in Dependency on the Bulk Stresses - Beyer, Florian; Löffler, Maria; Willner, Kai; Engel, Ulf; Merklein, Marion (Tribology in Industry, 2016)
The aim of this work is the improvement of a constitutive friction law which has been identified for the specific demands of sheet-bulk metal-forming. The constitutive friction law determines the friction shear stress in dependency on the plastic smoothing of the surface roughness, which also affects the real contact area. An experimental setup is introduced to determine the change of the surface roughness, which is influenced by the tensile bulk stress in the workpiece. In order to model the experimental results, a well-established half-space model is presented and improved to consider strain hardening. The half-space model is used to determine the change of the contact area as a function of the tensile bulk stress. This interdependency is also reflected by the proposed constitutive friction law.
Keywords: friction; constitutive friction law; half-space model; elasto-plastic contact; strain hardening; bulk stresses; sheet-bulk metal forming

Entwicklung und Evaluierung einer Schubversuchsvorrichtung auf Basis einer Schubfeld-konstruktion für statische und zyklische Beanspruchungen - Diel, Sergej; Huber, Otto (5. Landshuter Leichtbau-Colloquium - Leichtbau und nachhaltige Mobilität, 2011)
Es wird eine neuartige Schubversuchsvorrichtung für  Werkstoffe mit geringen Steifigkeiten vorgestellt. Die  Vorrichtung basiert auf dem Prinzip einer Schubfeldkonstruktion und erzeugt bei kleinen Deformationen einen annähernd reinen und homogenen  Schubspannungszustand. Die Schubversuchsvorrichtung  kann für statische und zyklische Beanspruchungen   eingesetzt werden und erlaubt die Verwendung von vergleichsweise dicken Proben. Aus diesem Grund ist die  Vorrichtung insbesondere zur Prüfung von zellularen   Werkstoffen geeignet. Mit Hilfe von analytischen Berechnungen und FEM-Simulationen wird der Verzerrungs- und Spannungszustand in der Schubprobe   untersucht. Es werden erste Versuchsergebnisse am  Beispiel eines zellularen Verbundwerkstoffes gezeigt und  diskutiert.
UnivIS-Import:2015-04-16:Pub.2011.tech.FT.FT-TM.entwic_9

Environmental Influences on the Fatigue Assessment of Austenitic and Ferritic Steel Components Including Welds - Roth, Armin; Herbst, Matthias; Rudolph, Jürgen; Wilhelm, Paul; Schuler, Xaver; Herter, Karl-Heinz; Kammerer, Matthias; Weißenberg, Thomas (Proceedings of the ASME 2014 Pressure Vessels & Piping Conference, 2014)

Evaluating the impact of filler size and filler content on the stiffness, strength, and toughness of polymer nanocomposites using coarse-grained molecular dynamics - Weber, Felix; Steinmann, Paul; Pfaller, Sebastian; Ries, Maximilian; Dötschel, Vincent (Engineering Fracture Mechanics, 2024)
Their great versatility makes polymer nanocomposites an important class of engineering materials. In order to gain detailed insights into the nanoscale mechanisms underlying their macroscopic mechanical properties, molecular dynamics (MD) simulations are a valuable tool to complement experimental studies. In this work, we modify the analytical potential functions of an efficient bead–spring model representing a generic polymer nanocomposite to account for the breaking of covalent bonds. We perform uniaxial tensile simulations of double-notched specimens and validate the model using experimental trends for overall stiffness, strength, and toughness. First, we study the effects of sample size, notch geometry, strain rate, temperature, and molar mass for the pure thermoplastic matrix material. Second, we analyze the influence of filler size and filler content on the mechanical behavior of the polymer nanocomposite. With this study, we show that in both the development of new materials and the optimization of established materials, it is possible to gain important preliminary insights into the effects of pertinent material characteristics with a simple MD setup, which can then be further refined by increasing the complexity of the material description and the boundary condition
Keywords: Polymer nanocomposites; Modeling and simulation; Molecular dynamics; Mechanical properties; Fracture of polymers

Evaluation of the influence of varying electrode materials within the thermo-crimping process - Spreng, Simon; Gläßel, Tobias; Hoetzel, Stefan; Schäfer, Heiko; Wunder, David; Franke, Jörg (2015 5th International Conference on Electric Drives Production, EDPC 2015 - Proceedings, 2015)
In the field of electric drives manufacturing, the thermo-crimping process is one major technology to join insulated copper wires with belonging current carrying parts. However, due to its operating principle, this technology has to be associated with strong disadvantages e.g. the excessive tool attrition leading to an immoderate amount of maintenance operations. For this reason, this paper focuses on the investigation of varying crimping electrode materials, whereas the objectives product quality, tool attrition and process energy are analyzed.
CRIS-Team Scopus Importer:2023-03-07
Keywords: crimping tool; electric drives manufacturing; joining; thermo-crimping

Evaluation of the surface fatigue behavior of amorphous carbon coatings through cyclic nanoindentation - Weikert, Tim; Wartzack, Sandro; Baloglu, Maximilian Volkan; Willner, Kai; Gabel, Stefan; Merle, Benoit; Pineda, Fabiola; Walczak, Magdalena; Marian, Max; Rosenkranz, Andreas; Tremmel, Stephan (Surface & Coatings Technology, 2021)
Diamond-like carbon (DLC) coatings, frequently used to reduce wear and friction in machine components as well as on forming tools, are often subjected to cyclic loading. Doping of DLC coatings with metals or metal carbides as well as the usage of multilayer architectures represent promising approaches to enhance toughness, which is beneficial for the coatings’ behavior under cyclic loading. In this study, we utilized cyclic nanoindentation to characterize the tribologically induced surface fatigue behavior of single-layer tungsten-doped (a-C:H:W) and multilayer silicon oxide containing (a-C:H:Si:O/a-C:H)25 amorphous carbon coatings under cyclic loading. Columnar growth was observed for both coatings by focused ion beam microscopy and scanning electron microscopy, while the multilayer architecture of the (a-C:H:Si:O/a-C:H)25 coating was verified by the silicon content using glow-discharge optical emission spectroscopy. In cyclic nanoindentation of the (a-C:H:Si:O/a-C:H)25 multilayer coating, stepwise small changes in indentation depth were observed over several indentation cycles. The surface fatigue process of the single-layer a-C:H:W covered a smaller number of indentation cycles and was characterized by an early steep increase of the static displacement signal. Microscopical analyses hint at grain deformation, sliding at columnar boundaries, and grain detachment as underlying fatigue mechanisms of the a-C:H:W coating, while the (a-C:H:Si:O/a-C:H)25 multilayer coating showed transgranular crack propagation and gradual fracturing. In case of the (a-C:H:Si:O/a-C:H)25 multilayer coating, superior indentation hardness (HIT) and indentation modulus (EIT) as well as a higher HIT3/EIT2 ratio suggest a higher resistance to plastic deformation. A high HIT3/EIT2 ratio, being an indicator for hindered crack initiation, combined with the capability of stress relaxation in soft layers contributed to the favorable surface fatigue behavior of the (a-C:H:Si:O/a-C:H)25 multilayer coating observed in this cyclic nanoindentation studies.
Keywords: Diamond-like carbon; Cyclic nanoindentation; Surface fatigue; Multilayer architecture

Evolution of cell cracks in PV-modules under field and laboratory conditions - Buerhop, Claudia; Wirsching, Sven; Bemm, Andreas; Pickel, Tobias; Hohmann, Philipp; Nieß, Monika; Vodermayer, Christian; Huber, Alexander; Glück, Bernhard; Mergheim, Julia; Camus, Christian; Hauch, Jens; et al. (Progress in Photovoltaics, 2017)
Damaged modules, especially with cell cracks, can be observed quite often in photovoltaicinstallations. Little knowledge exists about long‐term stability of precracked modules at real operating conditions. Previous investigations and existing standards focus on the degradation of new, defect‐free modules. This work highlights a twofold approach for life‐time study of precracked modules: (1) outdoor exposure of 54 precracked modules for 1 year and (2) artificial stressing of 20 representative precracked modules with a novel load test setup simulating snow and wind loads. The outdoor exposure reveals that at moderate weather conditions, no changes were detectable, neither in electric performance nor in EL‐images. However, the accelerated static load tests with stepwise increasing pressures point out that above a certain threshold, cracks grow. Below this threshold, formerly unseen cracks become visible at the loaded stage. In addition, modules with a smaller number of damaged cells have a stronger tendency to degrade further than modules with an already large number of cracked cells. Remarkably, the power output measured with a solar simulator after a stress test up to 2500 Pa (describing conservative proof conditions for severe snow loads according IEC 61215) remains unchanged for almost all modules.
Keywords: cracks; electroluminescence; field test; mechanically loading; performance; pre‐cracked modules

Experimental and numerical analysis of tribological effective surfaces for forming tools in Sheet-Bulk Metal Forming - Kersting, Petra; Gröbel, Daniel; Merklein, Marion; Peter, Sieczkarek; Wernicke, Sebastian; Tekkaya, A. Erman; Krebs, Eugen; Freiburg, Dennis; Biermann, Dirk; Weikert, Tim; Tremmel, Stephan; Stangier, Dominic; et al. (Production Engineering, 2016)
Sheet-Bulk Metal Forming (SBMF) allows the manufacture of complex parts with integrated functional form elements, such as teeth and thickened areas. Therefore, bulk forming operations are applied to sheets with initial thicknesses of 2 or 3 mm. The design and functionality of the tools are as important as the process itself. Therefore, the working group “Tools” of the Transregional Collaborative Research Centre on Sheet-Bulk Metal Forming (CRC/TR73) focuses on the optimization of the technical tool design. By varying topographies or applying tailored coatings, the friction behavior is changed to achieve a better form filling and to reduce process forces during the forming operations. In this paper, the potential of different tailored surfaces is validated by simulations and experimental studies. The tribological behavior of 14 surface microstructures is evaluated using a half-space model in order to select structures suitable for application. Those were characterized experimentally by ring-compression and pin-extrusion tests. The determined friction factors were used in a forming simulation to predict the form filling of small cavities in a flow forming operation. Furthermore, special attention is paid to the utilization of the anisotropic behavior of specific structures. The results were validated by an incremental gear forming process.
Keywords: Sheet-Bulk Metal Forming; Tailored surfaces; Milling technologies; Coating technologies; Forming simulations; Tribology simulation

Experimental and numerical investigation of the electro-mechanical response of particle filled elastomers - Part I: Experimental investigations - Mehnert, Markus; Faber, Jessica; Hossain, Mokarram; Chester, Shawn A.; Steinmann, Paul (European Journal of Mechanics A-Solids, 2022)
Electro-active polymers (EAPs) have the ability to undergo large deformations upon the stimulation by an electric field. They offer new design possibilities in a variety of applications, such as simple soft and flexible actuators, stretchable sensors, and energy harvesters. In the subclass of dielectric elastomers, the operation principle relies on the Coulomb forces between charged electrodes that deform the soft polymer. As the forces are dependent on the permittivity of the dielectric, the addition of filler particles with a high permittivity is a promising approach to increase the overall electro-mechanical coupling. This contribution presents the results of various mechanical and electro-mechanical experiments conducted with the silicone Elastosil P 7670TM filled with Barium-Titanate particles. These experiments are performed in such a fashion that the obtained results are well suited for the identification of the necessary material parameters of an electro-viscoelastic modeling approach in Part II of this contribution (Mehnert et al. Submitted).
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Keywords: Dielectric elastomers; Electro-active polymers; Electro-mechanics; Particle filled polymers

Experimental and numerical investigation of the photo-mechanical response of azobenzene filled soft elastomers, Part I: Experimental investigations - Mehnert, Markus; Moreno Mateos, Miguel Angel; Griwatz, Jan H.; Müsse, Silke; Wegner, Hermann A.; Steinmann, Paul (Extreme Mechanics Letters, 2024)
Photosensitive elastomers have the ability to undergo significant deformations upon the illumination by light of a specific wave length. Compared to other non-mechanical stimuli used in materials such as electro- or magneto-active polymers, light offers interesting advantages such as ultra high application speed and spatial precision. Moreover, as light powers and controls the movement of the material, the need for stiff wiring or external energy sources is eliminated. This becomes especially important in the design of miniature sized applications such as nano-scale robots. In the scope of the present work the conversion of photonic energy into a mechanical response originates from switching molecules embedded into a soft polymer matrix. Upon stimulation by UV-light, these molecules can switch from their stable trans - into a meta-stable cis-isomer, which induces a mechanical response on the macro scale. Depending on the experiment this can be visible as a deformation of the material or an increase in stiffness. This contribution presents the results of various mechanical and photo-mechanical experiments performed with the silicone Elastosil P 7670™ mixed with azobenzene molecules. These experiments are conducted in such a fashion that the obtained results are well suited for the identification of material parameters that arise from a photo-viscoelastic continuum modeling approach.<br
Keywords: Photo-sensitive materials; Soft elastomers; Photo-mechanics

Experimental and numerical investigations of the electro-mechanical response of particle filled elastomers—Part II: Continuum modeling approach - Mehnert, Markus; Faber, Jessica; Hossain, Mokarram; Chester, Shawn A.; Steinmann, Paul (European Journal of Mechanics A-Solids, 2022)
A comprehensive experimental study performed under a combination of electro-mechanical loads on a particle-filled silicone as a representative of dielectric elastomers is presented in the Part I of this work (Mehnert et al., submitted, 2021). The constitutive modeling and numerical simulation of electro-active polymers are essential fields of research in order to increase the acceptance of this group of soft smart materials in real-life applications. However, only few contributions containing constitutive modeling approaches are combined with experimental data obtained from electro-mechanically coupled loading conditions due to the complexity of corresponding experiments. In this contribution, we aim to develop an electro-mechanically coupled model, which closely replicates the response of a silicone polymer filled with a high dielectric permittivity filler of varying fractions that are characterized under a combination of electric and mechanical loads. Once the model is calibrated with the experimental data described in Part I of this contribution, it is used for a simple illustrative application example showcasing the capability of the model and the influence of the different material characteristics.
CRIS-Team Scopus Importer:2022-07-01
Keywords: Dielectric elastomers; Electro-active polymers; Electro-mechanics; Particle filled polymers

Experimental and numerical investigations of the electro-viscoelastic behavior of VHB 4905TM - Mehnert, Markus; Mokarram, Hossain; Steinmann, Paul (European Journal of Mechanics A-Solids, 2019)
Dielectric elastomers are a class of electro-active polymers (EAPs) that can be used for the development of simple soft actuators, sensors and energy harvesters. Their operation principle is based on the interaction of quasi-static electric charges in combination with soft dielectrics and deformable electrodes. Due to their ability to undergo large deformations with a time dependent material response of the underlying polymer, the mechanical behaviors of EAPs can be described by a finite strain viscoelastic material model [1]. This model is here augmented in order to account for the influence of the electro-mechanical coupling. In this contribution we pursue a comprehensive electro-mechanical characterization of the popular dielectric polymer VHB 4905™. In contrast to the results of the electro-mechanical experiments published previously [2] all of these experiments are conducted without the application of a pre-stretch and are therefore well suited for the identification of the coupling parameters of the material model. The presented model shows excellent agreements with experimental findings.
CRIS-Team Scopus Importer:2019-06-18

Experimental and Simulative Investigations of Tribology in Sheet-Bulk Metal Forming - Beyer, Florian; Blum, Heribert; Kumor, Dustin; Rademacher, Andreas; Willner, Kai; Schneider, Thomas (Key Engineering Materials, 2015)
Friction has a considerable influence in metal forming both in economic and technical terms. This is especially true for sheet-bulk metal forming (SBMF). The contact pressure that occurs here can be low making Coulomb’s friction law advisable, but also very high so that Tresca’s friction law is preferable. By means of an elasto-plastic half-space model rough surfaces have been investigated, which are deformed in such contact states. The elasto-plastic half-space model has been verified and calibrated experimentally. The result is the  development of a constitutive friction law, which can reproduce the frictional interactions for both low and high contact pressures. In addition, the law gives conclusion regarding plastic smoothening of rough surfaces. The law is implemented in the framework of the finite element method (FEM). However, compared to usual friction relations the tribological interplay presented here comes with the disadvantage of rising numerical effort. In order to minimise this drawback, a model adaptive finite element simulation is performed additionally. In this approach, contact regions are identified, where a conventional friction law is applicable, where the newly developed constitutive friction law should be used, or where frictional effects are negligible. The corresponding goal-oriented indicators are derived based on the “dual-weighted-residual” (DWR) method taking into account both the model and the discretisation error. This leads to an efficient simulation that applies the necessary friction law in dependence of contact complexity.
Keywords: Friction; simulation; model adaptivity

Experimental Investigations on Environmentally Assisted Fatigue of Ferritic and Austenitic Materials Including Dissimilar Metal Welds - Schuler, Xaver; Herter, Karl-Heinz; Kammerer, Matthias; Rudolph, Jürgen; Wilhelm, Paul (Manuscripts of the 41th MPA Seminar, 2015)

Experimental setup for normal contact stiffness measurement of technical surfaces with geometrical irregularities - Görke, Daniel; Willner, Kai (Experimental Techniques, 2009)
A normal contact test setup that is capable of measuring the elastoplastic deformation of a joint during loading and the elastic spring-back during unloading has been presented. The deformation is measured by two extensometers, which are clamped at the bottom and at the top specimen. The normal contact behavior of surfaces, which are made of different materials, sizes, and roughness parameters, is tested. The application of two extensometers is necessary to measure the bending, which can occur during the experiments. Finite element models with geometrical irregularities are applied to examine more closely the larger elastic spring-back of unloaded stainless steel surfaces. The determined pressure-approach relationships can, be used for simulations of bolted joints. Geometrical irregularities cause a large scattering of the elastic joint deflection if the contact surface has a small area or is made of a material with a high Young's modulus.
UnivIS-Import:2015-03-09:Pub.2009.tech.FT.FT-TM.experi_5

Experimental study and numerical modelling of VHB 4910 polymer - Mokarram, Hossain; Steinmann, Paul; Vu, Duc Khoi (Computational Materials Science, 2012)
VHB 4910 is an important polymeric material that has potential use as electro-active polymer in producing actuators. Such polymer, a member of the acrylic polymer group, is a very soft viscoelastic material. In this contribution, a comprehensive mechanical characterization of this important viscoelastic material has been carried out using different standard experiments such as single-step relaxation tests, multi-step relaxation tests and loading-unloading cyclic tests. In modelling the mechanical behaviour, a modified version of the micro-mechanically motivated Bergström-Boyce viscoelastic model has been used along with a finite linear evolution law. The model validation shows its excellent capability to predict the experimental results. © 2012 Elsevier B.V. All rights reserved.
UnivIS-Import:2015-04-14:Pub.2012.tech.FT.FT-TM.experi
Keywords: Micro-mechanical model; VHB 4910; Viscoelasticity

Experimental verification of a benchmark forming simulation - Landkammer, Philipp; Loderer, Andreas; Krebs, Eugen; Söhngen, Benjamin; Steinmann, Paul; Hausotte, Tino; Kersting, Petra; Willner, Kai; Biermann, Dirk (Key Engineering Materials, 2015)
Forming of near-net-shaped and load-adapted functional components, as it is developed in the Transregional Collaborative Research Centre on Sheet-Bulk Metal Forming SFB/TR 73, causes different problems, which lead to non-optimal manufacturing results. For these high complex processes the prediction of forming effects can only be realized by simulations. A stamping process of pressing eight punches into a circular blank is chosen for the considered investigations. This reference process is designed to reflect the main aspects, which strongly affect the final outcome of forming processes. These are the orthotropic material behaviour, the optimal design of the initial blank and the influences of different contact and friction laws. The aim of this work is to verify the results of finite element computations for the proposed forming process by experiments. Evaluation methods are presented to detect the influence of the anisotropy and also to quantify the optimal blank design, which is determined by inverse form finding. The manufacturing accuracy of the die plate and the corresponding roughness data of the milled surface are analysed, whereas metrological investigations are required. This is accomplished by the help of advanced measurement techniques like a multi-sensor fringe projection system and a white light interferometer. Regarding the geometry of the punches, micromilling of the die plate is also a real challenge, especially due to the hardness of the high-speed steel ASP 2023 (approx. 63 HRC). The surface roughness of the workpiece before and after the forming process is evaluated to gain auxiliary data for enhancing the friction modelling and to characterise the contact behaviou
UnivIS-Import:2015-03-09:Pub.2015.tech.FT.lfmt.experi
Keywords: Evaluation; Metal Forming; Simulation

Experimentelle und Angewandte Mechanik - Ein Querschnitt - Willner, Kai; Hanss, M. (Der Andere Verlag, 2006)
UnivIS-Import:2015-04-02:Pub.2006.tech.FT.FT-TM.experi

Experimentelle und numerische Untersuchung des Einflusses variabler Betriebstemperaturen auf das Trag- und Versagensverhalten struktureller Klebverbindungen unter Crashbelastung - Schmelzle, Lars; Mergheim, Julia; Possart, Gunnar; Steinmann, Paul; Striewe, Marius; Meschut, Gerson (22. Kolloquium: Gemeinsame Forschung in der Klebtechnik, 2022)

Experimentelle und simulative Untersuchung der zeit- und ortsaufgelösten Temperaturfelder beim selektiven Strahlschmelzen von Kunststoffen - Greiner, Sandra; Soldner, Dominic; Jaksch, Andreas; Zhao, Meng; Mergheim, Julia; Steinmann, Paul; Wudy, Katrin; Drummer, Dietmar (6. Industriekolloquium des Sonderforschungsbereichs 814, 2018)

Experimentelle Verifizierung eines Benchmark-Umformprozesses - Landkammer, Philipp; Söhngen, Benjamin; Loderer, Andreas; Krebs, Eugen; Steinmann, Paul; Willner, Kai; Hausotte, Tino; Wiederkehr (geb. Kersting), Petra; Biermann, Dirk (Tagungsband zum 18. Workshop Simulation in der Umformtechnik & 3. Industriekolloquium Blechmassivumformung 2015 - DFG Transregio 73, 2015)
UnivIS-Import:2015-04-17:Pub.2015.tech.FT.lfmt.experi_8

Exploring the interplay between cellular development and mechanics in the developing human brain - Zarzor, Mohammad Saeed; Käßmair, Stefan; Steinmann, Paul; Blümcke, Ingmar; Budday, Silvia (Proceedings in Applied Mathematics and Mechanics, 2021)
The human brain has a complex structure on both cellular and organ scales. This structure is closely related to the brain's abilities and functions. Disruption of one of the biological processes occurring during brain development on the cellular scale may affect the cortical folding pattern of the brain on the organ scale. However, the link between disruptions in cellular brain development and associated cortical malformation remains largely unknown. From a mechanical perspective, the forces generated during development lead to mechanical instability and, eventually, the mergence of cortical folds. To fully understand mechanism underlying malformations of cortical development, it is key to consider both the events that occur on the cellular scale and the mechanical forces generated on the organ scale. Here we present a computational model describing cellular division and migration on the cellular scale, as well as growth and cortical folding on the tissue or organ scale, in a continuous way by a coupled finite growth and advection-diffusion model. We introduce the cell density as an independent field controlling the volumetric growth. Furthermore, we formulate a positive relation between cell density and cortical layer stiffness. This allows us to study the influence of the migration velocity, the cell diffusivity, the local stiffness, and the local connectivity of cells on the cortical folding process and mechanical properties during normal and abnormal brain development numerically. We show how an increase in the density of the neurons increases the layer's mechanical stiffness. Moreover, weWe validate our simulation results through the comparison with histological sections of the fetal human brain. The current model aims to be a first step towards providing a reliable platform to systematically evaluate the role of different cellular events on the cortical folding process and vice vers

Exploring the role of the outer subventricular zone during cortical folding through a physics-based model - Zarzor, Mohammad Saeed; Blümcke, Ingmar; Budday, Silvia (eLife, 2023)
The human brain has a highly complex structure both on the microscopic and on the macroscopic scales. Increasing evidence has suggested the role of mechanical forces for cortical folding - a classical hallmark of the human brain. However, the link between cellular processes at the microscale and mechanical forces at the macroscale remains insufficiently understood. Recent findings suggest that an additional proliferating zone, the outer subventricular zone (OSVZ), is decisive for the particular size and complexity of the human cortex. To better understand how the OSVZ affects cortical folding, we establish a multifield computational model that couples cell proliferation in different zones and migration at the cell scale with growth and cortical folding at the organ scale by combining an advection-diffusion model with the theory of finite growth. We validate our model based on data from histologically stained sections of the human fetal brain and predict 3D pattern formation. Finally, we address open questions regarding the role of the OSVZ for the formation of cortical folds. The presented framework not only improves our understanding of human brain development, but could eventually help diagnose and treat neuronal disorders arising from disruptions in cellular development and associated malformations of cortical development.
CRIS-Team Scopus Importer:2023-04-28
Keywords: finite element simulations; human; human brain development; multifield modeling; neuroscience; outer radial glial cells; outer subventricular zone; physics of living systems

Extended general interfaces: Mori–Tanaka homogenization and average fields - Firooz, Soheil; Chatzigeorgiou, George; Steinmann, Paul; Javili, Ali (International Journal of Solids and Structures, 2022)
A well-established methodology to capture interphases in heterogeneous materials is to replace them by a zero-thickness interface model. Commonly accepted interface models intuitively assume that to satisfy the angular momentum balance, interfaces must coincide with the mid-layer of their corresponding interphases. Recently, via adopting weighted averages, an extended general interface model has been developed that allows for arbitrary interface positions while fulfilling the angular momentum balance. This manuscript incorporates this novel interface model into the Mori–Tanaka method within the framework of homogenization. Analytical solutions are developed to determine effective properties as well as average local fields for fiber-reinforced and particle-reinforced composites. Computational simulations using the finite element method (FEM) are carried out to compare with the analytical solutions. Through a set of numerical examples, the significance of the interface position on the overall response of heterogeneous materials is highlighted. Our extended framework clarifies various ambiguous observations originating from the trivial assumption of restricting the interface position to the mid-plane. One advantage of the current interface model is that it covers both the elastic and cohesive interface models at its limits and therefore the analytical solutions are widely applicable regardless of the interface type.
CRIS-Team Scopus Importer:2022-09-09
Keywords: Composites; Extended general interface; Mori–Tanaka homogenization; Size effects

Extending a generic and fast coarse-grained molecular dynamics model to examine the mechanical behavior of grafted polymer nanocomposites - Ries, Maximilian; Reber, Sebastian; Steinmann, Paul; Pfaller, Sebastian (Forces in Mechanics, 2023)
Polymer nanocomposites are an important class of materials for engineering applications due to their high versatility and good mechanical properties combined with low density. By directly attaching the polymer chains to the nanofillers, the so-called grafting, a better load transfer between matrix and filler is achieved, and, in addition, a better dispersion of the fillers is obtained. Both result in enhanced mechanical properties. Since experimental investigations on the nanoscale are extremely challenging, complementary numerical studies are needed to unravel the mechanical behavior of polymer nanocomposites. To this end, molecular dynamics is ideally suited since it captures the microstructure, but is also numerically expensive. Therefore, this contribution presents a fast coarse-grained molecular dynamics model for the investigation of the mechanical behavior of grafted polymer nanocomposites. For this purpose, we extend an existing model by grafting bonds, which allows us to compare the effect of untreated and grafted fillers directly. In particular, we investigate the influence of filler content, grafting degree, and filler size on the stiffness and strength of the polymer (grafted) nanocomposites. We conclude that the grafting bonds have little effect on the stiffness, while the strength is significantly improved compared to the untreated fillers, which is in agreement with the literature. The presented molecular dynamics model for polymer grafted nanocomposites provides the basis for further investigations, particularly of the crucial matrix-filler interphase. In addition, this contribution translates molecular dynamics insights into mechanical properties, which bridges the gap to the engineering scale and thus represents a step towards exploiting the full potential of polymer (grafted) nanocomposites.
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Keywords: Coarse graining; Grafted polymer nanocomposites; Mechanical properties; Modeling and simulation; Molecular dynamics; Polymer nanocomposites

Extension of the Arruda-Boyce model to the modelling of the curing process of polymers - Mokarram, Hossain; Steinmann, Paul (Proceedings of Applied Mathematics and Mechanics (PAMM), 2011)
A phenomenologically motivated finite strain general frame work to simulate the curing of polymer have been developed and discussed in our recently published papers [2, 4]. The Arruda-Boyce model is a classical hyperelastic model for polymeric materials. This contribution presents an extension of the Arruda-Boyce model towards modelling the curing process of polymers following our previous framework. In this paper, we will show how to model the elastic behaviour and shrinkage effects of the polymer curing process in the isothermal case using the Arruda-Boyce model. Several numerical examples have been demonstrated to verify our newly  proposed modified approach in case of curing process.
UnivIS-Import:2015-04-16:Pub.2011.tech.FT.FT-TM.extens_5

Extensive CGMD simulations of atactic PS providing pseudo experimental data to calibrate nonlinear inelastic continuum mechanical constitutive laws - Ries, Maximilian; Possart, Gunnar; Steinmann, Paul; Pfaller, Sebastian (Polymers, 2019)
In this contribution, we present a characterization methodology to obtain pseudo experimental deformation data from CG MD simulations of polymers as an inevitable prerequisite to choose and calibrate continuum mechanical constitutive laws. Without restriction of generality, we employ a well established CG model of atactic polystyrene as exemplary model system and simulate its mechanical behavior under various uniaxial tension and compression load cases. To demonstrate the applicability of the obtained data, we exemplarily calibrate a viscoelastic continuum mechanical constitutive law. We conclude our contribution by a thorough discussion of the findings obtained in the numerical pseudo experiments and give an outline of subsequent research activities. Thus, this work contributes to the field of multiscale simulation methods and adds a specific application to the body of knowledge of CG MD simulations.
CRIS-Team Scopus Importer:2019-12-03
Keywords: Material characterization; Mechanical properties of polymers; Molecular dynamics; Simulation of polymers

Failure of Silicone Breast Implants – New Insights by Mapping the Mechanical Properties of Implant Shells - Schubert, Dirk W.; Horch, Raymund E.; Kaschta, Joachim; Daenicke, Jonas; Walter, Bastian (13th Bayreuth Polymer Symposium, 2013)

Failure of Silicone Breast Implants – New Insights by Mapping the Mechanical Properties of Implant Shells - Schubert, Dirk W.; Kaschta, Joachim; Horch, Raymund E.; Walter, Bastian; Daenicke, Jonas (Book of Abstracts, 2013)

Failure of Silicone Breast Implants – Novel Insights by Mapping the Mechanical Properties of Implant Shells - Schubert, Dirk W.; Horch, Raymund E.; Kaschta, Joachim; Daenicke, Jonas; Walter, Bastian (Nordic Polymer Days, 2013)

Fast 3D crack growth analyses by the combination of fast BEM techniques - Weber, Wilhelm; Kolk, Karsten; Kuhn, Günther (Proceedings of the 17th International Conference on Computer Methods in Mechanics, 2007)
UnivIS-Import:2015-04-16:Pub.2007.tech.FT.FT-TM.fast3d

Fatigue Approach for Addressing Environmental Effects in Fatigue Usage Calculation - Wilhelm, Paul; Steinmann, Paul; Rudolph, Jürgen (Atw-International Journal For Nuclear Power, 2015)

Fatigue Strain-Life Behavior of Austenitic Stainless Steels in Pressurized Water Reactor Environments - Wilhelm, Paul; Steinmann, Paul; Rudolph, Jürgen (Proceedings of the ASME 2015 Pressure Vessels & Piping Conference, 2015)

FE2 simulations of magnetorheological elastomers: influence of microscopic boundary conditions, microstructures and free space on the macroscopic responses of MREs - Zabihyan, Reza; Mergheim, Julia; Pelteret, Jean-Paul; Brands, Benjamin; Steinmann, Paul (International Journal of Solids and Structures, 2020)
In the current work, the response of heterogeneous magnetorheological elastomers (MREs) which are loaded by external magnetic fields in the absence and also in the presence of free space is studied. A fully-coupled two-scale finite element computational homogenization procedure is used to derive the material response at the macro-scale from the averaged response of the underlying micro-scale problem. Different combinations of boundary conditions, that satisfy the Hill-Mandel condition and are based on the primary variables of the magneto-elastic enthalpy and energy functionals are applied to solve the micro-scale boundary value problem. Furthermore, the influences of various microstructures on the macroscopic response of the MREs are investigated. The results indicate that the choice of microscopic boundary conditions and microstructure types can significantly affect the macroscopic responses of MREs.
CRIS-Team Scopus Importer:2020-03-17
Keywords: Boundary conditions; FE; Homogenization; Magneto-elasticity; Magneto-mechanics; Magnetorheological elastomers (MREs)

Fertigungsgenauigkeit beim Drehen steigern - Einfluss der Prozessparameter auf die Maßhaltigkeit bei der Trockenbearbeitung - Aurich, Jan C.; Zimmermann, Marco; Steinmann, Paul; Schindler, Stefan (VDI-Z Integrierte Produktion, 2015)
Werkstück und Werkzeug erfahren während der spanenden Bearbeitung eine von der Belastungshöhe abhängige Wärmedehnung, welche die Maßhaltigkeit negativ beeinflusst. Um die Maßhaltigkeit zu verbessern, gilt es insbesondere bei der Trockenbearbeitung Prozessparameter zur Zerspanung einzusetzen, welche geringe Wärmeeinträge in das Werkstück und das Werkzeug verursachen. In diesem Beitrag werden Einflüsse der Prozessparameter auf die thermische Belastung und die Maßhaltigkeit des Werkstücks sowie eine simulationsgestützte Methode zur Prozessauslegung im Hinblick auf eine hohe Maßhaltigkeit vorgestellt.
UnivIS-Import:2015-07-08:Pub.2015.tech.FT.FT-TM.fertig

Fifty Shades of Brain: A Review on the Mechanical Testing and Modeling of Brain Tissue - Budday, Silvia; Ovaert, Timothy; Holzapfel, Gerhard A.; Steinmann, Paul; Kuhl, Ellen (Archives of Computational Methods in Engineering, 2020)
Brain tissue is not only one the most important but also the most complex and compliant tissue in the human body. While long underestimated, increasing evidence confirms that mechanics plays a critical role in modulating brain function and dysfunction. Computational simulations–based on the field equations of nonlinear continuum mechanics–can provide important insights into the underlying mechanisms of brain injury and disease that go beyond the possibilities of traditional diagnostic tools. Realistic numerical predictions, however, require mechanical models that are capable of capturing the complex and unique characteristics of this ultrasoft, heterogeneous, and active tissue. In recent years, contradictory experimental results have caused confusion and hindered rapid progress. In this review, we carefully assess the challenges associated with brain tissue testing and modeling, and work out the most important characteristics of brain tissue behavior on different length and time scales. Depending on the application of interest, we propose appropriate mechanical modeling approaches that are as complex as necessary but as simple as possible. This comprehensive review will, on the one hand, stimulate the design of new experiments and, on the other hand, guide the selection of appropriate constitutive models for specific applications. Mechanical models that capture the complex behavior of nervous tissues and are accurately calibrated with reliable and comprehensive experimental data are key to performing reliable predictive simulations. Ultimately, mathematical modeling and computational simulations of the brain are useful for both biomedical and clinical communities, and cover a wide range of applications ranging from predicting disease progression and estimating injury risk to planning surgical procedures.<br

Finite element formulations for 3d convex polyhedra in nonlinear continuum mechanics - Kraus, Markus; Steinmann, Paul (International Journal of Computational Methods in Engineering Science and Mechanics, 2012)
In this paper, we present finite element formulations for general three-dimensional convex polyhedra for use in a common finite element framework that are well suited, e.g., for modeling complex granular materials and for mesh refinements. Based on an universally applicable interpolant for any convex polyhedron, different interpolation schemes are investigated in the context of nonlinear elastostatics. The modeling benefits and the numerical performance regarding the mechanical response and the computational cost are analyzed by several examples.
UnivIS-Import:2015-03-09:Pub.2012.tech.FT.FT-TM.finite

Finite element modeling of residual stress and geometrical error formations in selective laser melting of metals - Bruna-Rosso, Claire; Mergheim, Julia; Previtali, Barbara (Proceedings of the Institution of Mechanical Engineers Part C-Journal of Mechanical Engineering Science, 2020)
Recent works, both numerical and experimental, on residual stress and geometrical errors in selective laser melting-produced parts highlighted the preponderance of these phenomena. However, their mechanisms of appearance are not yet fully explained. An in-house finite element model was developed and implemented to reproduce their formations. The consistence of the model with existing simulation results and with respect to experimental observations was checked. Simulations were then performed using a computational design of experiments to better comprehend the underlying phenomena and the influence of the laser speed and power. Relationships between process parameters and residual stress, plastic strain, and geometrical errors formations have been put into evidence which can support optimization procedures at design stage.
CRIS-Team Scopus Importer:2020-08-14
Keywords: finite element modeling; geometrical errors; residual stress; Selective laser melting; thermo-mechanical model

Finite element modeling of traumatic brain injury: Areas of future interest - Griffiths, Emma; Budday, Silvia (Current Opinion in Biomedical Engineering, 2022)
The use of the finite element (FE) method to simulate traumatic brain injury (TBI) has been an area under development and research for many years. The aim is to accurately reproduce and evaluate the resulting brain damage that would otherwise be inaccessible. Computational simulations can assist the diagnosis of injuries and early detection of long-term damage in order to advance preventative measures and implement early treatments. Here, we discuss a few new and emerging trends of FE models for TBI. We highlight advancements in two main areas: FE head models and brain tissue material models. We discuss how FE models can be improved to have greater anatomical and mechanical biofidelity, resulting in more accurate TBI simulations. Our aim is to stimulate future research activities in important areas that have so far been underexplored and can significantly accelerate the relevance of TBI FE models for clinical use in the future.
CRIS-Team Scopus Importer:2022-11-25
Keywords: Damage; Finite element method; Head models; Material modeling; Traumatic brain injury

Finite element model to calculate the thermal expansion of the tool and the workpiece in dry turning - Schindler, Stefan; Zimmermann, Marco; Aurich, Jan C.; Steinmann, Paul (Proceedia CIRP, 2014)
Dry cutting is an important issue with regard to the economy and ecology of machining. The absence of the cutting fluid reduces both the costs for machining and the risk of ecological hazards. However, the missing convection through the cutting fluid increases the temperatures of the workpiece and the tool, and thus their thermal expansions. As a result, remarkable deviations from the nominal workpiece geometry occur. To enhance the accuracy of machining when dry turning, the thermal expansions of the tool and the workpiece can be calculated prior to actual turning using finite element (FE) models in order to adapt the nominal depth of cut accordingly. Therefore, an experimentally validated (using aluminum as the workpiece material) FE model is presented. The FE model inputs the heat flux into the tool and the workpiece as boundary conditions. The heat flux is applied locally and temporally discretized to the workpiece and the tool in the chip formation area. Their thermal expansions can thus be calculated in terms of the cutting condition used and the tool position, whereby process planning regarding the machining accuracy is facilitated. © 2014 Published by Elsevier B.V.
UnivIS-Import:2015-04-16:Pub.2013.tech.FT.FT-TM.modeli
Keywords: Dry turning; Finite element; Thermal expansion

Finite Element Problems with Uncertain Parameters - Willner, Kai; Hanss, M. (Proceedings of the 6th Pan-American Congress of Applied Mechanics PACAM VI., 1999)
UnivIS-Import:2015-04-16:Pub.1999.tech.FT.FT-TM.finite_7

Finite element simulation of the magneto-mechanical response of a magnetic shape memory alloy sample - Wang, Jiong; Steinmann, Paul (Philosophical Magazine, 2013)
In this paper, the stress- and magnetic field-induced variant reorientation in a magnetic shape memory alloy (MSMA) sample is simulated by using the finite element method. This model is set up based on a three-dimensional setting with the whole sample and the surrounding space taken into account. A typical loading pattern is proposed on the sample. The unknowns of the model governing system include the spatial displacement vector, the scalar magnetic potential and some internal variables related to the effective magnetization vector. By considering the different properties of the unknowns, an iterative computational scheme is proposed to derive the numerical solutions. With the obtained solutions, the magneto-mechanical response of the MSMA sample under different field and stress levels can be predicted. The distributions of the variant state and the effective magnetization in the sample can also be determined. By comparing with the experimental results, it is found that the numerical solutions obtained in this model can predict the response of the MSMA sample at a quantitative level. © 2013 Copyright Taylor and Francis Group, LLC.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.finite
Keywords: finite element simulation; iterative computational scheme; magnetic shape memory alloy; magneto-mechanical response; numerical solution

Finite strain modelling for the curing process in magneto-viscoelasticity - Mokarram, Hossain; Saxena, Prashant; Steinmann, Paul (Proceedings on 22nd ACME Conference on Computational Mechanics, 2014)
UnivIS-Import:2015-04-16:Pub.2014.tech.FT.FT-TM.finite_9

Finite Strain Viscoelastic Models to Simulate the Curing Process of Polymers - Mokarram, Hossain; Possart, Gunnar; Steinmann, Paul (Proceedings of 1st International Conference on Material Modelling, 2009)
UnivIS-Import:2015-04-16:Pub.2009.tech.FT.FT-TM.finite_7

Flow relations and yield functions for dissipative strain-gradient plasticity - Carstensen, Carsten; Ebobisse, François; McBride, Andrew T.; Reddy, B. Daya; Steinmann, Paul (Advanced Structured Materials, 2017)
In this work we carry out a theoretical investigation of a dissipative model of rate-independent strain-gradient plasticity. The work builds on the investigation in [1], which in turn was inspired by the investigations in [4] of responses to nonproportional loading in the form of surface passivation. We recall the global nature of the flow relation when expressed in terms of the Cauchy stress and dissipation function. We highlight the difficulties encountered in attempts to obtain dual forms of the flow relation and associated yield functions, for the continuous and discrete problems, and derive upper bounds on the global yield function.
CRIS-Team Scopus Importer:2022-08-05

Folding drives cortical thickness variations - Holland, Maria A.; Budday, Silvia; Li, Gang; Shen, Dinggang; Goriely, Alain; Kuhl, Ellen (European Physical Journal - Special Topics, 2020)
The cortical thickness is a characteristic biomarker for a wide variety of neurological disorders. While the structural organization of the cerebral cortex is tightly regulated and evolutionarily preserved, its thickness varies widely between 1.5 and 4.5 mm across the healthy adult human brain. It remains unclear whether these thickness variations are a cause or consequence of cortical development. Recent studies suggest that cortical thickness variations are primarily a result of genetic effects. Previous studies showed that a simple homogeneous bilayered system with a growing layer on an elastic substrate undergoes a unique symmetry breaking into a spatially heterogeneous system with discrete gyri and sulci. Here, we expand on that work to explore the evolution of cortical thickness variations over time to support our finding that cortical pattern formation and thickness variations can be explained – at least in part – by the physical forces that emerge during cortical folding. Strikingly, as growth progresses, the developing gyri universally thicken and the sulci thin, even in the complete absence of regional information. Using magnetic resonance images, we demonstrate that these naturally emerging thickness variations agree with the cortical folding pattern in n = 9 healthy adult human brains, in n = 564 healthy human brains ages 7–64, and in n = 73 infant brains scanned at birth, and at ages one and two. Additionally, we show that cortical organoids develop similar patterns throughout their growth. Our results suggest that genetic, geometric, and physical events during brain development are closely interrelated. Understanding regional and temporal variations in cortical thickness can provide insight into the evolution and causative factors of neurological disorders, inform the diagnosis of neurological conditions, and assess the efficacy of treatment options.
CRIS-Team Scopus Importer:2020-11-20

Forces on micron-sized particles randomly distributed on the surface of larger particles and possibility of detachment - Cui, Yan; Sommerfeld, Martin (International Journal of Multiphase Flow, 2015)
Numerical calculations based on the Lattice-Boltzmann method were performed for a particle cluster consisting of a large carrier particle covered with small spherical drug particles which were exposed to a constant velocity air flow. Prior to these studies, the simulations were validated based on a test case where a single particle is situated on a plane wall and exposed to a linear shear flow. The present simulations were compared with analytical results and other simulations. Moreover, the required small particle resolution and the domain size were properly selected based on an extensive numerical study. The diameter of the carrier particles was 100 μm, while the fine particles had diameters of 3 μm and 5 μm, respectively. The range of Reynolds numbers considered was between 1 and 200. Moreover, the coverage degree of the carrier by the small particles was varied in the simulations between 10% and 50%, and this influence on the detachment was determined. From these simulations the fluid dynamic forces on the drug particles were extracted in dependence of the angular position in order to estimate the possibility of drug particle detachment. Detachment might occur through lift-off, sliding or rolling. Lift-off was found to be not possible due to the acting small normal forces even at Re = 200. The probability of sliding and rolling detachment in dependence of the angular position was estimated based on measured adhesion properties, i.e. van der Waals force, adhesion surface energy and friction coefficient. With these studies it is aimed to understand drug particle detachment from carrier particles in an inhaler device as a basis of modelling and optimising dry powder inhalation.<br
Keywords: Carrier covered with drug powder; Dry powder inhaler; Carrier particles; Fluid forces on drug particles; Flow about the particle cluster; Probability of drug detachment; Lattice-Boltzmann Method

Fractional and fractal order effects in soft elastomers: Strain rate and temperature dependent nonlinear mechanics - Stanisauskis, Eugenia; Mashayekhi, Somayeh; Pahari, Basanta; Mehnert, Markus; Steinmann, Paul; Oates, William (Mechanics of Materials, 2022)
Soft dielectric elastomers are commonly used in applications where large deformation is prevalent such as energy harvesters, sensors, and soft actuators. The thermo-mechanical response of these elastomers is important in order to accurately describe the viscoelastic behavior over a broad range of operating conditions. Fractal characteristics of the dielectric elastomer VHB 4905 and their connection to fractional order viscoelasticity are analyzed to better understand viscoelasticity over a range of elevated temperatures starting at room temperature. We extend prior work in viscoelasticity to include excluded volume effects as a function of temperature. A fractal hyperelastic model is combined with a fractional order viscoelastic model and validated experimentally. Bayesian uncertainty methods are used to quantify the material parameters and their influence on temperature dependent viscoelasticity measurements. The model fits are compared to previously collected temperature dependent viscoelastic measurements on VHB 4905 for temperatures ranging from 23 °C to 60 °C. Based on fractional order viscoelasticity, we infer that the excluded volume parameter is negative and initially decreases before reaching a constant value near 50 °C.
CRIS-Team Scopus Importer:2022-07-08
Keywords: Excluded volume; Fractal media; Fractional derivative; Viscoelasticity; Zimm model

Fully Coupled Frictional Contact Using Elastic Halfspace Theory - Willner, Kai (Journal of Tribology, 2008)
The effect of dry metallic friction can be attributed to two major mechanisms: adhesion and ploughing. While ploughing is related to severe wear and degradation, adhesion can be connected to pure elastic deformations of the contacting bodies and is thus the predominant mechanism in a stable friction pair. The transmitted friction force is then proportional to the real area of contact. Therefore, a lot of effort has been put into the determination of the fraction of real area of contact under a given load. A broad spectrum of analytical and numerical models has been employed. However, it is quite common to employ the so-called Mindlin assumptions, where the contact area is determined by the normal load only, disregarding the influence of friction. In the subsequent tangential loading, usually the contact pressure distribution is kept fixed such that the coupling between the tangential and normal solutions is neglected. Here, a numerical solution scheme based on elastic halfspace theory for frictional contact problems is presented where full coupling between the normal and tangential tractions and displacements is taken into account. Several examples show the influence of the coupling effects, but also the limitations for the analysis of rough contacts. Copyright © 2008 by ASME.
UnivIS-Import:2015-03-09:Pub.2008.tech.FT.FT-TM.fullyc
Keywords: Elastic contact; Friction; Halfspace theory; Rough surfaces

Fuzinsumo ‐ Fuzzy investigation with surrogate models - Oberleiter, Thomas; Willner, Kai (PAMM, Volume 17, 2018)
In this contribution, we investigate the accuracy of surrogate models for fuzzy systems. Within a virtual tolerance analysis, unknown uncertainties are considered by fuzzy numbers. These fuzzy numbers consist of higher‐dimensional intervals, where each interval is assigned a membership value. To reproduce fuzzy numbers correctly, a large number of system evaluations is needed. Instead of evaluating numerically expensive full systems, we employ surrogate models with radial basis functions. In order to find sufficiently accurate surrogate models with as few as possible sampling points, we investigate the influence of the sampling points on the respective fuzzy number intervals. As an example, we investigate the tilting of an X‐ray aperture, which shows different accuracy for different sampling strategies. The reference results for the nonlinear multi‐body system are calculated by a Matlab optimizer and are compared to the results of the surrogate model

Fuzzy arithmetical approach to the solution of finite element problems with uncertain parameters - Hanss, M.; Willner, Kai (Mechanics Research Communications, 2000)
The application of fuzzy arithmetic to solve finite element problems with uncertain parameters is a powerful but problematic tool. Although the natural uncertainties associated with material variability can be taken into account successfully, the additional artificial uncertainties that arise from some computational aspects in the finite element method distort the result and must therefore be minimized. Thus, to achieve reasonable results, the different numerical techniques for the solution of finite element problems should not be applied in their common form, but should be modified with respect to a reduction of the critical fuzzy arithmetical operations that can cause artificial uncertainties.
UnivIS-Import:2015-03-09:Pub.2000.tech.FT.FT-TM.afuzzy

Fuzzy arithmetical modeling and simulation of structures with uncertain parameters - Willner, Kai; Geisler, Johannes; Hanss, M. (Proceedings of the 2. Workshop on Advanced Computational Engineering Mechanics, 2005)
UnivIS-Import:2015-04-16:Pub.2005.tech.FT.FT-TM.fuzzya

Fuzzy arithmetical modeling and simulation of vibrating structures with uncertain parameters - Hanss, M.; Willner, Kai (Noise and Vibration Engineering, 2004)
A general method for the simulation and analysis of systems with uncertain parameters is presented. In this concept, the uncertain parameters are modeled by fuzzy numbers in contrast to random numbers in stochastic approaches. After an introduction to fuzzy arithmetic, the transformation method is presented a practical implementation which allows the use of the fuzzy concept in conjunction with existing simulation environments. As a result of the simulation of the model, it is possible to quantify the overall uncertainty of the outputs, providing a worst-case scenario. Additionally, the uncertain model parameters can be rated with respect to their influence on the overall output uncertainty. As examples, some finite element applications of the fuzzy arithmetical approach are presented and discussed: the frequency response function of a vibrating plate and the vibration behavior of an engine hood in the presence of uncertain model parameters.
UnivIS-Import:2015-04-16:Pub.2004.tech.FT.FT-TM.fuzzya_4

Fuzzy dynamics of multibody systems with polymorphic uncertainty in the material microstructure - Pivovarov, Dmytro; Hahn, Verena; Steinmann, Paul; Willner, Kai; Leyendecker, Sigrid (Computational Mechanics, 2019)
This paper deals with the fuzzy dynamics of multibody systems with polymorphic uncertainty in the material microstructure. Macroscopic material properties are obtained using fuzzy-stochastic FEM based computational homogenization. In particular, the spectral stochastic local FEM is utilized to simulate a representative volume element of the microstructure. Forward dynamics of the macroscopic system is modeled using the Graph Follower algorithm. Thereby we propagate the uncertainty from the lowest level of material microstructure to the highest level of multibody dynamics. Differences in the propagation of epistemic and aleatoric uncertainties to the macroscale and their influence on the multibody dynamics are discussed. A particular example of a multibody system used in this paper is a multistory frame, whereby the considered heterogeneous material is a cement-based concrete.
CRIS-Team Scopus Importer:2019-07-09
Keywords: Computational homogenization; Epistemic uncertainty; Forward dynamics simulation; Fuzzy numbers; Stochastic FEM; α-cut-optimization

Fuzzy Sensitivity Analysis in the Context of Dimensional Management - Oberleiter, Thomas; Heling, Björn; Schleich, Benjamin; Willner, Kai; Wartzack, Sandro (ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering, 2018)
Real components always deviate from their ideal dimensions. This makes every component, even a serial production, unique. Although they look the same, differences can always be observed due to different scattering factors and variations in the manufacturing process. All these factors inevitably lead to parts that deviate from their ideal shape and, therefore, have different properties than the ideal component. Changing properties can lead to major problems or even failure during operation. It is necessary to specify the permitted deviations to ensure that every single product nevertheless meets its technical requirements. Furthermore, it is necessary to estimate the consequences of the permitted deviations, which is done via tolerance analysis. During this process, components are assembled virtually and varied with the uncertainties specified by the tolerances. A variation simulation is one opportunity to calculate these effects for geometric deviations. Since tolerance analysis enables engineers to identify weak points in an early design stage, it is important to know the contribution that every single tolerance has on a certain quality-relevant characteristic, to restrict or increase the correct tolerances. In this paper, a fuzzy-based method to calculate the sensitivity is introduced and compared with the commonly used extended Fourier amplitude sensitivity test (EFAST) method. Special focus of this work is the differentiation of the sensitivity for the total system and the sensitivities for the subsystems defined by the α-cuts of the fuzzy numbers. It discusses the impact of the number of evaluations and nonlinearity on sensitivity for EFAST and the fuzzy-based meth

Fuzzy-Stochastic FEM-based homogenization framework for materials with polymorphic uncertainties in the microstructure - Pivovarov, Dmytro; Oberleiter, Thomas; Willner, Kai; Steinmann, Paul (International Journal for Numerical Methods in Engineering, 2018)

General imperfect interfaces - Javili, Ali; Käßmair, Stefan; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2014)
The objective of this contribution is to develop a thermodynamically consistent theory for general imperfect interfaces and to establish a unified computational framework to model all classes of such interfaces using the finite element method. The interface is termed general imperfect in the sense that it allows for a jump of the temperature as well as for a jump of the normal heat flux across the interface. Conventionally, imperfect interfaces with respect to their thermal behavior are restricted to being either highly-conducting (HC) or lowly-conducting (LC) also known as Kapitza. For a HC interface the temperature is continuous across the interface while the jump of the normal heat flux is admissible. On the contrary, a LC interface does not allow for a jump of the heat flux across the interface but it does allow for a temperature jump. The temperature jump of a LC interface is frequently assumed to be proportional to the average heat flux across the interface. In this contribution we prove that this common assumption is indeed an appropriate condition to (sufficiently and not necessarily) satisfy the second law of thermodynamics. While HC and LC interfaces are generally accepted and well established today, the general imperfect interfaces remain poorly understood. Here we propose a thermodynamically consistent theory of general imperfect interfaces and we show that the dissipative structure of the interface suggests firstly to classify such interfaces as semi-dissipative (SD) and fully-dissipative (FD). Secondly, for a FD interface the interface temperature shall be considered as an independent degree of freedom and a new (constitutive) equation is obtained to calculate the interface temperature using a new interface material parameter i.e. the sensitivity. Furthermore, we show how all types of interfaces are derived from a FD general imperfect interface model. This finding allows us to establish a unified finite element framework to model all classes of interfaces. Full details of the novel numerical scheme are provided. Key features of general imperfect interfaces are then elucidated via a series of three-dimensional numerical examples. In particular, we show that according to the second law the interface temperature may not necessarily be the average of (or even between) the temperatures across the interface. Finally, we recall since the influence of interfaces on the overall response of a body increases as the scale of the problem decreases, this contribution has certain applications to nano-composites.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.genera
Keywords: General imperfect interface; Highly-conducting; Lowly-conducting; Kapitza; Nano-materials; Finite element method

Generalized interfaces enabling macroscopic modeling of structural adhesives and their failure - Spannraft, Lucie; Possart, Gunnar; Steinmann, Paul; Mergheim, Julia (Forces in Mechanics, 2022)
This contribution presents a geometrically linear and thermodynamically consistent model for generalized mechanical interfaces. The interface's response is kinematically non-coherent, i.e. allows for a displacement jump and for anisotropic cohesive failure, and kinetically non-coherent, i.e. allows for traction jumps across the interface and membrane damage. The traction jump ensues from an interfacial (in)elasticity formulation which introduces additional membrane stiffness and membrane stresses under in-plane stretch in the interface. The cohesive and membrane degradations are coupled via damage variables determined by the different deformation modes to account for their interaction. A numerical example applies the presented model to brittle interfaces adhesively bonding two substrates. By subjecting the interface to a small in-plane stretch prior to performing a peel test, the influence of damage coupling on the mechanical response is illustrated.
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Keywords: Anisotropic cohesive zone; Damage; Generalized interfaces; Interface (in)elasticity; Structural adhesives

Generalized interfaces via weighted averages for application to graded interphases at large deformations - Saeb, Saba; Firooz, Soheil; Steinmann, Paul; Javili, A. (Journal of the Mechanics and Physics of Solids, 2021)
Finite-thickness interphases between different constituents in heterogeneous materials are often replaced by a zero-thickness interface model. Commonly accepted interface models intuitively assume that the interface layer is situated exactly in the middle of its associated interphase. Furthermore, it has been reported in the literature that this assumption is necessary to guarantee the balance of angular momentum on the interface. While the interface coincides with the mid-layer of a uniform interphase, we argue that this assumption fails to sufficiently capture the behavior of graded or inhomogeneous interphases. This contribution extends the formulation of the general interface model to account for arbitrary interface positions. The issue of angular momentum balance on general interfaces is critically revisited. It is proven that the interface position does not necessarily have to coincide with the mid-layer in order to satisfy the angular momentum balance. The analysis here leads to a unique definition of the controversially discussed interface configuration. The presented general interface model is essentially based upon the weighted average operator instead of the commonly accepted classical average operator. The framework is geometrically exact and suitable for finite deformations. The significance of the interface position is demonstrated via a series of examples where the interface position is identified based on a full resolution interphase.
CRIS-Team Scopus Importer:2021-02-05
Keywords: Cohesive interface; General interface model; Interface elasticity; Interphase; Weighted average

Geometrical Foundations of Continuum Mechanics - Steinmann, Paul (Springer, 2015)

Geometrical Influence on Material Properties for Ti6Al4V Parts in Powder Bed Fusion - Nahr, Florian; Rasch, Michael; Burkhardt, Christian; Renner, Jakob; Baumgärtner, Benjamin; Hausotte, Tino; Körner, Carolin; Steinmann, Paul; Mergheim, Julia; Schmidt, Michael; Markl, Matthias (Journal of Manufacturing and Materials Processing, 2023)
One major advantage of additive manufacturing is the high freedom of design, which supports the fabrication of complex structures. However, geometrical features such as combined massive volumes and cellular structures in such parts can lead to an uneven heat distribution during processing, resulting in different material properties throughout the part. In this study, we demonstrate these effects, using a complex structure consisting of three conic shapes with narrow cylinders in between hindering heat flux. We manufacture the parts via powder bed fusion of Ti6Al4V by applying a laser beam (PBF-LB/M) as well as an electron beam (PBF-EB). We investigate the impact of the different thermal regimes on the part density, microstructure and mechanical properties aided by finite element simulations as well as by thermography and X-ray computed tomography measurements. Both simulations and thermography show an increase in inter-layer temperature with increasing part radius, subsequently leading to heat accumulation along the build direction. While the geometry and thermal history have a minor influence on the relative density of the parts, the microstructure is greatly affected by the thermal history in PBF-LB/M. The acicular martensitic structure in the narrow parts is decomposed into a mix of tempered lath-like martensite and an ultrafine 𝛼 + 𝛽 microstructure with increasing part radius. The EBM part exhibits a lamellar 𝛼 + 𝛽 microstructure for both the cylindric and conic structures. The different microstructures directly influence the hardness of the parts. For the PBF-LB part, the hardness ranges between 400 HV0.5 in the narrow sections and a maximum hardness of 450 HV0.5 in the broader sections, while the PBF-EB part exhibits hardness values between 280 and 380 HV0.
Keywords: PBF-LB/M; PBF-EB; Ti6Al4V; simulation; thermography

Geometrically exact elastoplastic rods: determination of yield surface in terms of stress resultants - Herrnböck, Ludwig; Kumar, Ajeet; Steinmann, Paul (Computational Mechanics, 2021)
This work addresses the determination of yield surfaces for geometrically exact elastoplastic rods. Use is made of a formulation where the rod is subjected to an uniform strain field along its arc length, thereby reducing the elastoplastic problem of the full rod to just its cross-section. By integrating the plastic work and the stresses over the rod’s cross-section, one then obtains discrete points of the yield surface in terms of stress resultants. Eventually, Lamé curves in their most general form are fitted to the discrete points by an appropriate optimisation method. The resulting continuous yield surfaces are examined for their scalability with respect to cross-section dimensions and also compared with existing analytical forms of yield surfaces.
CRIS-Team Scopus Importer:2021-03-05
Keywords: Elastoplasticity; Geometrically exact elastoplastic rods; J2-plasticity; Yieldsurfaces in terms of stress resultants

Geometrically nonlinear continuum thermomechanics coupled to diffusion: a framework for case II diffusion - McBride, Andrew; Bargmann, Swantje; Steinmann, Paul (Advances in Extended and Multifield Theories for Continua, 2011)
This chapter introduces a geometrically nonlinear, continuum thermomechanical framework for case II diffusion: a type of non-Fickian diffusion characterized by the wave-like propagation of a low-molecular weight solvent in a polymeric solid. The key objective of this contribution is to derive the coupled system of governing equations describing case II diffusion from fundamental balance principles. A general form for the Helmholtz energy is proposed and the resulting constitutive laws are derived from logical, thermodynamically consistent argumentation. The chapter concludes by comparing the model developed here to various others in the literature. The approach adopted to derive the governing equations is not specific to case II diffusion, rather it encompasses a wide range of applications wherein heat conduction, species diffusion and finite inelastic effects are coupled. The presentation is thus applicable to the generality of models for non-Fickian diffusion: an area of increasing research interest. © 2011 Springer-Verlag Berlin Heidelberg.
UnivIS-Import:2015-04-20:Pub.2011.tech.FT.FT-TM.geomet

Geometrically nonlinear continuum thermomechanics with surface energies coupled to diffusion - McBride, Andrew; Javili, Ali; Steinmann, Paul; Bargmann, Swantje (Journal of the Mechanics and Physics of Solids, 2011)
Surfaces can have a significant influence on the overall response of a continuum body but are often neglected or accounted for in an ad hoc manner. This work is concerned with a nonlinear continuum thermomechanics formulation which accounts for surface structures and includes the effects of diffusion and viscoelasticity. The formulation is presented within a thermodynamically consistent framework and elucidates the nature of the coupling between the various fields, and the surface and the bulk. Conservation principles are used to determine the form of the constitutive relations and the evolution equations. Restrictions on the jump in the temperature and the chemical potential between the surface and the bulk are not a priori assumptions, rather they arise from the reduced dissipation inequality on the surface and are shown to be satisfiable without imposing the standard assumptions of thermal and chemical slavery. The nature of the constitutive relations is made clear via an example wherein the form of the Helmholtz energy is explicitly given. © 2011 Elsevier Ltd.
UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.geomet_1
Keywords: Constitutive behaviour; Diffusion; bulk and surface; Finite strain; Thermomechanical process

Geometrically nonlinear design of compliant mechanisms: Topology and shape optimization with stress and curvature constraints - Stankiewicz, Gabriel; Dev, Chaitanya; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2022)
In this work, we exploit a sequential topology and shape optimization framework to design compliant mechanisms. We pay particular attention to a refined and exact design of flexure hinges via shape optimization in a geometrically nonlinear setting. We propose improved adaptive shape and domain refinement strategies for the embedding domain discretization method (EDD) to achieve numerically and geometrically accurate designs of the flexure hinges. Furthermore, to account for durability and manufacturability of the flexure hinges, we employed local stress constraints and a curvature constraint. The local stress constraints are integrated into an augmented Lagrange functional together with the output displacement to form a combined objective response. The design update is realized by employing and adapting the traction method for the specifics of the embedded boundary. Hence, the curvature constraint does not appear in a standard response form, but is rather introduced into the auxiliary boundary value problem (BVP) of the traction method via a penalty functional. The novelties of this work include: (1) enhanced adaptive shape and domain refinement strategies for EDD; (2) geometrically nonlinear shape optimization using EDD; (3) adapted traction method with curvature constraint.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).
CRIS-Team WoS Importer:2022-07-15

Geometrically Nonlinear Gravito-Elasticity: Hyperelastostatics Coupled to Newtonian Gravitation - Steinmann, Paul (International Journal of Engineering Science, 2011)
A theory of nonlinear elasticity is presented that incorporates a spatially non-constant Newtonian gravitational field as is appropriate if deformable heavy masses of finite volume are considered. For Newtonian gravitation the mass density is a sink for the (scaled) gravitational field. This Gauss-type law for gravitation is incorporated into the mechanical balance equations of linear and angular momentum as well as into the thermomechanical balance equations of energy and entropy. To this end, a total energy density as well as total Piola and Cauchy stresses are introduced that directly capture the contribution of Newtonian gravitation. For the nonlinear elastic case the pertinent relations for the gravito-elastically coupled problem are recovered from a variational setting in terms of the nonlinear deformation map and a gravitational potential. © 2011 Elsevier Ltd. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.geomet_9
Keywords: Coupled gravito-elasticity; Hyperelasticity; Newtonian gravitation

Geometrically nonlinear higher-gradient elasticity with energetic boundaries - Javili, Ali; Dell´Isola, Francesco; Steinmann, Paul (Journal of the Mechanics and Physics of Solids, 2013)
The objective of this contribution is to formulate a geometrically nonlinear theory of higher-gradient elasticity accounting for boundary (surface and curve) energies. Surfaces and curves can significantly influence the overall response of a solid body. Such influences are becoming increasingly important when modeling the response of structures at the nanoscale. The behavior of the boundaries is well described by continuum theories that endow the surface and curve with their own energetic structures. Such theories often allow the boundary energy density to depend only on the superficial boundary deformation gradient. From a physical point of view though, it seems necessary to define the boundary deformation gradient as the evaluation of the deformation gradient at the boundary rather than its projection. This controversial issue is carefully studied and several conclusions are extracted from the rigorous mathematical framework presented. In this manuscript the internal energy density of the bulk is a function of the deformation gradient and its first and second derivatives. The internal energy density of the surface is, consequently, a function of the deformation gradient at the surface and its first derivative. The internal energy density of a curve is, consequently, a function of the deformation gradient at the curve. It is shown that in order to have a surface energy depending on the total (surface) deformation gradient, the bulk energy needs to be a function of at least the first derivative of the deformation gradient. Furthermore, in order to have a curve energy depending on the total (curve) deformation gradient, the bulk energy needs to be a function of at least the second derivative of the deformation gradient. Clearly, the surface elasticity theory of Gurtin and Murdoch is intrinsically limited since it is associated with the classical (firstorder) continuum theory of elasticity in the bulk. In this sense this contribution shall be also understood as a higher-gradient surface elasticity theory. © 2013 Elsevier Ltd. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.geomet
Keywords: Cosserat continua; Generalized continua; Higher-gradient elasticity; Nano-materials; Surface elasticity

Gradient Enhanced Crystal Plasticity in Additive Manufacturing Identification of a Macroscopic Yield Criterion - Kergaßner, Andreas; Mergheim, Julia; Steinmann, Paul (Proceedings in Applied Mathematics and Mechanics, 2019)
In this contribution the mechanical behavior of additively manufactured Inconel 718 (IN 718) is modeled on the meso and macro scale. Gradient enhanced crystal plasticity is utilized to capture the kinematics of crystallographic slips and grain boundaries on the meso scale. The material model is solved on a representative volume element (RVE) by means of the Finite Element Method. In order to represent additively manufactured material, the RVE is based on a numerical grain growth simulation of the solidification during additive manufacturing. Mesoscopic elastic behavior and the initial yield locus are transferred to the macro scale by numerical homogenization and used to identify the parameters for a quartic yield function which is able to capture the highly anisotropic material behavior.<br

Grain boundary interaction based on gradient crystal inelasticity and decohesion - Spannraft, Lucie; Ekh, Magnus; Larsson, Fredrik; Runesson, Kenneth; Steinmann, Paul (Computational Materials Science, 2020)
This paper presents a model for geometrically non-coherent grain boundary interaction premised on gradient-extended crystal inelasticity. The appropriate kinematics, the constitutive relations and the balance equations are established for a polycrystal including grain interaction. More specifically, this contribution proposes a coupling of the microtraction and grain boundary decoheion, which is represented as damage. As a consequence, decohesion exerts an impact on the standard tractions as well as on the microtractions along the grain boundaries. The appropriate modeling framework is assessed in terms of numerical results for a bicrystal that is subjected to simple shear. A comparison with the situation without such coupling effect shows that the microtractions along the grain boundary reduce for increasing damage and a microfree boundary is approached when the damage approaches unity.
CRIS-Team Scopus Importer:2020-03-17
Keywords: Boundary conditions; Decohesion; Gradient crystal plasticity; Grain boundary interaction

Growth-induced instabilities of an elastic film on a viscoelastic substrate: Analytical solution and computational approach via eigenvalue analysis - Valizadeh, Iman; Steinmann, Paul; Javili, Ali (Journal of Mechanics of Materials and Structures, 2018)
The objective of this contribution is to study for the first time the growth-induced instabilities of an elastic film on a viscoelastic substrate using an analytical approach as well as computational simulations via eigenvalue analysis. The growth-induced instabilities of a thin film on a substrate is of particular interest in modeling living tissues such as skin, brain, and airways. The analytical solution is based on Airy's stress function adopted to viscoelastic constitutive behavior. The computational simulations, on the other hand, are carried out using the finite deformation continuum theory accounting for growth via the multiplicative decomposition of the deformation gradient into elastic and growth parts. To capture the critical growth of elastic films and the associated folding pattern, eigenvalue analysis is utilized, in contrast to the commonly used perturbation strategy. The eigenvalue analysis provides accurate, reliable, and reproducible solutions as contrasted to the perturbation approach. The numerical results obtained from the finite element method show an excellent agreement between the computational simulations and the proposed analytical solution.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Finite element method; Growth-induced instabilities; Viscoelasticity; Wrinkling

Guidelines for Addressing Environmentally Assisted Fatigue in Fatigue Usage Calculation and Further Recommendations - Wilhelm, Paul; Steinmann, Paul; Rudolph, Jürgen (Compacts of the 44th AMNT, 2013)

Halfspace modeling of elastic-plastic contact of rough surfaces - Hauer, Franz; Willner, Kai (COMPLAS XI, 2011)
Friction has a significant influence on the tool lifetime and the quality of products in manufacturing processes. Real surfaces are always rough, so that for moderate loads contact occurs only at surface roughness peaks. Thus the real contact area A real is smaller than the apparent contact area A 0. Adhesive forces, which are an important contribution to friction, can only be transferred within A real. Consequently A real has to be determined in order to analyse the tribological behaviour of technical surfaces. The halfspace approach is used because of its advantage in numerical effort compared to the Finite-Element-Method. Due to the fact that contact pressures can be very large the plastic deformation of roughness peaks has to be taken into account. Therefore a three-dimensional plasticity algorithm is implemented into the halfspace model.
UnivIS-Import:2015-04-16:Pub.2011.tech.FT.FT-TM.halfsp_9
Keywords: Computational plasticity; Contact; Halfspace; Metal forming

Halfspace Simulation of Rough Surface Contact in Metal Forming - Hauer, Franz; Willner, Kai (10th World Congress on Computational Mechanics, 2012)
UnivIS-Import:2015-04-16:Pub.2012.tech.FT.FT-TM.halfsp_3

Hard-magnetic phenomena enable autonomous self-healing elastomers - Garcia-Gonzalez, Daniel; Ter-Yesayants, Tigran; Moreno Mateos, Miguel Angel; Lopez-Donaire, Maria Luisa (Composites Part B-Engineering, 2023)
We propose a new concept of self-healing soft material that does not require external actuation to heal after rupture. This consists of a sticky and soft elastomeric matrix filled with hard-magnetic particles. When the material breaks into two or more parts and these are approached to each other, the magnetic particles with residual magnetisation interact closing the crack. Then, if new mechanical loading is applied, the composite acts as a continuum structure transmitting internal forces homogeneously until reaching a new failure strain threshold. We demonstrate this novel concept with experiments under tensile loading and with a magneto-mechanical constitutive model that explains the healing mechanisms. The results indicate that the proposed soft materials are able to, after several fracture cycles, sustain mechanical loading beyond 20 % strains without compromising the structural integrity. The healed material experiences no mechanical degradation during cyclic loading and healing cycles. Moreover, on its healed state, it can sustain higher stresses than the original material without residual magnetisation. We demonstrate that the strain at failure is determined by the combined effect of magnetic and adhesive contributions, which are modulated by the applied deformation rate. Furthermore, we reveal that the combination of soft and hard magnetic particles in a hybrid magnetorheological elastomer enables superior healing performance.
Created from Fastlane, Scopus look-up
Keywords: Magneto-mechanics; Magnetorheological elastomers (MREs); Multifunctional materials; Self-healing; Soft robotics

Hard magnetics in ultra-soft magnetorheological elastomers enhance fracture toughness and delay crack propagation - Moreno Mateos, Miguel Angel; Hossain, Mokarram; Steinmann, Paul; Garcia-Gonzalez, Daniel (Journal of the Mechanics and Physics of Solids, 2023)
Pre-existing flaws in highly stretchable elastomers trigger fracture under large deformations. For multifunctional materials, fracture mechanics may be influenced by additional physical phenomena. This work studies the implications of hard magnetics on the fracture behaviour of ultra-soft magnetorheological elastomers (MREs). We experimentally demonstrate that MREs with remanent magnetisation have up to a 50% higher fracture toughness than non pre-magnetised samples. Moreover, we report crack closure due to the magnetic field as a mechanism that delays the opening of cracks in pre-magnetised MREs. To overcome experimental limitations and provide further understanding, a phase-field model for the fracture of MREs is conceptualised. The numerical model incorporates magneto-mechanical coupling to demonstrate that the stress concentration at the crack tip is smaller when the MRE is pre-magnetised. Overall, this work unveils intriguing applications for functional actuators, with better fracture behaviour and potential better performance under cyclic loading.
CRIS-Team Scopus Importer:2023-02-10
Keywords: Experimental mechanics; Hard magnetics; Multifunctional materials; Phase-field modelling; Soft fracture; Ultra-soft magnetorheological elastomers

High gradient magnetic particle separation in a channel with bifurcations - Zadravec, M.; Hribersek, Matjaz; Steinmann, Paul; Ravnik, J. (Engineering Analysis With Boundary Elements, 2014)
Micro particle separation from solid-liquid suspension under the influence of hydrodynamic and magnetic forces in a channel with bifurcation is studied numerically by applying the Boundary Element Method based fluid flow solver. The particle trajectories are computed using the Lagrangian particle tracking, where the forces on particles are computed based on the point particle representation. In the separator due to the bifurcation channel geometry the magnetic particles experience varying Kelvin force as they travel along the channel, although in the same direction the high gradient magnetic field does not change. In this way, the interplay of hydrodynamic and magnetic forces leads to changes in collection efficiency of the separator. A comparison with magnetic separation in the narrow channel design is done and recommendation for optimal choice of fluid flow rate and magnitude of external magnetic field is discussed.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Bifurcation; Boundary element method; High gradient magnetic separation; Particle tracking

Highly-conductive energetic coherent interfaces subject to in-plane degradation - Esmaeili, Ali; Javili, Ali; Steinmann, Paul (Mathematics and Mechanics of Solids, 2016)
The presence of an interface can influence the thermo-mechanical response of a body. This influence is especially pronounced at small scales where the interface area to bulk volume ratio significantly increases. Since the thermo-mechanical properties of an interface can differ from those of the bulk, within interface continuum theory an interface is endowed with its own thermo-mechanical energetic structure. To date, the effects of interface in-plane damage on the thermo-mechanical response of a highly conductive interface have not been accounted for. Therefore in this contribution the computational aspects of thermo-mechanical solids containing highly conductive interfaces subject to in-plane degradation are studied. To this end, the equations governing a fully non-linear transient problem are given. They are solved using the finite element method. The results are illustrated through a series of three-dimensional numerical examples for various interfacial parameters. In particular a comparison is made between the results of the intact and the degraded highly conductive interface formulation.

Homogenization and modelling of technical textiles - Fillep, Sebastian; Mergheim, Julia; Steinmann, Paul (European Congress on Computational Methods in Applied Sciences and Engineering Proceedings, 2012)
UnivIS-Import:2015-04-16:Pub.2012.tech.FT.FT-TM.homoge_5

Homogenization in periodically heterogeneous elastic bodies with multiple micro contact - Fillep, Sebastian; Orlik, Julia; Bare, Zoufine; Steinmann, Paul (Mathematics and Mechanics of Solids, 2013)
The aim of this contribution is to compute the effective in-plane tension and shear behaviour of textile-like elastic materials, that is, plates or  shells with a periodic micro-structure composed of long woven or  knitted fibres. The knitting or weaving results in multiple periodic  contact between fibres. Mathematically the problem can be formulated as anin-plane elasticity problem defined in a heterogeneous domain with ε-periodic micro-structure, including multiple micro-contact between the structural components, which is described by the  Signorini and Tresca-friction contact conditions.The asymptotic  analysis and homogenized limit for such problems was recently obtained by Damlamian et al. via periodicunfolding strategy. These  results are briefly recalled in the paper. The obtained two-scale  algorithm is implemented for some specific textile materials, which are macroscopic shells with a 3-D microstructure including contact. For  each  macroscopic deformation state, a contact problem in the  periodicity  cell or representative volume element is solved and the  corresponding non-linear macroscopic stress–strain relation is   obtained. The results are illustrated by the simulation of woven and knitted textiles.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.homoge_38
Keywords: Contact problems; effective elasto-plasticity; textile structures

Homogenization of Composites With Extended General Interfaces: Comprehensive Review and Unified Modeling - Firooz, Soheil; Steinmann, Paul; Javili, A. (Applied Mechanics Reviews, 2021)
Interphase regions that form in heterogeneous materials through various underlying mechanisms such as poor mechanical or chemical adherence, roughness, and coating, play a crucial role in the response of the medium. A well-established strategy to capture a finite thickness interphase behavior is to replace it with a zero-thickness interface model characterized by its own displacement and/or traction jumps, resulting in different interface models. The contributions to date dealing with interfaces commonly assume that the interface is located in the middle of its corresponding interphase. This paper revisits this assumption and introduces an extended general interface model, wherein a unifying approach to the homogenization of heterogeneous materials embedding interfaces between their constituents is developed within the framework of linear elasticity. Through utilizing a weighted average operator, we demonstrate that the assumption of enforcing the interface to coincide with the midlayer is not required and thereby develop a new class of interfaces where the interface is allowed to take any arbitrary position between its bulk neighbors. The proposed novel interface model can recover any of the classical interface models. Next, via incorporating this extended general interface model into homogenization, we develop bounds and estimates for the overall moduli of fiber-reinforced and particle-reinforced composites as functions of the interface position and properties. Finally, we carry out a comprehensive numerical study to highlight the influence of interface position, stiffness ratio, and interface parameters on the overall properties of composites. The developed interface-enhanced homogenization framework also successfully captures size effects, which are immediately relevant to emerging applications of nanocomposites due to their pronounced interface effects at small scales.
CRIS-Team WoS Importer:2021-09-10

Homogenization of fully nonlinear rod lattice structures: on the size of the RVE and micro structural instabilities - Herrnböck, Ludwig; Steinmann, Paul (Computational Mechanics, 2021)
This work investigates the possibility of applying two-scale computational homogenization to rod lattice structures emerging, for instance, from additive manufacturing. The influence of the number of unit cells within the representative volume element (RVE), thus, the RVE’s size on the homogenized mechanical response is studied for occurring microscopic structural instabilities. Therein, the macro-scale, described in terms of three-dimensional continuum mechanics, is coupled to the micro-scale described by geometrically exact rods, enabling arbitrary large deformations and rotations. A special feature of the presented framework is that the rods building the lattice structures are not restricted to deform purely elastically but may deform inelastically. The mechanical response of lattice structures is investigated by applying the developed homogenization method to an exemplary lattice. Under special loads the structure reaches an instable state and may buckle. The appearance of instabilities depends on the geometric properties of the lattice’s underlying rods and the RVE’s size.
CRIS-Team Scopus Importer:2021-12-17
Keywords: Geometrically exact elastoplastic rods; Multiscale homogenization; Structural instability

Homogenization of heterogeneous, fibre structured materials - Fillep, Sebastian; Mergheim, Julia; Steinmann, Paul (COMPLAS XII - XII Inernational Conference on Computational Plasticity. Fundamentals and Applications, 2013)
This contribution presents a multi-scale homogenization method to model fibre structured materials. On the macroscopic level textiles are characterized by a large area-to-thickness ratio, such that a discretization with shell elements is numerically efficient. The material behavior is strongly influenced by the heterogeneous micro structure. To capture the contact on the micro level, the RVE is explicitly modelled by means of a volumetric micro sample and a shell specific homogenization scheme is applied to transfer the microscopic response to the macro level. Theoretical aspects are discussed and a numerical example for contact behavior of a periodic knitted structure is given.
UnivIS-Import:2015-04-16:Pub.2013.tech.FT.FT-TM.homoge
Keywords: Contact; Homogenization; Hysteresis; Multi-scale; Shell kinematic; Technical textiles

Hybrid magnetorheological elastomers enable versatile soft actuators - Moreno Mateos, Miguel Angel; Hossain, Mokarram; Steinmann, Paul; Garcia-Gonzalez, Daniel (npj Computational Materials, 2022)
Recent advances in magnetorheological elastomers (MREs) have posed the question on whether the combination of both soft- and hard-magnetic particles may open new routes to design versatile multifunctional actuators. Here, we conceptualise ultra-soft hybrid MREs (≈1–10 kPa stiffness) combining experimental and computational approaches. First, a comprehensive experimental characterisation is performed. The results unravel that the magneto-mechanical performance of hybrid MREs can be optimised by selecting an adequate mixing ratio between particles. Then, a multi-physics computational framework provides insights into the synergistic magneto-mechanical interactions at the microscale. Soft particles amplify the magnetisation and hard particles contribute to torsional actuation. Our numerical results suggest that the effective response of hybrid MREs emerges from these intricate interactions. Overall, we uncover exciting possibilities to push the frontiers of MRE solutions. These are demonstrated by simulating a bimorph beam that provides actuation flexibility either enhancing mechanical bending or material stiffening, depending on the magnetic stimulation.
CRIS-Team Scopus Importer:2022-08-05

Hyperelastic analysis based on a polygonal finite element method - Rajagopal, Amirtham; Kraus, Markus; Steinmann, Paul (Mechanics of Advanced Materials and Structures, 2018)
In this contribution, we present a novel polygonal finite element method applied to hyperelastic analysis. For generating polygonal meshes in a bounded period of time, we use the adaptive Delaunay tessellation (ADT) proposed by Constantinu et al. [1]. ADT is an unstructured hybrid tessellation of a scattered point set that minimally covers the proximal space around each point. In this work, we have extended the ADT to nonconvex domains using concepts from constrained Delaunay triangulation (CDT). The proposed method is thus based on a constrained adaptive Delaunay tessellation (CADT) for the discretization of domains into polygonal regions. We involve the metric coordinate (Malsch) method for obtaining the interpolation over convex and nonconvex domains. For the numerical integration of the Galerkin weak form, we resort to classical Gaussian quadrature based on triangles. Numerical examples of two-dimensional hyperelasticity are considered to demonstrate the advantages of the polygonal finite element method.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Adaptive Delaunay tessellation; hyperelasticity; polygonal finite element; polygonal interpolant

Hyperelastic models for rubber-like materials: Consistent tangent operators and suitability for Treloar's data - Steinmann, Paul; Mokarram, Hossain; Possart, Gunnar (Archive of Applied Mechanics, 2012)
Rubber-like materials consist of chain-like macromolecules that are more or less closely connected to each other via entanglements or cross-links. As an idealisation, this particular structure can be described as a completely random three-dimensional network. To capture the elastic and nearly incompressible mechanical behaviour of this material class, numerous phenomenological and micro-mechanically motivated models have been proposed in the literature. This contribution reviews fourteen selected representatives of these models, derives analytical stress-stretch relations for certain homogeneous deformation modes and summarises the details required for stress tensors and consistent tangent operators. The latter, although prevalently missing in the literature, are indispensable ingredients in utilising any kind of constitutive model for the numerical solution of boundary value problems by iterative approaches like the Newton-Raphson scheme. Furthermore, performance and validity of the models with regard to the classical experimental data on vulcanised rubber published by Treloar (Trans Faraday Soc 40:59-70, 1944) are evaluated. These data are here considered as a prototype or worst-case scenario of highly nonlinear elastic behaviour, although inelastic characteristics are clearly observable but have been tacitly ignored by many other authors. © Springer-Verlag 2012.
UnivIS-Import:2015-03-09:Pub.2012.tech.FT.FT-TM.hypere
Keywords: Hyperelasticity; Micro-mechanical model; Phenomenological model; Rubber-like material

Hyperelastic parameter identification of human articular cartilage and substitute materials - Weizel, A.; Distler, Thomas; Detsch, Rainer; Boccaccini, Aldo R.; Paulsen, Friedrich; Seitz, H.; Budday, Silvia; Bräuer, Lars (Journal of the Mechanical Behavior of Biomedical Materials, 2022)
Numerical simulations are a valuable tool in the field of tissue engineering for cartilage repair and can help to understand which mechanical properties affect the behavior of chondrocytes and contribute to the success or failure of surrogate materials as implants. However, special attention needs to be paid when identifying corresponding material parameters in order to provide reliable numerical predictions of the material's response. In this study, we identify hyperelastic material parameters for numerical simulations in COMSOL Multiphysics (R) v. 5.6 for human articular cartilage and two surrogate materials, commercially available ChondroFiller(liquid), and oxidized alginate-gelatin (ADA-GEL) hydrogels. We consider several hyperelastic isotropic material models and provide separate parameter sets for the unconditioned and the conditioned material response, respectively, based on previously generated experimental data including both compression and tension experiments. We compare a direct parameter identification approach assuming homogeneous deformation throughout the specimen and an inverse approach, where the experiments are simulated using a finite element model with realistic boundary conditions in COMSOL Multiphysics (R) v. 5.6. We demonstrate that it is important to consider both compression and tension data simultaneously and to use the inverse approach to obtain reliable parameters. The one-term Ogden model best represents the unconditioned response of cartilage, while the conditioned response of cartilage and ADA-GEL is equally well represented by the two-term Ogden and five-term Mooney-Rivlin models. The five-term Mooney-Rivlin model is also most suitable to model the unconditioned response of ADA-GEL. For ChondroFiller(liquid), we suggest using the five-term Mooney-Rivlin or two-term Ogden model for the unconditioned and the two-term Ogden model for the conditioned material response. These results will help to choose appropriate material models and parameters for simulations of whole joints or to advance mechanical-stimulation assisted cartilage tissue engineering in the future.
CRIS-Team WoS Importer:2022-07-01
Keywords: Parameter identification; Finite hyperelasticity; Human articular cartilage; Hydrogels; Tissue engineering

Identification of contact parameters for dry friction joints - Willner, Kai (PROCEEDINGS OF INTERNATIONAL CONFERENCE ON NOISE AND VIBRATION ENGINEERING (ISMA2018) / INTERNATIONAL CONFERENCE ON UNCERTAINTY IN STRUCTURAL DYNAMICS (USD2018), 2018)
CRIS-Team WoS Importer:2019-06-04

Identification of elastoplastic microscopic material parameters within a homogenization scheme - Schmidt, Ulrike; Mergheim, Julia; Steinmann, Paul (International Journal for Numerical Methods in Engineering, 2015)
A two-scale parameter identification approach is investigated. The microscopic material parameters of a two-scale model are identified by comparing macroscopic simulation data with macroscopic full-field measurements of the micro-structured specimen. Gradient-based solution strategies are employed for the optimization problem of the two-scale parameter identification. In particular, two approaches for the gradient calculation are investigated: the finite difference method is compared with a newly introduced semi-analytical scheme. The focus lies on the identification of microscopic elastoplastic material parameters. The presented identification example with artificial data confirms a reduced computational effort and advantageous convergence for the semi-analytical approach within the two-scale parameter identification. A drawback is the increase in memory requirement.

Identification of nonlinear kinematic hardening parameters for sheet metal from biaxial loading tests - Söhngen, Benjamin; Willner, Kai (XIV International Conference on Computational Plasticity. Fundamentals and Applications, 2017)
In this work an anisotropic material model at finite strains with nonlinear mixed (isotropic and kinematic) hardening is used for the identification of the hardening parameters of sheet steel. The algorithmic system is thereby reduced to a single equation return mapping. For the identification, a cruciform specimen is loaded biaxially in an alternating shear test to provoke the kinematic hardening behavior and prevent the sheet from buckling. The material parameters are found through an optimization strategy by comparing the deformation field from the experiment to that from a finite element (FE) simulation. The resulting cost function is minimized by means of a gradient-based metho
Keywords: Kinematic Hardening; Anisotropic Plasticity; Parameter Identification; Biaxial Loading; Sheet Metal

Identification of orthotropic plastic material parameters for deep-drawing steel using DIC and FEMU - Schmaltz, Stefan; Willner, Kai (COMPLAS XI Proceeding (CD), 2011)
In this paper the deep-drawing sheet steel DC04, representative for sheet-bulk metal forming processes, is characterized through uni- and biaxial tensile and compression tests. The orthotropic plastic material parameters for the Hill 1948 yield surface are identified in two different ways. The first one utilizes uniaxial tensile experiments with specimen in three angles to the rolling direction of the sheet (0, 45 and 90 degree) and the plastic material parameters are calculated through the Lankford coefficients. Second a Finite Element Model Updating (FEMU) procedure is introduced. By taking the measured full-field displacement data and the forces of the biaxial tensile experiments better fitting parameters are identified at reasonable experimental costs.
UnivIS-Import:2015-04-16:Pub.2011.tech.FT.FT-TM.identi
Keywords: Computational Plasticity; FEMU; Parameter Identification; Sheet steel

Identification of the lamination stack's behavior simulated with a multi-scale homogenization using a progressive contact formulation - Luchscheider, Vera; Maidorn, Mischa; Willner, Kai (PAMM 2014, 2014)
UnivIS-Import:2015-04-16:Pub.2014.tech.FT.FT-TM.identi_8

Identification of thermal effects on the diameter deviation of inhomogeneous aluminum metal matrix composite workpieces when dry turning - Schindler, Stefan; Zimmermann, Marco; Aurich, Jan C.; Steinmann, Paul (Production Engineering, 2015)
The use of dry cutting is associated with considerable thermal loads on the machine tool, the tool and the workpiece because of the missing heat convection through the cutting fluid. These thermal loads cause thermal expansions of the components. The accuracy of machining is thus decreased. In recent years, particularly the thermal expansions of the workpiece and the tool attained significance due to the increased demands on the machining accuracy. Aluminum metal matrix composites (Al-MMCs) show a poor machinability due to the reinforcement of light metal alloys via hard and abrasive materials. Dry turning of such composites is therefore accompanied with high thermal workpiece and tool loads. In this paper, finite element models of the workpiece and the tool are used in order to calculate the temperature distribution and thus the thermally induced expansion of the workpiece and the tool when turning AL-MMC regarding the cutting condition used. The removal of material and the heat flow to the environment are considered. The required boundary conditions (e.g. the heat flow into the workpiece) for the simulations were determined using experimental results. A new evaluation method of experimental diameter measurement validates the numerically calculated diameter deviations and reveals a considerable effect of the thermal expansions of the workpiece and the tool on the accuracy of machining.
UnivIS-Import:2015-07-08:Pub.2015.tech.FT.FT-TM.identi
Keywords: Thermo-elastic deformations; Aluminum metal matrix composite; Cutting condition; Machining accuracy; Finite element simulation

Identification of the yield surface for sheet steel using an optical measurement system - Schmaltz, Stefan; Willner, Kai (Proceedings of the 10th Youth Symposium on Experimental Solid Mechanics, 2011)
UnivIS-Import:2015-04-16:Pub.2011.tech.FT.FT-TM.identi_2

Identification of weak spots in the metrological investigation of dynamic machine behaviour - Brecher, C.; Denkena, B.; Grossmann, K.; Steinmann, Paul; Bouabid, A.; Heinisch, D.; Hermes, R.; Löser, M. (Production Engineering, 2012)
Both the measurement of frequency response functions and the modal analysis are established tools for the measurement of the dynamic compliance of machine tools. State of the art measurement technique enables an allocation of dynamic weak points of the machine structure and optimization of the machine design on the basis of these measurement results. In recent applications the metrological investigation is used for the parameterization and the verification of simulation models to describe the dynamic behaviour of machine tools, which demands high standards regarding to the quantitative quality of measurement results. This paper describes the interlaboratory comparison test, which has been carried out at well-known German research institutes and was initiated by the Laboratory for Machine Tools and Production Engineering (WZL) of the RWTH Aachen. In this regard, the question is discussed, to what extent the compliance behaviour of machine structures under real process conditions corresponds to behaviour, determined in metrological investigation under idealized test conditions. © 2011 German Academic Society for Production Engineering (WGP).
CRIS-Team Scopus Importer:2022-08-05
Keywords: Dynamic compliance behaviour; Frequency response function measurement; Interlaboratory comparison test; Stability simulation

Illustration of an improved non-invasive form finding algorithm - Caspari, Michael; Landkammer, Philipp; Steinmann, Paul (21st International ESAFORM Conference on Material Forming, 2018)
Shape optimization is commonly used in various fields of metal forming. Merklein et al. [6] introduced a novel class of forming process, sheet bulk metal forming (SBMF), which is being continuously improved and applied within the collaborative research group TR73. For SBMF, non-invasive form finding is used to optimize the shape of semi-finished products, which is adapted to the forming process a priori, as it is general practice for tailored blanks. The node-based, non-invasive algorithm minimizes the differences between the spatial configuration and the prescribed discretized target configuration by updating the material configuration iteratively up to the optimum semi-finished product geometr
Keywords: Form finding; Inverse problems; Metal forming; Non-invasive methods; Shape Opitmization; H-adaptivity

Impact of the unimodal molar mass distribution on the mechanical behavior of polymer nanocomposites below the glass transition temperature: A generic, coarse-grained molecular dynamics study - Ries, Maximilian; Laubert, Lukas; Steinmann, Paul; Pfaller, Sebastian (European Journal of Mechanics A-Solids, 2024)
Polymer nanocomposites (PNCs) have shown great potential to meet the ever-growing requirements of modern engineering applications. Nowadays, molecular dynamics (MD) simulations are increasingly employed to complement experimental work and thereby gain a deeper understanding of the complex structure–property relations of PNCs. However, with respect to the thermoplastic's mechanical behavior, the role of its average molar mass M¯n is rarely addressed, and many MD studies only consider uniform (monodispersed) polymers. Therefore, this contribution investigates the impact that M¯n and the dispersity Đ have on the stiffness and strength of PNCs through coarse-grained MD. To this end, we employed a Kremer–Grest bead–spring model and observed the expected increase in the mechanical performance of the neat polymer for larger M¯n. Our results indicated that the unimodal molar mass distribution does not impact the mechanical behavior in the investigated dispersity range 1.0≤Đ≤1.09. For the PNC, we obtained the same M¯n-dependence and Đ-independence of the mechanical properties over a wide range of filler sizes and contents. This contribution proves that even simple MD models can reproduce the experimentally well researched effect of the molar mass. Hence, this work is an important step in understanding the complex structure–property relations of PNCs, which is essential to unlock their full potential.
CRIS-Team Scopus Importer:2024-07-12
Keywords: Coarse graining; Glassy polymer; Mechanical properties; Molar mass distribution; Molecular dynamics; Polymer nanocomposites

Implementation of generalized mechanical interfaces - Spannraft, Lucie; Mergheim, Julia; Steinmann, Paul (Proceedings in Applied Mathematics and Mechanics, 2019)
For an accurate approximation of the mechanical behavior of interfaces undergoing tension, shear and in‐plane stretch deformation, the definition of an appropriate interface constitutive model is crucial. Distinct interface models, such as cohesive zone models are well investigated. However, only little research considering energetic interface models, especially inelastic models, and generalized mechanical interfaces is conducted. Although multiple possibilities to apply cohesive zone models in commercial software exist, to the authors' knowledge, the material properties provided are generally limited by basic cohesive laws and any definition of energetic interface models lacks. In order to benefit from the advantages of commercial FE software, a generalized mechanical interface model is implemented in ABAQUS. The employed constitutive model combines a cohesive zone model with an energetic interface model.<br

Implementation of Parameterized Work Piece Deviations and Measurement Uncertainties into Performant Meta-models for an Improved Tolerance Specification - Müller, Andreas; Oberleiter, Thomas; Willner, Kai; Hausotte, Tino (Proceedings of the Design Society: International Conference on Engineering Design, 2019)
Geometrical work piece deviations are unavoidable and directly affect the function and quality of technological products. Tolerance management is regarded as a crucial subtask of the development of technological products, because it ensures the function as well as a sufficient product quality while maintaining reasonable production costs. That means, that geometric tolerances as an essential part of the product description greatly affect the functional capability, manufacturability, mountability, verifiability and the costs of the final product. The research group FOR 2271 was founded to enable the computer-aided specification of tolerances, which meet the requirements of production, assembly, verification and function by close cooperation between the departments responsible for product design, assembly and metrology. The aim of this contribution is to determine the manufacturing process scatter as well as the measurement uncertainty and establish ways and means to include that information into efficient meta-models, ultimately enabling improved and accurate tolerance analyse
Keywords: Tolerance representation and management; Uncertainty; Product modelling / models

Implementierung und Anpassung eines Materialmodells für FE-Simulationen in der Blechmassivumformung. Colloquium on metal forming - Schmaltz, Stefan; Willner, Kai (Proceedings of XXXII. Colloquium on metal forming, 2013)
UnivIS-Import:2015-04-16:Pub.2013.tech.FT.FT-TM.implem_9

Improvements on a non-invasive, parameter-free approach to inverse form finding - Landkammer, Philipp; Caspari, Michael; Steinmann, Paul (Computational Mechanics, 2018)
Our objective is to determine the optimal undeformed workpiece geometry (material configuration) within forming processes when the prescribed deformed geometry (spatial configuration) is given. For solving the resulting shape optimization problem—also denoted as inverse form finding—we use a novel parameter-free approach, which relocates in each iteration the material nodal positions as design variables. The spatial nodal positions computed by an elasto-plastic finite element (FE) forming simulation are compared with their prescribed values. The objective function expresses a least-squares summation of the differences between the computed and the prescribed nodal positions. Here, a recently developed shape optimization approach (Landkammer and Steinmann in Comput Mech 57(2):169–191, 2016) is investigated with a view to enhance its stability and efficiency. Motivated by nonlinear optimization theory a detailed justification of the algorithm is given. Furthermore, a classification according to shape changing design, fixed and controlled nodal coordinates is introduced. Two examples with large elasto-plastic strains demonstrate that using a superconvergent patch recovery technique instead of a least-squares (L2" id="MathJax-Element-1-Frame" role="presentation" style="position: relative;" tabindex="0">L2)-smoothing improves the efficiency. Updating the interior discretization nodes by solving a fictitious elastic problem also reduces the number of required FE iterations and avoids severe mesh distortions. Furthermore, the impact of the inclusion of the second deformation gradient in the Hessian of the Quasi-Newton approach is analyzed. Inverse form finding is a crucial issue in metal forming applications. As a special feature, the approach is designed to be coupled in a non-invasive fashion to arbitrary FE softwar
Keywords: Shape optimization; Inverse problems; Elasto-plasticity; Metal forming; Recovery techniques

Indentation of a Functionally Graded Elastic Solid: Application of an Adhesively Bonded Plate Model - Selvadurai, A.P.S.; Gaul, L.; Willner, Kai (Computational Methods in Contact Mechanics IV, 1999)
UnivIS-Import:2015-04-16:Pub.1999.tech.FT.FT-TM.indent

Influence of elastomeric matrix and particle volume fraction on the mechanical response of magneto-active polymers - Garcia-Gonzalez, Daniel; Moreno Mateos, Miguel Angel; Valencia, Leticia; Arias, Angel; Velasco, Diego (Composites Part B-Engineering, 2021)
Magneto-active polymers (MAPs) are revolutionising the fields of material science and solid mechanics as well as having an important presence in the bioengineering community. These composites consist of a polymeric matrix (i.e., elastomer) filled with magnetic particles (i.e., iron particles). When bonded together, these two phases form a continuum solid that, under the application of an external magnetic field, mechanically reacts leading to changes in shape and volume or/and alterations in its rheological properties. Such a magneto-mechanical response is determined by the material properties of the polymeric matrix and magnetic particles. In this work, we present the mechanical characterisation of MAPs constituted by PDMS filled with carbonyl iron powder (CIP) particles. To this end, sixteen different combinations of elastomeric base/crosslinker mixing ratio (from 5:1 to 20:1) and particles’ volume fraction (from 0% to 30%) are tested under tensile loading. These results are analysed and provide the bases for the formulation of a nonlinear constitutive model that accounts for these dependencies. The modelling approach is extended to incorporate magneto-mechanical effects. Finally, the complete model is used to provide theoretical guidance for magneto-active systems, highlighting potential applications in epithelial wound healing stimulation.
Created from Fastlane, Scopus look-up
Keywords: Constitutive modelling; Crosslinking; Magneto-active polymer (MAP); Magneto-mechanics; Mechanical characterisation; Multifunctional composites

Influence of Fractal Surface Parameters on the Elasto-Plastic Contact Behavior of Rough Surfaces - Willner, Kai (Journal of Tribology, 2008)
In a recent paper (2004, "Elasto-Plastic Normal Contact of Three-Dimensional Fractal Surfaces Using Halfspace Theory," J. Tribol., 126, pp. 28-33) the author developed a halfspace model for the elasto-plastic normal contact of rough surfaces. This model is now used to study the inuence of intrinsic surface pa-rameters on constitutive contact laws, such as load-gap relation and load-area relation, for a specic type of surface topography known as fractal-regular surfaces. Numerical investigations show that the fractal dimension has only minor inuence on the load-gap relationship, which is mostly determined by the dimensionless ratio between the transition length and the rms values of the height data. Due to the fractal nature of the surfaces at the small wavelength limit, initial deformation will always be in the plastic range. The load-area relation becomes then completely independent of the geometric surface parameters and is determined by material properties alone, at least if the predicted plastic defor-mation occurs at a length scale larger than the atomic scale. © 2008 by ASME.
UnivIS-Import:2015-03-09:Pub.2008.tech.FT.FT-TM.influe_1
Keywords: Elasto-plastic contact; Fractal-regular surface; Halfspace theory

Influence of Kinematic Hardening on Clinch Joining of Dual-Phase Steel HCT590X Sheet Metal - Friedlein, Johannes; Mergheim, Julia; Steinmann, Paul (Minerals, Metals and Materials Series, 2022)
Nowadays, clinching is a widely used joining technique, where sheets are joined by pure deformation to create an interlock without the need for auxiliary parts. This leads to advantages such as reduced joining time and manufacturing costs. On the other hand, the joint strength solely relies on directed material deformation, which renders an accurate material modelling essential to reliably predict the joint forming. The formation of the joint locally involves large plastic strains and possibly complex non-proportional loading paths, as typical of many metal forming applications. Consequently, a finite plasticity formulation is utilised incorporating a Chaboche–Rousselier kinematic hardening law to capture the Bauschinger effect. Material parameters are identified from tension–compression tests on miniature specimens for the dual-phase steel HCT590X. The resulting material model is implemented in LS-Dyna to study the locally diverse loading paths and give a quantitative statement on the importance of kinematic hardening for clinching. It turns out that the Bauschinger effect mainly affects the springback of the sheets and has a smaller effect on the joint forming itself.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Bauschinger effect; Clinching; Kinematic hardening; Material modelling; Parameter identification

Influence of magnetic boundary conditions on the quantitative modelling of magnetorheological elastomers - Moreno Mateos, Miguel Angel; Danas, Kostas; Garcia-Gonzalez, Daniel (Mechanics of Materials, 2023)
The complex magneto-mechanical coupling that governs the material response of magnetorheological elastomers (MREs) requires computational tools to assist the design process. Computational models are usually based on finite element frameworks that often simplify and idealise the magnetic source and the associated magnetic boundary conditions (BCs). However, these simplifications may lead to important disagreement between the actual material behaviour and the modelled one, even at the qualitative level. In this work, we provide a comprehensive study on the influence of magnetic BCs and demonstrate the importance of considering them in the overall material-structure modelling strategy. To this end, we implement a magneto-mechanical framework to model the response of soft- and hard-magnetic MREs under magnetic fields generated by an idealised far-field uniform magnetic source, a permanent magnet, a coil system, and an electromagnet with two iron poles. The results unveil remarkable heterogeneities in computed local magnetostriction and magnetic fields depending on the magnetic setup used. A detailed discussion based on material and structural contributions provides a robust, rigorous, and necessary modelling route for future works.
CRIS-Team Scopus Importer:2023-08-11
Keywords: Boundary conditions; Computational mechanics; Magneto-mechanics; Magnetorheological elastomers; Magnetostriction

Influence of plastic orthotropy on clinching of sheet metal - Friedlein, Johannes; Bielak, Christian; Böhnke, Max; Bobbert, Mathias; Meschut, Gerson; Mergheim, Julia; Steinmann, Paul (Materials Research Proceedings, 2023)
Clinching is a versatile mechanical joining method for assembling different sheet metal materials without auxiliary elements in short process times. The joint strength, however, solely relies on the material condition and its targeted interlock formation. Therefore, accurate material models are necessary incorporating all relevant phenomena to reliably predict the material behaviour. We extend a finite elastoplastic material model by incorporating the plastic orthotropy of the sheet metal in the joining process simulation. The anisotropy is captured by different variants of the 3D Hill 1948 yield function with associative and non-associative plastic flow. The constitutive models and the 3D clinching simulation are outlined and utilised to study the influence of plastic orthotropy focusing on the aluminium alloy EN AW-6014.
CRIS-Team Scopus Importer:2023-04-28
Keywords: Anisotropy; Clinching; Modelling

Influence of the Constitutive Contact Law on the Anisotropic Material Parameters of Sheet-Layered Lamination Stacks - Baloglu, Maximilian Volkan; Willner, Kai (2018 8th International Electric Drives Production Conference (EDPC), 2018)
The specific design of components like rotor and stator as sheet-layered lamination stacks results in a structural behavior that is heavily dependent on the sheet interactions on the microscale. Due to the manufacturing process, these thin laminations may be just stacked and held together e.g. by welding or clamps, such that frictional contact of rough surfaces between single sheets is taking place and significantly affects the overall deformation behavior. Here, the elastic anisotropic, more precisely transversely isotropic, material parameters describing these lamination stacks are identified with the help of the homogenization taking efficiently care of the microstructure. For this purpose, different constitutive contact laws in normal direction capturing the sheet interactions by a penalty formulation and their effect on the macroscopic quantities are presented to emphasize the importance of this model parameter. Furthermore, it is shown that the derived stress-strain relation is identical to results of a numerical homogenization, where a representative volume element is simulated by the Finite-Element method incorporating Zero-Thickness elements for the contact simulation. The numerical results are finally compared to experiments showing a good accordance.<br
Keywords: lamination stack; homogenization; constitutive modeling; material modeling; contact mechanics

Insights into the Microstructural Origin of Brain Viscoelasticity - Reiter, Nina; Roy, Biswaroop; Paulsen, Friedrich; Budday, Silvia (Journal of Elasticity, 2021)
Mechanical aspects play an important role in brain development, function, and disease. Therefore, continuum-mechanics-based computational models are a valuable tool to advance our understanding of mechanics-related physiological and pathological processes in the brain. Currently, mainly phenomenological material models are used to predict the be- havior of brain tissue numerically. The model parameters often lack physical interpretation and only provide adequate estimates for brain regions which have a similar microstructure and age as those used for calibration. These issues can be overcome by establishing advanced constitutive models that are microstructurally motivated and account for regional heterogeneities through microstructural parameters. In this work, we perform simultaneous compressive mechanical loadings and microstruc- tural analyses of porcine brain tissue to identify the microstructural mechanisms that under- lie the macroscopic nonlinear and time-dependent mechanical response. Based on experimental insights into the link between macroscopic mechanics and cellular rearrangements, we propose a microstructure-informed finite viscoelastic constitutive model for brain tissue. We determine a relaxation time constant from cellular displacement curves and introduce hyperelastic model parameters as linear functions of the cell density, as determined through histological staining of the tested samples. The model is calibrated using a combination of cyclic loadings and stress relaxation experiments in compression. The presented consider- ations constitute an important step towards microstructure-based viscoelastic constitutive models for brain tissue, which may eventually allow us to capture regional material hetero- geneities and predict how microstructural changes during development, aging, and disease affect macroscopic tissue mechanics.
Keywords: Brain tissue; Finite viscoelasticity; Microstructure; Constitutive modeling; Parameter identification

Insights into the viscohyperelastic response of soft magnetorheological elastomers: Competition of macrostructural versus microstructural players - Lucarini, Sergio; Moreno Mateos, Miguel Angel; Danas, Kostas; Garcia-Gonzalez, Daniel (International Journal of Solids and Structures, 2022)
Magnetorheological elastomers (MREs) are multifunctional composites that consist of an elastomeric matrix filled with magnetic particles. These materials respond to an external magnetic field by mechanically deforming and/or changing their magnetorheological properties. Such a multi-physical response has made them extraordinary candidates for a wide variety of applications in soft robotics and bioengineering. However, there are still some gaps of knowledge that prevent the optimal design and application of these MREs. In this regard, the effect of viscoelastic mechanisms remains elusive from a microstructural perspective. To the best of the authors’ knowledge, this work provides for the first time a numerical homogenization analysis for various magneto-active microstructures accounting for viscous deformation mechanisms. To this end, we propose an incremental variational formulation that incorporates viscoelasticity via internal variables, which is properly modified to deal with the continuity of Maxwell stresses. The proposed framework is applied to study the magneto-mechanical couplings in extremely soft MREs (stiffness < 10 kPa). Such a soft matrix promotes microstructural rearrangements while transmitting internal forces leading to macrostructural synergistic responses. The constitutive parameters are calibrated with experimental tests. The numerical results are accompanied with original magnetostriction tests considering different sample geometries and confined magneto-mechanical tests, reporting the macroscopic response. The results obtained in this work suggest that the effective magneto-mechanical response of the MRE is the outcome of a competition between macrostructural and local microstructural responses, where viscous mechanisms play a relevant role.
Created from Fastlane, Scopus look-up
Keywords: Constitutive modeling; Magnetorheological elastomer (MRE); Microstructural homogenization; Multifunctional composites; Viscoelasticity

In Situ Measurements of Interfacial Contact Pressure During Impact Hammer Tests - Seeger, Benjamin; Butaud, Pauline; Baloglu, Maximilian Volkan; Du, Fei; Brake, Matthew; Schwingshackl, Christoph (Nonlinear Dynamics, Volume 1; Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics 2018, 2018)
Understanding the nonlinear dynamical contact interactions within joints is crucial for understanding and predicting the dynamics of assembled structures. In spite of this, most experimental investigations focused on the global vibration behavior, since the local interactions at the interface cannot be observed with standard techniques. In the present work, an advance contact pressure measurement system is used in a unique way to analyze, in situ, the interfacial contact pressures and the contact area inside a bolted lap joint connecting two beams (Brake-Reuß beam). An important feature of the measurement system is that it is designed for frequency ranges including the typical vibration frequency of the Brake-Reuß beam’s first eigenmode, and thus permits measurement under dynamic excitation. The dynamics of the contact pressures were investigated with different bolt torque levels and with different excitation levels. The experiments found that significant variations of the contact state occurred and that the contact pressure measurement system could adequately resolve this effect. The influence of the measurement system itself on the global vibration response of the Brake-Reuß beam was shown to be tolerable.<br
Keywords: Assembly; Lapjoint; Nonlinear; Experimental; Pressure sensor

Integrating The Mechanical Domain Into Seed Approach - Dworschak, Fabian; Kügler, Patricia; Schleich, Benjamin; Wartzack, Sandro (Proceedings of the 22nd International Conference on Engineering Design (ICED19), 2019)
Data-driven technologies have found their way into all areas of engineering. In product development they can accelerate the customization to individualized requirements. Therefore, they need a database that exceeds common product data management systems. The creation of this database proves to be challenging because in addition to explicit standards and regulations the product design contains implicit knowledge of product developers. Hence, this paper presents an approach for the semantic integration of the engineering design (SeED). The goal is an automated design of an ontology, which represents the product design in detail. SeED fulfils two tasks. First, the ontology provides a machine-processable representation of the products design, which enables all kind of data-driven technologies. Among other representations, the ontology contains formal logics and semantics. Accordingly, it is a more comprehensible solution for product developers and knowledge engineers. Second, the detailed representation enables discovering of intrinsic knowledge, e.g. design patterns in product generations. Consequently, SeED is a novel approach for efficient semantic integration of the product d
Keywords: Semantic data processing; Engineering ontologies; Engineering data acquisition; Implicit knowledge integration

Interface properties influence the effective dielectric constant of composites - Chatzigeorgiou, George; Javili, Ali; Steinmann, Paul (Philosophical Magazine, 2015)
In this work we propose a micromechanics model, based on the composite spheres assemblage method, for studying the electrostatic behaviour of particle and porous composites when the interface between the particle (or the pore) and the matrix has its own independent behaviour. Examples from experimental results in porous media and particle composites are utilized to demonstrate the models capabilities. The current model shows a better agreement with experiments compared with other available studies. Furthermore, it is shown that the interface dielectric constant is independent of the experiments which prove its nature as a material parameter.
CRIS-Team Scopus Importer:2022-08-05
Keywords: coating; electrical properties; fibre/matrix bond; interface; nanocomposites

Introduction of a computational approach for the design of composite structures at the early embodiment design stage - Klein, Daniel; Malezki, Waldemar; Wartzack, Sandro (Proceedings of the 20th International Conference on Engineering Design (ICED15), Vol. 4: Design for X, 27.-30. Juli 2015, Mailand, 2015, S. 11-20., 2015)
UnivIS-Import:2015-10-26:Pub.2015.tech.FT.FT-KLMEFK.introd

Inverse analysis for heterogeneous materials and its application to viscoelastic curing polymers - Klinge, Sandra; Steinmann, Paul (Computational Mechanics, 2015)
This contribution aims at achieving two important goals: First, it outlines a numerical inverse homogenization strategy able to recover material parameters of the microstructure by using results of macroscopic tests. Second, it considers parameter identification for viscoelastic heterogeneous materials, which is a step providing the basis for the further extension toward the general treatment of dissipative processes. The approach proposed couples the Levenberg–Marquardt method with the multiscale finite element method. In this combination, the former is a gradient-based optimization strategy used to minimize a merit function while the latter is a numerical homogenization technique needed to solve the direct problem. The specific example studied in the paper deals with the investigation of a composite consisting of a viscoelastic curing polymer and a nonlinear elastic material. It proposes a three-step procedure for the evaluation of its material parameters and discusses the accuracy and the uniqueness of the solution.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Finite element; Homogenization; Inverse problem; Polymers; Viscoelastic

Inverse form finding with H-adaptivity and an application to a notch stamping process - Caspari, Michael; Landkammer, Philipp; Steinmann, Paul (Proceedings of the 14th International Conference on Computational Plasticity - Fundamentals and Applications, 2017)
The aim is to determine the optimized semi-finished workpiece geometry to its given target geometry after a forming process. Hereby, a novel approach for inverse form finding, a type of a shape optimization, is applied to a notch stamping process. As a special feature, h-adaptive mesh refinement is considered within the iteratively performed forming simulatio
Keywords: H-adaptivity; Inverse form finding; Metal forming; Shape optimization

Inverse identification of region-specific hyperelastic material parameters for human brain tissue - Hinrichsen, Jan; Reiter, Nina; Bräuer, Lars; Paulsen, Friedrich; Käßmair, Stefan; Budday, Silvia (Biomechanics and Modeling in Mechanobiology, 2023)
The identification of material parameters accurately describing the region-dependent mechanical behavior of human brain tissue is crucial for computational models used to assist, e.g., the development of safety equipment like helmets or the planning and execution of brain surgery. While the division of the human brain into different anatomical regions is well established, knowledge about regions with distinct mechanical properties remains limited. Here, we establish an inverse parameter identification scheme using a hyperelastic Ogden model and experimental data from multi-modal testing of tissue from 19 anatomical human brain regions to identify mechanically distinct regions and provide the corresponding material parameters. We assign the 19 anatomical regions to nine governing regions based on similar parameters and microstructures. Statistical analyses confirm differences between the regions and indicate that at least the corpus callosum and the corona radiata should be assigned different material parameters in computational models of the human brain. We provide a total of four parameter sets based on the two initial Poisson’s ratios of 0.45 and 0.49 as well as the pre- and unconditioned experimental responses, respectively. Our results highlight the close interrelation between the Poisson’s ratio and the remaining model parameters. The identified parameters will contribute to more precise computational models enabling spatially resolved predictions of the stress and strain states in human brains under complex mechanical loading conditions.<br

Inverse identification of region-specific hyperelastic material parameters for human brain tissue - Hinrichsen, Jan; Reiter, Nina; Bräuer, Lars; Paulsen, Friedrich; Käßmair, Stefan; Budday, Silvia (Biomechanics and modeling in mechanobiology, 2023)
The identification of material parameters accurately describing the region-dependent mechanical behavior of human brain tissue is crucial for computational models used to assist, e.g., the development of safety equipment like helmets or the planning and execution of brain surgery. While the division of the human brain into different anatomical regions is well established, knowledge about regions with distinct mechanical properties remains limited. Here, we establish an inverse parameter identification scheme using a hyperelastic Ogden model and experimental data from multi-modal testing of tissue from 19 anatomical human brain regions to identify mechanically distinct regions and provide the corresponding material parameters. We assign the 19 anatomical regions to nine governing regions based on similar parameters and microstructures. Statistical analyses confirm differences between the regions and indicate that at least the corpus callosum and the corona radiata should be assigned different material parameters in computational models of the human brain. We provide a total of four parameter sets based on the two initial Poisson’s ratios of 0.45 and 0.49 as well as the pre- and unconditioned experimental responses, respectively. Our results highlight the close interrelation between the Poisson’s ratio and the remaining model parameters. The identified parameters will contribute to more precise computational models enabling spatially resolved predictions of the stress and strain states in human brains under complex mechanical loading conditions.
CRIS-Team Scopus Importer:2023-09-15
Keywords: Finite element method; Finite hyperelasticity; Human brain tissue; Ogden model; Parameter identification

Inverse Parameter Identification for Orthotropic Elasto-Plastic Sheet-Steel - Söhngen, Benjamin; Willner, Kai (Proceedings in Applied Mathematics and Mechanics, 2015)
In this contribution the Finite Element Model Updating (FEMU) approach is utilized to determine the material parameters of sheet-steel. From experimental testing it is observed that the considered cold-rolled steel exhibits orthotropic behaviour. To regard this in the simulation, a user-implemented material model based on a quadratic yield function is used. Via the method of digital image correlation (DIC), the displacement field of a biaxially loaded specimen is measured from images taken at different stages of loading. Comparing the experimentally determined displacements to those obtained by simulation an error measure is defined which can be minimized by optimization algorithms. Starting with initial values for the orthotropic elasto-plastic material parameters, the FEM model is thus updated consecutively until a specified error margin is reached. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinhei
Keywords: Anisotropic Plasticity; Inverse Parameter Identification; FEMU

Inverse parameter identification of an anisotropic plasticity model for sheet metal - Friedlein, Johannes; Wituschek, Simon; Lechner, Michael; Mergheim, Julia; Steinmann, Paul (INTERNATIONAL DEEP-DRAWING RESEARCH GROUP CONFERENCE (IDDRG 2021), 2021)
CRIS-Team WoS Importer:2021-11-05

Investigating different friction models for the stick‐slip effect with nodal contact - Akar, Özge; Willner, Kai (Proceedings in Applied Mathematics and Mechanics, 2021)
Friction is an indispensable phenomenon since it appears in many natural phenomena as well as in industrial applications. Especially the so‐called stick‐slip‐effect in dynamic applications can cause undesirable effects like noise and wear. Hence, it is of great importance to investigate and understand friction in detail in order to avoid those phenomena with negative consequences. The goal of this investigation is to observe a three‐dimensional wire‐like beam clamped on one side and free on the other, that is excited at one node with a constant force. Thereby friction is induced to the system and the stick‐slip‐effect occurs. The Fast Nonlinear Analysis Algorithm is used to solve the nonlinear equation computationally. First, dry friction is simulated varying the number of sliders in the Iwan model and applying different friction distribution models. Viscous and Stribeck friction are included afterwards. The obtained results are compared with respect to the simulation time.<br

Investigating the Modal Behavior of a Violin Top and a Back Plate - Akar, Özge; Willner, Kai (Conference Proceedings of the Society for Experimental Mechanics Series, 2022)
Regarding structural dynamic behavior, the violin is a very versatile entity to study, since it combines many different effects in one single structure. Investigating this instrument means dealing with the uncertainty in natural materials, geometric nonlinearities, many interfaces, and sound radiation. Hence, this multifaceted structure serves as research subject for present work. The study starts with modal analyses of the raw spruce and maple woods, with the intention to show that an a priori material parameter identification is possible. The identified values serve as input for the orthotropic violin plates in the associated finite element model. Using 2D laser scanning vibrometry, the modal parameters are obtained for each plate. The components are supported on soft foams and on cotton wool in order to show the significant deviations in the measurement results with varying foam compliances.
CRIS-Team Scopus Importer:2022-08-26
Keywords: FEM; LDV; Modal; Violin

Investigation of 3D crack propagation problems via fast BEM formulations - Kuhn, Günther; Weber, Wilhelm; Kolk, Karsten (Computational Mechanics, 2005)
The simulation of 3D fatigue crack growth is investigated and in combination with suitable experiments it is aimed to identify a reliable crack growth criterion. To perform the crack growth simulation as effectively as possible the boundary element method (BEM) in terms of the 3D Dual BEM is utilized. The relevant boundary integral equations are evaluated in the framework of a collocation procedure. To compress the system matrix and to speed-up the solution procedure the adaptive cross approximation (ACA) method is applied. It is an algebraic technique acting purely on the system matrix itself. The efficiency of this procedure with respect to crack problems will be shown on both a standard fracture specimen and an industrial application. © Springer-Verlag 2005.
UnivIS-Import:2015-03-09:Pub.2005.tech.FT.FT-TM.invest
Keywords: 3D Crack growth; 3D Dual BEM; ACA; Low-rank approximation

Investigation of a Bolted Friction Resonator in the Frequency Domain - Süß, Dominik; Willner, Kai (Proceedings of the 85th Annual Meeting of the International Association of Applied Mathematics and Mechanics, 2014)
UnivIS-Import:2015-10-26:Pub.2014.tech.FT.FT-TM.invest

Investigation of a jointed friction oscillator using the multiharmonic balance method - Süß, Dominik; Willner, Kai (Mechanical Systems and Signal Processing, 2014)
This paper covers the investigation of a nonlinear jointed structure in the frequency domain. Due to frictional nonlinearities the behavior of that system is approximated using the Multiharmonic Balance Method (MHBM). Two models of different complexity are presented. The first is a simple three degree-of-freedom model which is valid because of the special design of the structure. This model enables a very fast and accurate prediction of the stationary behavior of the real system. In order to attain a more general way of modeling structures including joints, the second model is a Finite Element (FE) model. For the discretization of the contact plane, “Zero Thickness” (ZT) elements are implemented. These elements allow the application of nearly arbitrary constitutive laws for describing the dynamic joint behavior. Here a coupled three dimensional contact law including dry friction effects is applied and the needed partial derivatives for the MHBM procedure are given analytically. Using measurements from the real structure and performing a model updating process, the parameters of the two presented models are estimated. The calculation results are compared to measurements in the frequency as well as in the time domain.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.invest_3
Keywords: Structural dynamics; Bolted joint; Multiharmonic Balance; FEM; Contact element

Investigation of a nonlinear piezoelectric energy harvester with advanced electric circuits with the finite element method - Hegendörfer, Andreas; Steinmann, Paul; Mergheim, Julia (SN Applied Sciences, 2022)
Abstract: In this contribution, a system simulation method based on the finite element method (FEM) is applied to simulate a strongly coupled bimorph piezoelectric vibration-based energy harvester (PVEH) with various nonlinear, non-ideal and active circuits: The standard circuit, the synchronized switch harvesting on inductor circuit and the synchronized electric charge extraction circuit are considered. Furthermore, nonlinear elastic behavior of the piezoelectric material is taken into account and harmonic base excitations of different magnitudes at a fixed frequency are applied. The holistic FEM-based system simulation approach solves the complete set of piezoelectric equations together with the equation of the electric circuit such that all electromechanical coupling phenomena are taken into account. This fully coupled numerical analysis enables the detailed evaluation of the influences of the electric circuits on the vibrational behavior and the harvested energy of the PVEH with respect to the magnitude of base excitation. Results from literature on the efficiency of electric circuits are confirmed and interactions between mechanical and electrical nonlinearities of PVEHs are revealed. Article highlights: System simulations of a mechanically and electrically nonlinear piezoelectric energy harvester are performed using only one software tool.The infuence of electric circuits on the vibration behavior and the effciency of an energy harvester are investigated in detail.Interactions between mechanical and electrical nonlinearities of an energy harvester are revealed.
CRIS-Team Scopus Importer:2022-04-15
Keywords: Coupled problem; Finite element method; Multiphysics simulation; Numerical simulation; Piezoelectric energy harvesting

Investigation of interphase effects in silica-polystyrene nanocomposites based on a hybrid molecular-dynamics-finite-element simulation framework - Pfaller, Sebastian; Possart, Gunnar; Steinmann, Paul; Rahimi, Mohammad; Müller-Plathe, Florian; Böhm, Michael C. (Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2016)
A recently developed hybrid method is employed to study the mechanical behavior of silica-polystyrene nanocomposites (NCs) under uniaxial elongation. The hybrid method couples a particle domain to a continuum domain. The region of physical interest, i.e., the interphase around a nanoparticle (NP), is treated at molecular resolution, while the surrounding elastic continuum is handled with a finite-element approach. In the present paper we analyze the polymer behavior in the neighborhood of one or two nanoparticle(s) at molecular resolution. The coarse-grained hybrid method allows us to simulate a large polymer matrix region surrounding the nanoparticles. We consider NCs with dilute concentration of NPs embedded in an atactic polystyrene matrix formed by 300 chains with 200 monomer beads. The overall orientation of polymer segments relative to the deformation direction is determined in the neighborhood of the nanoparticle to investigate the polymer response to this perturbation. Calculations of strainlike quantities give insight into the deformation behavior of a system with two NPs and show that the applied strain and the nanoparticle distance have significant influence on the deformation behavior. Finally, we investigate to what extent a continuum-based description may account for the specific effects occurring in the interphase between the polymer matrix and the NPs.
EAM Import::2019-03-13

Investigation of jointed structures using the multiharmonic balance method - Süß, Dominik; Willner, Kai; Jerschl, Martin; Jerschl, Martin (Conference Proceedings of the Society for Experimental Mechanics Series, 2013)
This paper deals with the investigation of a jointed structure in the frequency domain. Because of the nonlinearity of most jointed systems the steady state response shall be calculated utilizing the Multiharmonic Balance Method (MHBM). In the framework of this method the response displacements of the system are assumed to be periodic and are approximated by a Fourier-type series expansion considering a limited number of harmonic parts. The MHBM is presented for a system containing a bolted lap joint. For the contacting bodies small deformations and linear elastic material behavior are assumed. The system will be modeled with the Finite Element Method (FEM) using so called Zero Thickness (ZT) elements for discretizing the contact plane. Since this contact area is known and only small relative displacements occur, the suggested contact element is well suited for the present problem. The ZT elements contain a three-dimensional nonlinear contact law considering dry friction effects. A model updating process is used to fit the calculation results with respect to the measured data of a real system. © The Society for Experimental Mechanics, Inc. 2013.
UnivIS-Import:2015-04-16:Pub.2013.tech.FT.FT-TM.invest_5
Keywords: Contact element; FEM; Harmonic balance; Jointed structure; Structural dynamics

Investigation of string motions of bowed string instruments: A finite element approach - Akar, Özge; Willner, Kai (Conference Proceedings of the Society for Experimental Mechanics Series, 2021)
The bowed string motion of violin strings is examined using finite element analysis. The string is modeled as a bar with a finite number of elements, whereas the bow is one single node. The cause of the sound is the stick-slip effect, which occurs at steady bowing of a string. The contact area between the bow node and one string node is modeled as nodal contact. This work aims at investigating the Schelleng Diagram as well as the Guettler diagram. The Schelleng diagram shows bow force over bowing position and identifies the area of normal sound, i.e. the Helmholtz motion (von Helmholtz, Von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik. Vieweg, Braunschweig, 1863), overtone sound and raucous sound, the latter depicts bow force over bow acceleration in order to find a proper parameter configuration for “perfect bowing starts”. The influence of different friction curves of the rosin are modeled and simulated as well, which has been tested and investigated extensively in the literature mainly experimentally, see e.g (Smith, Woodhouse, J Mech Phys Solids 48(8):1633–1681, 2000). An overall research of the finite-element modeling of bowed strings is started with this new simulation and modeling set-up. The numerical results will be compared to experimental results in future work.
Created from Fastlane, Scopus look-up
Keywords: Finite element modeling; Guettler diagram; Helmholtz motion; Schelleng diagram; Stick-slip effect

Investigation of the Helmholtz Motion of a Violin String: A Finite Element Approach - Akar, Özge; Willner, Kai (Journal of Vibration and Acoustics-Transactions of the Asme, 2020)
In the context of this work, a violin string motion is examined using a finite element approach. The string is formulated via ideal string elements and is bowed at one point on the string; hence, there is a nodal contact between the bow and the string. The bow movement induces the stick-slip effect, which is the cause for the violin string sound. The present paper aims at the investigation of the stick-slip phenomenon of bowed strings, considering well-known bowed string effects like the Helmholtz corner modulation, the Schelleng ripples, and the flattening effect. One key element that is used in this work is the Schelleng diagram, which indicates the "perfect" bow force depending on the bowing position. Within these parameters, the Helmholtz motion is carried out. Additionally, different friction characteristic curves are applied in order to study the impact of the rosin on the string motion.
CRIS-Team WoS Importer:2020-10-02

Investigation of the influence of nano-sized particles on the entanglement distribution of a generic polymer nanocomposite using molecular dynamics - Seibert, Jakob; Pfaller, Sebastian; Ries, Maximilian (Mathematics and Mechanics of Solids, 2023)
The addition of nano-sized filler particles to polymers leads to significant improvements in their mechanical properties. These can be traced back to the matrix–filler interactions of the interphase, which can be analyzed using molecular dynamic simulations. Usually, research in this context studies the general number of entanglements or the radius of gyration. However, this publication presents a novel approach by investigating the radial distribution of entanglements in an effort to characterize the interphase. To this end, we employ a coarse-grained model for a generic polymer composite and study multiple systems with varying particle radius and matrix–filler adhesion. Furthermore, the highly customizable and computationally efficient nanocomposite system developed during this research serves as a foundation for the further characterization of polymer nanocomposites and their interphases.
CRIS-Team Scopus Importer:2023-12-15
Keywords: chain entanglement density; distribution functions; interphase; Molecular dynamics; polymer nanocomposite

Investigation of the Mechanical Behavior of Polystyrene using Molecular Dynamics - Ries, Maximilian; Steinmann, Paul; Pfaller, Sebastian (Proceedings in Applied Mathematics and Mechanics, 2019)
Polymer nanocomposites exhibit highly promising material properties caused by their molecular structure. Multiscale techniques are used to gain a deeper understanding of the influence of molecular mechanisms on the macro scale. Especially domain composition coupling approaches, e.g. the Capriccio method [1], require a precise match of the constitutive models of the coupled domains. To this end, in this contribution a methodology to characterize the material behavior of polymers using the widely used Molecular Dynamics approach is presented. Exemplary, polystyrene is investigated as a model system and the results of time proportional and time periodic uniaxial deformation tests as well as relaxation and creep tests are briefly discussed.<br

Investigation of the tribological behaviour of microstructures for controlling the material flow in sheet-bulk metal forming - Löffler, Maria; Engel, Ulf; Willner, Kai; Beyer, Florian; Merklein, Marion (CIRP Journal of Manufacturing Science and Technology, 2018)
Sheet-bulk metal forming (SBMF) processes are characterized by a successive and/or simultaneous occurrence of different load conditions with regard to stress and strain states. These conditions significantly influence the material flow and thus the geometrical accuracy of the produced components. To improve the product quality a control of the material flow is required. A suitable approach is given by a local modification of the tribological conditions using surface modifications of tool or workpiece. To control the material flow, methods to adjust the friction are needed. Within the present study, microstructured workpiece surfaces to reduce the friction are investigated. The aim of the study is the determination of the tribological mechanisms of this kind of surface modifications. To identify the mechanisms a combined experimental and numerical approach was used. The use of such a combined approach revealed that the structure volume and the interaction between different types of structures significantly influence the friction reducing potential of microstructured workpiece surfaces.<br
Keywords: Sheet-bulk metal forming; Tribology; Surface modification; Surface analysis; Modelling

Investigations of the influence of geometrical irregularities and roughness on the normal contact stiffness of joints - Görke, Daniel; Willner, Kai (Proceedings of the 79th Annual Meeting of the International Association of Applied Mathematics and Mechanics, 2008)
UnivIS-Import:2015-04-16:Pub.2008.tech.FT.FT-TM.invest_0

Investigations on residual stress generation in full-forward-extrusion - Landkammer, Philipp; Jobst, Andreas; Kiener, Christoph; Steinmann, Paul; Merklein, Marion (Production Engineering, 2019)
Within cold-forming processes, the influence of forming induced residual stresses is a critical issue regarding the life-time behaviour of the formed components. However, a targeted use of forming-induced residual stresses is also capable to improve the components properties. The rotation-symmetrical full-forward extrusion is used as a reference process to investigate the generation of residual stresses within manufacturing. A novel and generally applicable computational evaluation procedure is introduced, which achieves to compute and visualize the evolution of the residual stress state during the entire forming operation. Simulative results are compared with their experimental counterparts. The near-surface residual stresses in the formed component are evaluated in axial and tangential direction by X-ray diffraction. Indentation tests are used to determine the micro-hardness inside the components and optical instruments quantify geometrical difference
Keywords: Residual stresses· Full-forward-extrusion· Experimental validation· Advanced post processing

Investigations on the polygonal finite element method: Constrained adaptive Delaunay tessellation and conformal interpolants - Kraus, Markus; Rajagopal, Amirtham; Steinmann, Paul (Computers & Structures, 2013)
We present a polygonal finite element method based on constrained adaptive Delaunay tessellation and conformal interpolants on arbitrary polygons. For mesh generation we use the adaptive Delaunay tessellation, an unstructured hybrid tessellation of a scattered point set that minimally covers the proximal space around each point, which is here extended to non-convex domains. Various types of polygonal interpolants are implemented. For the numerical integration of the Galerkin weak form we resort to classical Gaussian quadrature applied on triangular subdomains. The performance and efficiency of the interpolation and implementation are investigated for two dimensional elasticity in a stochastical analysis on random and regular meshes. © 2013 Elsevier Ltd. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.invest
Keywords: Constrained adaptive Delaunay tessellation; Patch test; Polygonal finite element; Polygonal interpolation

Isogeometric Analysis of 2D Gradient Elasticity - Fischer, Paul; Mergheim, Julia; Steinmann, Paul; Mueller, Ralf; Klassen, Markus (Computational Mechanics, 2010)
UnivIS-Import:2015-04-14:Pub.2010.tech.FT.FT-TM.isogeo

Kinematical ‘Balances’* - Steinmann, Paul (Spatial and Material Forces in Nonlinear Continuum Mechanics, 2022)
This chapter applies the formats of the generic balances to the spatial and material tangent, cotangent, and measure maps to formulate what, for the sake of semantic unification, may be called kinematical ‘balances’.
CRIS-Team Scopus Importer:2022-04-15

Kinematics at Singular Sets - Steinmann, Paul (Spatial and Material Forces in Nonlinear Continuum Mechanics, 2022)
This chapter revisits the relevant continuum kinematics at singular sets, i.e. at singular surfaces and at singular curves and points, thereby elaborating on the jumps in the nonlinear deformation maps and their associated tangent, cotangent, and measure maps.
CRIS-Team Scopus Importer:2022-04-15

Kinematics in Bulk Volumes - Steinmann, Paul (Spatial and Material Forces in Nonlinear Continuum Mechanics, 2022)
This chapter recalls the pertinent spatial and material continuum kinematics in bulk volumes, thereby focusing on the nonlinear deformation maps, their associated tangent, cotangent and measure maps, and expresses their compatibility conditions.
CRIS-Team Scopus Importer:2022-04-15

Kinematics on Dimensionally Reduced Smooth Manifolds - Steinmann, Paul (Spatial and Material Forces in Nonlinear Continuum Mechanics, 2022)
This chapter reviews continuum kinematics on dimensionally reduced smooth manifolds, i.e. on boundary surfaces and on boundary curves, with an emphasis on the nonlinear deformation maps and their associated tangent, cotangent, and measure maps.
CRIS-Team Scopus Importer:2022-04-15

Konstitutives Reibgesetz zur Beschreibung und Optimierung von Tailored Surfaces - Henneberg, Johannes; Beyer, Florian; Willner, Kai; Merklein, Marion (23. Umformtechnisches Kolloquium Hannover: Aktuelle Entwicklungen im Bereich der Umformtechnik, 2020)

Kontinuums- und Kontaktmechanik - Willner, Kai (Springer-Verlag, 2003)
UnivIS-Import:2015-04-02:Pub.2003.tech.FT.FT-TM.kontin

Konzept für den MBSE-Einsatz zur automatisierten Individualisierung von komplexen Produkten - Dworschak, Fabian; Zirngibl, Christoph; Schleich, Benjamin; Wartzack, Sandro (Beiträge zum 30. DfX-Symposium, 2019)
Due to increasing market transparency, companies are mainly focusing on development of customized products. In this course, a competitive advantage should be achieved through the automated adaptation of product characteristics. In order to achieve this, development engineers focus primarily on modifying existing designs and refrain from re-running the entire product development process (PDP). However, this approach is primarily limited to the CAD environment. Previous phases of the PDP are not integrated, leading to a lack of traceability and continuity. Media breaks and API conflicts arise which increase costs. In order to make use of this potential, this article shows a concept for integration of all phases of the RFLP approach into a tool for customization of adaptation construction
Keywords: Model Based Systems Engineering; RFLP; Design for X

Kriech- und Kriecherholungsmessungen zur Charakterisierung von Materialien mit langer charakteristischer Zeit - Walter, Bastian; Kaschta, Joachim (Geesthachter Polymertage: Rheologie von Polymeren für Forschung und Anwendung, 2016)

LEFM is agnostic to geometrical nonlinearities arising at atomistic crack tips - Lakshmipathy, Tarakeshwar; Steinmann, Paul; Bitzek, Erik (Forces in Mechanics, 2022)
Various fields such as mechanical engineering, materials science, etc., have seen a widespread use of linear elastic fracture mechanics (LEFM) at the continuum scale. LEFM is also routinely applied to the atomic scale. However, its applicability at this scale remains less well studied, with most studies focusing on non-linear elastic effects. Using a harmonic “snapping spring” nearest-neighbor potential which provides the closest match to LEFM on a discrete lattice, we show that the discrete nature of an atomic lattice leads to deviations from the LEFM displacement field during energy minimization. We propose that these deviations can be ascribed to geometrical nonlinearities since the material does not have a nonlinear elastic response prior to bond breaking. We demonstrate that crack advance and the critical stress intensity factor in an incremental loading scenario is governed by the collectively loaded region, and can not be determined analytically from the properties (max. elongation, max. sustained forc, etc.) of the stressed crack tip bond alone.<br

Lifetime and Degradation of Pre-damaged PV-Modules – Field study and lab testing - Buerhop, Claudia; Wirsching, Sven; Gehre, Simon; Pickel, Tobias; Winkler, Thilo; Bemm, Andreas; Mergheim, Julia; Camus, Christian; Hauch, Jens; Brabec, Christoph (44th IEEE Photovoltaic Specialists Conference, 2017)
The presence of pre-cracked PV-modules in modern PV-plants is well-known. The evolution and actual impact of the cracks on electrical yield under real operation conditions is not yet understood but of great relevance. Established standards cannot reveal the relevant effects. Therefore, a unique threefold analysis is applied: 1) field exposure, 2) using a new accelerated loading test, and 3) Finite Elements (FEM) simulations. For the first time, we present comparative Electroluminescence (EL-) images recorded in the field and during load testing. Crack growth is studied in terms of the monitored weather conditions and the applied load simulating static snow and wind loads.

Macroscopic modelling of the selective beam melting process - Riedlbauer, Daniel-Rouven; Mergheim, Julia; Steinmann, Paul; McBride, Andrew (Proceedings in Applied Mathematics and Mechanics, 2012)
UnivIS-Import:2015-04-16:Pub.2012.tech.FT.FT-TM.macros_9

Macroscopic simulation and experimental measurement of melt pool characteristics in selective electron beam melting of Ti-6Al-4V - Riedlbauer, Daniel-Rouven; Scharowsky, Thorsten; Singer, Robert; Steinmann, Paul; Körner, Carolin; Mergheim, Julia (International Journal of Advanced Manufacturing Technology, 2017)
Selective electron beam melting of Ti-6Al-4V is a promising additive manufacturing process to produce complex parts layer-by-layer additively. The quality and dimensional accuracy of the produced parts depend on various process parameters and their interactions. In the present contribution, the lifetime, width and depth of the pools of molten powder material are analyzed for different beam powers, scan speeds and line energies in experiments and simulations. In the experiments, thin-walled structures are built with an ARCAM AB A2 selective electron beam melting machine and for the simulations a thermal finite element simulation tool is used, which is developed by the authors to simulate the temperature distribution in the selective electron beam melting process. The experimental and numerical results are compared and a good agreement is observed. The lifetime of the melt pool increases linearly with the line energy, whereby the melt pool dimensions show a nonlinear relation with the line energy.
Keywords: Additive manufacturing; Selective electron beam melting; Ti-6Al-4V; Heat transfer simulation; Melt pool characteristics

Magnetic force and torque on particles subject to a magnetic field - Vogel, Franziska Anna; Pelteret, Jean-Paul; Käßmair, Stefan; Steinmann, Paul (European Journal of Mechanics A-Solids, 2014)
Materials that are sensitive to an applied magnetic field are of increased interest and use to industry and researchers. The realignment of magnetizable particles embedded within a substrate results in a deformation of the material and alteration of its intrinsic properties. An increased understanding of the influence of the particles under magnetic load is required to better predict the behaviour of the material. In this work, we examine two distinct approaches to determine the resulting magnetic force and torque generated within a general domain. The two methodologies are qualitatively and quantitatively compared, and we propose scenarios under which one is more suitable for use than the other. We also describe a method to compute the generated magnetic torque. These post-processing procedures utilize results derived from a magnetic scalar-potential formulation for the large deformation magneto-elastic problem. We demonstrate their application in several examples involving a single and two particle system embedded within a carrier matrix. It is shown that, given a chosen set of boundary conditions, the magnetic forces and torques acting on a particle are influenced by its shape, size and location within the carrier.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.magnet
Keywords: Magnetoactive materials; Magnetoelasticity; Finite-element method

Magneto-active polymers: Fabrication, characterisation, modelling and simulation at the micro- and macro-scale - Pelteret, Jean-Paul; Steinmann, Paul (De Gruyter, 2020)
From fabrication to testing and modeling this monograph covers all aspects on the materials class of magneto active polymers. The focus is on computational modeling of manufacturing processes and material parameters. As other smart materials, these elastomers have the ability to change electrical and mechanical properties upon application of magnetic fields. This allows for novel applications ranging from biomedical engineering to mechatronics. First coverage of fabrication processes, characterization tools and methods to model properties of magnetic elastomers. Documents results of ERC grant MOCOPOLY. Rich in multi-physics (electrodynamics, mechanics of soft matter) on a multi-scale.
CRIS-Team Scopus Importer:2020-12-04

Magneto-mechanical system to reproduce and quantify complex strain patterns in biological materials - Moreno Mateos, Miguel Angel; Gonzalez-Rico, Jorge; Nunez-Sardinha, Emanuel; Gomez-Cruz, Clara; Lopez-Donaire, Maria Luisa; Lucarini, Sergio; Arias, Angel; Muñoz-Barrutia, Arrate; Velasco, Diego; Garcia-Gonzalez, Daniel (Applied Materials Today, 2022)
Biological cells and tissues are continuously subjected to mechanical stress and strain cues from their surrounding substrate. How these forces modulate cell and tissue behavior is a major question in mechanobiology. To conduct studies under controlled varying physiological strain scenarios, a new virtually-assisted experimental system is proposed allowing for non-invasive and real-time control of complex deformation modes within the substrates. This approach is based on the use of extremely soft magneto-active polymers, which mimic the stiffness of biological materials. Thus, the system enables the untethered control of biological substrates providing reversible mechanical changes and controlling heterogeneous patterns. Motivated on a deep magneto-mechanical characterization across scales, a multi-physics and multi-scale in silico framework was developed to guide the experimental stimulation setup. The versatility and viability of the system have been demonstrated through its ability to reproduce complex mechanical scenarios simulating local strain patterns in brain tissue during a head impact, and its capability to transmit physiologically relevant mechanical forces to dermal fibroblasts. The proposed framework opens the way to understanding the mechanobiological processes that occur during complex and dynamic deformation states, e.g., in traumatic brain injury, pathological skin scarring or fibrotic heart remodeling during myocardial infarction.
Created from Fastlane, Scopus look-up
Keywords: Biomechanical stimulation; Computational modeling; Magneto-active materials; Mechanobiology; Multifunctional substrates

Magneto-Sensitive Elastomers: An Experimental Point of View - Walter, Bastian; Saxena, Prashant; Kaschta, Joachim; Schubert, Dirk W.; Steinmann, Paul (85th Annual Meeting of the International Association of Applied Mathematics and Mechanics, 2014)

Manufacturing constraints in parameter-free sensitivity-based shape optimization - Schmitt, Oliver; Friederich, Jan; Steinmann, Paul (Proceedings of 1st International Conference on Engineering and Applied Sciences Optimization, 2014)
Structural shape optimization has become an important tool in engineering when it comes to improving components with respect to a given cost function. However, in many applications the designer has to ensure that the optimized part is still manufacturable. This work introduces two approaches on how to handle manufacturing constraints in parameter- free sensitivity-based shape optimization. In the so-called implicit method the set of design nodes is split into two groups of optimization nodes and dependent nodes. The optimization nodes are then handled as design nodes, whereas the dependent nodes are coupled to the optimization nodes in such a way that the manufacturing constraint is fulfilled. By that procedure no additional constraints have to be appended to the optimization problem. When no dependency can be determined additional equality and inequality constraints have to be formulated in terms of the coordinates of the design nodes. In this case the formulation of manufacturing constraints may lead to a large number of inequalities. Since most optimization algorithms are not able to handle highly restricted problems the use of aggregation formulations is investigated.
UnivIS-Import:2015-04-16:Pub.2014.tech.FT.FT-TM.manufa_0
Keywords: Manufacturing constraints; Parameter-free; Sensitivity-based; Shape optimization

Manufacturing constraints in parameter-free shape optimization - Schmitt, Oliver; Friederich, Jan; Steinmann, Paul (PAMM, 2014)
Structural shape optimization has become an important tool for engineers when it comes to improving components with respect to a given goal function. During this process the designer has to ensure that the optimized part stays manufacturable. Depending on the manufacturing process several requirements could be relevant such as demolding or different kinds of symmetry. This work introduces two approaches on how to handle manufacturing constraints in parameter-free shape optimization. In the so–called explicit approach equality and inequality equations are formulated using the coordinates of the FE-nodes. These equations can be used to extend the optimization problem. Since the number of the additional constraint equations may be very large we apply aggregation formulations, e.g. the Kreisselmeier-Steinhauser function, if necessary. In the second approach, the so–called implicit method, the set of design nodes is split in two groups called optimization nodes and dependent nodes. The optimization nodes are now handled as design nodes but the dependent nodes are coupled to the optimization nodes in such a way that the manufacturing constraint is fulfilled. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
UnivIS-Import:2015-04-16:Pub.2014.tech.FT.FT-TM.manufa_3

Material model identification for DC04 based on the numerical modelling of the polycrystalline microstructure and experimental data - Lehmann, Eva; Schmaltz, Stefan; Germain, Sandrine; Fassmann, Dennis; Weber, Christoph; Loehnert, Stefan; Schaper, Mirko; Bach, Friedrich-Wilhelm; Steinmann, Paul; Willner, Kai; Wriggers, Peter (15th ESAFORM Conference Proceeding, 2012)
Sheet-bulk-metal forming processes require an accurate material model which is derived in this contribution. The microscopic model is based on a simulation of a real microstructure. A validation on the macroscopical scale is performed through the reproduction of the experimentally calculated yield surface based on the homogenised structural response of a corresponding deformed representative volume element (RVE). The microstructural material model is also compared with a macroscopical phenomenological model based on logarithmic strains. The homogenised microscopic model and the phenomenological macroscopic model are in good agreement with the evolution of the stresses and strains obtained during the experiments.© (2012) Trans Tech Publications.
UnivIS-Import:2015-04-16:Pub.2012.tech.FT.FT-TM.materi
Keywords: Anisotropic finite elastoplasticity; Homogenisation; Material modelling; Sheet-bulk-metal forming

Material modelling and parameter identification for sheet-bulk metal forming - Schmaltz, Stefan; Willner, Kai (Proceedings of the XII International Conference on Computational plasticity - Fundamentals and Applications, 2013)
In this paper an anisotropic material model at finite strain is implemented and utilised in a commercial Finite Element Software via a User-Subroutine. The material model is based on an additive split of the logarithmic strains to model the anisotropic finite strain behaviour of the material. The material parameters of the non-linear hardening and the orthotropic anisotropy are identified through an inverse Finite Element Model Updating procedure and verified with experimental testing. The chosen material is a sheet steel, which has a low initial yield strength and a high hardening capacity and therewith is typically used in deep-drawing and sheet-bulk metal forming processes.
UnivIS-Import:2015-04-16:Pub.2013.tech.FT.FT-TM.materi_6
Keywords: Anisotropy; Computational plasticity; FEMU; Parameter identification; Sheet-bulk metal forming

Material modelling of a sheet-layered lamination stack by homogenization - Baloglu, Maximilian Volkan; Willner, Kai (Proceedings in Applied Mathematics and Mechanics, 2016)
In electrical machines, sheet-layered lamination stacks play an important role for the mechanical behavior of the system. Especially the interlayer between individual sheets and their interaction have a severe influence on the structure. In the context of performance and computational effort, it is desirable to avoid a full FE simulation of a lamination stack with every single sheet. Therefore, homogenization techniques are presented to identify a transversely isotropic surrogate material model, while Zero-Thickness elements are utilized during this process to cover the interplay of single sheets. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
Keywords: lamination stack; numerical homogenization; material modelling; contact mechanics

Material Parameter Identification utilizing Optical Full-Field Strain Measurement and Digital Image Correlation - Schmaltz, Stefan; Willner, Kai (Proc. of ISEM-ACEM-SEM-7th ISEM12-Taipei Conference, (2012, 2012)
UnivIS-Import:2015-04-16:Pub.2012.tech.FT.FT-TM.materi_2

Material parameter optimization utilizing full-field strain measurement data and the Finite Element Method - Schmaltz, Stefan; Willner, Kai (Verformungskundliches Kolloquium Konferenz: XXXI, 2012)
UnivIS-Import:2015-04-16:Pub.2012.tech.FT.FT-TM.materi_8

Matrix-Free Locally Adaptive Finite Element Solution of Density-Functional Theory With Nonorthogonal Orbitals and Multigrid Preconditioning - Davydov, Denis; Heister, Timo; Kronbichler, Martin; Steinmann, Paul (physica status solidi (b), 2018)
In this paper, we propose a new numerical method to find the ground state energy of a given physical system within the Kohn–Sham density functional theory. The h-adaptive finite element method is adopted for spatial discretization and implemented with matrix-free operator evaluation. The ground state energy is found by performing unconstrained minimization with non-orthogonal orbitals using the limited memory Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. A geometric multigrid preconditioner is applied to improve the convergence. The clear advantage of the proposed approach is demonstrated on selected examples by comparing the performance to other methods such as preconditioned steepest descent minimization. The proposed method provides a solid framework toward (Formula presented.) (N) complexity for the locally adaptive real-space solution of density functional theory with finite elements.
CRIS-Team Scopus Importer:2022-08-05
Keywords: adaptive finite element method; density functional theory; geometric multigrids; matrix-free; quasi-Newton method

Mean zero artificial diffusion for stable finite element approximation of convection in cellular aggregate formation - Firooz, Soheil; Reddy, B. Daya; Zaburdaev, Vasily; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2024)
We develop and implement finite element approximations for the coupled problem of cellular aggregate formation. The equation governing evolution of cell density is convective in nature, necessitating a modification of standard approaches to circumvent the instabilities associated with standard finite element approximations. To this end, a novel mean zero artificial diffusion approach is proposed, in which the classical artificial diffusion term is replaced by one that is orthogonal to its projection on to continuous functions. The resulting approach for the convective equation is shown to be well-posed. A range of numerical results illustrate the stability and accuracy of the new approach, and its behaviour in comparison with an alternative approach using Taylor–Hood elements. The results also provide insights into the behaviour of cellular aggregates in the context of the model studied here.<br
Keywords: Convection–diffusion problems; Artificial diffusion; Convection-dominated problems; Taylor–Hood elements; Stable solutions

Measured and Simulated Contact Stiffness of Dry, Metallic Joints - Görke, Daniel; Willner, Kai (Extended Abstract in Proceedings of the 8th. World Congress on Computational Mechanics, 2008)
UnivIS-Import:2015-04-16:Pub.2008.tech.FT.FT-TM.measur

Mechanical Balances - Steinmann, Paul (Spatial and Material Forces in Nonlinear Continuum Mechanics, 2022)
This chapter details the generic balances for the case of mechanical balances of mass, spatial momentum, and its vector and scalar moment, respectively, with emphasis on their global and local formats and the distinction between material and spatial control volumes.
CRIS-Team Scopus Importer:2022-04-15

Mechanical behavior of the hippocampus and corpus callosum: An attempt to reconcile ex vivo with in vivo and micro with macro properties - Bertalan, Gergerly; Becker, Julia; Tzschätzsch, Heiko; Morr, Anna; Herthum, Helge; Shahryari, Mehrgan; Greenhalgh, Ryan D.; Guo, Jing; Schröder, Leif; Alzheimer, Christian; Budday, Silvia; Franze, Kristian; et al. (Journal of the Mechanical Behavior of Biomedical Materials, 2023)
Mechanical properties of brain tissue are very complex and vary with the species, region, method, and dynamic range, and between in vivo and ex vivo measurements. To reconcile this variability, we investigated in vivo and ex vivo stiffness properties of two distinct regions in the human and mouse brain - the hippocampus (HP) and the corpus callosum (CC) - using different methods. Under quasi-static conditions, we examined ex vivo murine HP and CC by atomic force microscopy (AFM). Between 16 and 40Hz, we investigated the in vivo brains of healthy volunteers by magnetic resonance elastography (MRE) in a 3-T clinical scanner. At high-frequency stimulation between 1000 and 1400Hz, we investigated the murine HP and CC ex vivo and in vivo with MRE in a 7-T preclinical system. HP and CC showed pronounced stiffness dispersion, as reflected by a factor of 32–36 increase in shear modulus from AFM to low-frequency human MRE and a 25-fold higher shear wave velocity in murine MRE than in human MRE. At low frequencies, HP was softer than CC, in both ex vivo mouse specimens (p < 0.05) and in vivo human brains (p < 0.01) while, at high frequencies, CC was softer than HP under in vivo (p < 0.01) and ex vivo (p < 0.05) conditions. The standard linear solid model comprising three elements reproduced the observed HP and CC stiffness dispersions, while other two- and three-element models failed. Our results indicate a remarkable consistency of brain stiffness across species, ex vivo and in vivo states, and different measurement techniques when marked viscoelastic dispersion properties combining equilibrium and non-equilibrium mechanical elements are considered.
CRIS-Team Scopus Importer:2023-01-06
Keywords: AFM; Atomic force microscopy; Brain tissue; Corpus callosum; Hippocampus; MR elastography; MRE; Viscoelasticity; White matter

Mechanical Behaviour of a Cellular Composite under Quasi-Static, Static and Cyclic Compression Loading - Diel, Sergej; Huber, Otto; Saage, Holger; Steinmann, Paul; Winter, Werner (Journal of Materials Science, 2012)
The quasi-static, static, and cyclic compressive behavior of a novel epoxy matrix cellular composite reinforced with glass foam granules is investigated. Three different grain-size fractions of the granules are used: 0.5-1, 1-2, and 2-4 mm. The density of the cellular composite varies between 0.65 and 0.82 g/cm 3. The material exhibits high specific compressive strength and stiffness within the class of cellular materials; these properties can be varied using appropriate size of granules. The glass foam granules increase the stiffness of the cellular composite compared to neat epoxy foam with the same weight. The measured elastic properties are in good agreement with results obtained from analytical and numerical homogenization methods. The fatigue behavior is determined in static tests and in cyclic tests at 1 and 20 Hz on one type of cellular composite. The fatigue process for cyclic loading is a result of an interaction between static and cyclic damage. The sensitivity to static damage is found to be higher than to cyclic damage. The damage behavior is investigated by evaluation specimen's stiffness and using scanning electron microscopy. © Springer Science+Business Media, LLC 2012.
UnivIS-Import:2015-03-09:Pub.2012.tech.FT.FT-TM.mechan_5

Mechanical characterization of human brain tissue - Budday, Silvia; Sommer, Gerhard; Birkl, Christoph; Langkammer, Christian; Haybaeck, Johannes; Kohnert, Julius; Bauer, Melanie; Paulsen, Friedrich; Steinmann, Paul; Kuhl, Ellen; Holzapfel, Gerhard A. (Acta Biomaterialia, 2017)
Mechanics are increasingly recognized to play an important role in modulating brain form and function. Computational simulations are a powerful tool to predict the mechanical behavior of the human brain in health and disease. The success of these simulations depends critically on the underlying constitutive model and on the reliable identification of its material parameters. Thus, there is an urgent need to thor- oughly characterize the mechanical behavior of brain tissue and to identify mathematical models that cap- ture the tissue response under arbitrary loading conditions. However, most constitutive models have only been calibrated for a single loading mode. Here, we perform a sequence of multiple loading modes on the same human brain specimen – simple shear in two orthogonal directions, compression, and tension – and characterize the loading-mode specific regional and directional behavior. We complement these three indi- vidual tests by combined multiaxial compression/tension-shear tests and discuss effects of conditioning and hysteresis. To explore to which extent the macrostructural response is a result of the underlying microstructural architecture, we supplement our biomechanical tests with diffusion tensor imaging and histology. We show that the heterogeneous microstructure leads to a regional but not directional depen- dence of the mechanical properties. Our experiments confirm that human brain tissue is nonlinear and vis- coelastic, with a pronounced compression-tension asymmetry. Using our measurements, we compare the performance of five common constitutive models, neo-Hookean, Mooney-Rivlin, Demiray, Gent, and Ogden, and show that only the isotropic modified one-term Ogden model is capable of representing the hyperelastic behavior under combined shear, compression, and tension loadings: with a shear modulus of 0.4–1.4 kPa and a negative nonlinearity parameter it captures the compression-tension asymmetry and the increase in shear stress under superimposed compression but not tension. Our results demonstrate that material parameters identified for a single loading mode fail to predict the response under arbitrary loading conditions. Our systematic characterization of human brain tissue will lead to more accurate com- putational simulations, which will allow us to determine criteria for injury, to develop smart protection sys- tems, and to predict brain development and disease progression.
Keywords: Human brain; Mechanical testing; Hyperelastic modeling; Mooney Rivlin model; Ogden model

Mechanical Interphases in Adhesives. Experiment, Modelling and Simulation - Possart, Gunnar (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2014)
UnivIS-Import:2016-07-26:Pub.2014.tech.FT.FT-TM.mechan

Mechanical, microstructural and in-situ neutron diffraction investigations of equi-biaxial Bauschinger effects in an interstitial-free DC06 steel - Härtel, Markus; Illgen, Christian; Panzner, Tobias; Bruder, Enrico; Schmaltz, Stefan; Van Petegem, Steven; Willner, Kai; Durst, Karsten; Van Swygenhoven, Helena; Wagner, Martin F.X. (International Journal of Plasticity, 2022)
Bauschinger effects typically describe a reduction of yield strength after a load path change under uniaxial loading conditions. Here, we use in-plane loading to investigate, for the first time, Bauschinger effects in the sheet metal DC06 under well-defined equi-biaxial loading conditions: We first performed equi-biaxial tensile tests with cruciform specimens up to different maximum tensile strains. Then, smaller specimens were prepared from the equi-biaxially deformed inner part of the cruciform specimens and subjected to equi-biaxial compression. The mechanical results show that the material exhibits distinct Bauschinger effects when subjected to equi-biaxial load path changes, which differ from similar observations under uniaxial loading. Specifically, biaxial Bauschinger effect factors quickly reach a level of saturation, whereas the uniaxial Bauschinger effect factors keep decreasing. These Bauschinger effects can be rationalized by considering the results of TEM and EBSD investigations at the different stages of biaxial loading, particularly by considering the evolution of dislocation densities and the formation of substructures, which are related to intergranular and intragranular stresses. Furthermore, residual stress measurements by XRD and in-situ neutron diffraction show an increase of compressive residual stresses after equi-biaxial tensile deformation and unloading. These residual stresses facilitate yielding during subsequent equi-biaxial compression and therefore also clearly contribute to the observed Bauschinger effects.
CRIS-Team Scopus Importer:2022-12-23

Mechanical properties of cell- and microgel bead-laden oxidized alginate-gelatin hydrogels - Distler, Thomas; Kretzschmar, Lena; Schneidereit, Dominik; Girardo, Salvatore; Goswami, Ruchi; Friedrich, Oliver; Detsch, Rainer; Guck, Jochen; Boccaccini, Aldo R.; Budday, Silvia (Biomaterials Science, 2021)
3D-printing technologies, such as biofabrication, capitalize on the homogeneous distribution and growth of cells inside biomaterial hydrogels, ultimately aiming to allow for cell differentiation, matrix remodeling, and functional tissue analogues. However, commonly, only the mechanical properties of the bioinks or matrix materials are assessed, while the detailed influence of cells on the resulting mechanical properties of hydro- gels remains insufficiently understood. Here, we investigate the properties of hydrogels containing cells and spherical PAAm microgel beads through multi-modal complex mechanical analyses in the small- and large- strain regimes. We evaluate the individual contributions of different filler concentrations and a non-fibrous oxi- dized alginate-gelatin hydrogel matrix on the overall mechanical behavior in compression, tension, and shear. Through material modeling, we quantify parameters that describe the highly nonlinear mechanical response of soft composite materials. Our results show that the stiffness significantly drops for cell- and bead concen- trations exceeding four million per milliliter hydrogel. In addition, hydrogels with high cell concentrations (≥6 mio ml−1) show more pronounced material nonlinearity for larger strains and faster stress relaxation. Our findings highlight cell concentration as a crucial parameter influencing the final hydrogel mechanics, with implications for microgel bead drug carrier-laden hydrogels, biofabrication, and tissue engineering.

Mechanical properties of gray and white matter brain tissue by indentation - Budday, Silvia; Nay, Richard; de Rooij, Rijk; Steinmann, Paul; Wyrobek, Thomas; Ovaert, Timothy; Kuhl, Ellen (Journal of the Mechanical Behavior of Biomedical Materials, 2015)
UnivIS-Import:2015-07-08:Pub.2015.tech.FT.FT-TM.mechan

Mechanische Aspekte bei der Entwicklung künstlicher Herzklappen - Bolz, Armin; Schaldach, Max; Winter, Werner (Biomedizinische Technik, 1990)
UnivIS-Import:2015-03-05:Pub.1990.tech.FT.FT-TM.mechan

Mechanisms of residual stress generation in full-forward-extrusion - Landkammer, Philipp; Jobst, Andreas; Kiener, Christoph; Steinmann, Paul; Merklein, Marion (Production Engineering, 2019)
LFT Import::2019-07-29 (2366)

Memory-based meso-scale modeling of Covid-19 - Kergaßner, Andreas; Burkhardt, Christian; Lippold, Dorothee; Kergaßner, Matthias; Pflug, Lukas; Budday, Dominik; Steinmann, Paul; Budday, Silvia (Computational Mechanics, 2020)
The COVID-19 pandemic has lead to an unprecedented world-wide effort to gather data, model, and understand the viral spread. Entire societies and economies are desperate to recover and get back to normality. However, to this end accurate models are of essence that capture both the viral spread and the courses of disease in space and time at reasonable resolution. Here, we combine a spatially resolved county-level infection model for Germany with a memory-based integro-differential approach capable of directly including medical data on the course of disease, which is not possible when using traditional SIR-type models. We calibrate our model with data on cumulative detected infections and deaths from the Robert-Koch Institute and demonstrate how the model can be used to obtain county- or even city-level estimates on the number of new infections, hospitality rates and demands of intensive care units. We believe that the present work may help guide decision makers to locally fine-tune their expedient response to potential new outbreaks in the near future.<br

Mesoscopic modelling of additively manufactured Inconel 718 - Kergaßner, Andreas; Mergheim, Julia; Steinmann, Paul (Proceedings 6th International Conference on Additive Technologies - iCAT2016, 2016)
In additive manufacturing complex parts are built from thin layers of powder material. In selective electron beam melting (SEBM), the powder is fused by the energy of an electron beam. The electron beam is guided by electromagnetic fields allowing a very fast deflection, and thus various scan strategies. By using these scan strategies, it is possible to influence the resulting mesostructure in the material, which may range from a columnar to an equiaxed grain structure. Different macroscopic mechanical properties are expected for altered grain structures. Long and oriented grains cause highly anisotropic behaviour and a uniform grain structure results in isotropic mechanical behaviour. In this contribution the macroscopic material behaviour is simulated by means of mesoscopic Finite Element simulations. A Voronoi tessellation method is used to model the grain structure of equiaxed Inconel 718. The thermo-mechanical behaviour is modelled using a thermo gradient crystal plasticity model on the mesoscale. Computational homogenization is used to identify temperature-dependent macroscopic mechanical parameters which are compared with experimental result
Keywords: Gradient crystal plasticity; Inconel 718; Columnar grains

Metallschaumverbundstrukturen - Prozesstechnologie und werkstoffmechanische Analyse - Ströhla, Stefan; Winter, Werner; Kuhn, Günther; Brunnbauer, Mathias; Hirschmann, Markus; Körner, Carolin; Singer, Robert; Dörfler, Stephan Manuel; Otto, Andreas (Robuste verkürzte Prozessketten für flächige Leichtbauteile, Industriekolloquium 2003 des SFB 396, 2003)
UnivIS-Import:2015-04-16:Pub.2003.tech.FT.FT-TM.metall

Methoden zur Reduzierung und Berücksichtigung der Unsicherheiten von dimensionellen Messgrößen in der Toleranzanalyse - Müller, Andreas; Heling, Björn; Schleich, Benjamin; Oberleiter, Thomas; Willner, Kai; Wartzack, Sandro; Hausotte, Tino (Industriekolloquium der Forschergruppe FOR 2271, 2019)

Micro-Macro Characterisation of DGEBA-Based Epoxies on the Way to Polymer Interphase Modelling - Possart, Gunnar; Steinmann, Paul; Presser, Melanie; Passlack, Sven; Geiß, Paul L.; Kopnarski, Michael; Brodyanski, Alexander (International Journal of Adhesion and Adhesives, 2009)
UnivIS-Import:2015-03-09:Pub.2009.tech.FT.FT-TM.microm

Micromechanics modeling of magneto-sensitive polymeric materials during curing - Chatzigeorgiou, George; Mokarram, Hossain; Meraghni, Fodil; Steinmann, Paul (ICCM International Conferences on Composite Materials, 2015)
This work proposes a coupled magneto-mechanical multi-scale model for simulating the curing process of magneto-sensitive polymers. In this type of composites, ferromagnetic particles are mixed with a liquid polymeric matrix in the uncured stage. The polymer curing process is a complex mechanism that transforms a fluid to a solid with time. In order to identify the overall response of the magneto-mechanically coupled polymeric composite, an extended Mori-Tanaka semi-analytical homogenization procedure is utilized that tranfers information from the micro to the macroscale. The stiffness gaining phenomenon as in the case of a curing process is realized by time-dependent material parameters appearing within the polymer piezomagnetic material tensors. Moreover, the volume reduction during curing is taken into account through a magnetic induction dependent shrinkage model. Several numerical examples illustrate the model capability to capture major observable phenomena in the curing process of polymeric composites under infinitesimal deformations and magnetic field.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Curing; Magneto-mechanics; Magneto-sensitive polymers; Mori-Tanaka; Shrinkage

Micromotion of Dental Implants: Basic Mechanical Considerations - Winter, Werner; Klein, Daniel; Karl, Matthias (Journal of Medical Engineering, 2013)
Micromotion of dental implants may interfere with the process of osseointegration. Using three different types of virtual biomechanical models, varying contact types between implant and bone were simulated, and implant deformation, bone deformation, and stress at the implant-bone interface were recorded under an axial load of 200 N, which reflects a common biting force. Without friction between implant and bone, a symmetric loading situation of the bone with maximum loading and displacement at the apex of the implant was recorded. The addition of threads led to a decrease in loading and displacement at the apical part, but loading and displacement were also observed at the vertical walls of the implants. Introducing friction between implant and bone decreased global displacement. In a force fit situation, load transfer predominantly occurred in the cervical area of the implant. For freshly inserted implants, micromotion was constant along the vertical walls of the implant, whereas, for osseointegrated implants, the distribution of micromotion depended on the location. In the cervical aspect some minor micromotion in the range of 0.75 μm could be found, while at the most apical part almost no relative displacement between implant and bone occurred.
UnivIS-Import:2015-04-14:Pub.2013.tech.FT.FT-KLMEFK.microm

Microscale modeling and homogenization of rope-like textiles - Fillep, Sebastian; Mergheim, Julia; Steinmann, Paul (Proc. Appl. Math. Mech., 2014)
UnivIS-Import:2015-10-26:Pub.2014.tech.FT.FT-TM.micros

Microscale modelling and homogenization of fiber structured materials - Fillep, Sebastian; Steinmann, Paul (Proceedings of Applied Mathematics and Mechanics (PAMM), 2011)
UnivIS-Import:2015-04-16:Pub.2011.tech.FT.FT-TM.micros_4

Micro-to-macro transition accounting for general imperfect interfaces - Javili, Ali; Steinmann, Paul; Mosler, Joern (Computer Methods in Applied Mechanics and Engineering, 2017)
The objective of this contribution is to establish a micro-to-macro transition framework to study the behavior of heterogeneous materials whereby the influence of interfaces at the microscale is taken into account. The term ``interface'' refers to a zero-thickness model that represents the finite thickness ``interphase'' between the constituents of the micro-structure. For geometrically equivalent samples, due to increasing area-to-volume ratio with decreasing size, interfaces demonstrate a more pronounced effect on the material response at small scales. A remarkable outcome is that including interfaces introduces a length-scale and our interface-enhanced computational homogenization captures a size effect in the material response even if linear prolongation conditions are considered. Furthermore, the interface model in this contribution is general imperfect in the sense that it allows for both jumps of the deformation as well as for the traction across the interface. Both cohesive zone model and interface elasticity theory can be derived as two limit cases of this general model. We establish a consistent computational homogenization scheme accounting for general imperfect interfaces. Suitable boundary conditions to guarantee meaningful averages are derived. Clearly, this general framework reduces to classical computational homogenization if the effect of interfaces is ignored. Finally, the proposed theory is elucidated via a series of numerical examples.
EAM Import::2019-03-12

Micro-to-macro transitions for continua with surface structure at the microscale - Javili, Ali; McBride, Andrew Trevor; Mergheim, Julia; Steinmann, Paul; Schmidt, Ulrike (International Journal of Solids and Structures, 2013)
A geometrically non-linear framework for micro-to-macro transitions is developed that accounts for the effect of size at the microscopic scale. This is done by endowing the surfaces of the microscopic features with their own (energetic) structure using the theory of surface elasticity. Following a standard first-order ansatz on the microscopic motion in terms of the macroscopic deformation gradient, a Hill-type averaging condition is used to link the two scales. The surface elasticity theory introduces two additional microscopic length scales: the ratio of the bulk volume to the energetic surface area, and the ratio of the surface and bulk Helmholtz energies. The influence of these microscopic length scales is elucidated via a series of numerical examples performed using the finite element method. © 2013 Elsevier Ltd. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.microt
Keywords: Homogenization; Nanomaterials; Size effects; Surface elasticity

Micro-to-macro transitions for heterogeneous material layers accounting for in-plane stretch - McBride, Andrew; Mergheim, Julia; Javili, Ali; Steinmann, Paul; Bargmann, Swantje (Journal of the Mechanics and Physics of Solids, 2012)
The computational micro-to-macro transition framework couples heterogeneities on the microscopic scale to the macroscopic response of a continuum. The objective here is to apply this framework to macroscopic material layers capable of undergoing an in-plane stretch in addition to the normal opening mode. This is achieved using the continuum interface theory of Gurtin and Murdoch (1975) which endows the interface with its own energetic structure. The relation of the macroscopic kinematic descriptors of the interface deformation to the averaged underlying microscopic quantities is consistently derived using the Hill-type averaging theorem. Key features of the theory are elucidated using a series of three-dimensional numerical examples.
UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.microt
Keywords: Micro-to-macro transitions; Microstructures; Constitutive behaviour; Finite elements

Modeling and simulation of curing and damage in thermosetting adhesives - Mergheim, Julia; Possart, Gunnar; Steinmann, Paul (Journal of Adhesion, 2013)
UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.modeli

Modeling and simulation of viscous electro-active polymers - Vogel, Franziska Anna; Göktepe, Serdar; Steinmann, Paul; Kuhl, Ellen (European Journal of Mechanics A-Solids, 2014)
Electro-active materials are capable of undergoing large deformation when stimulated by an electric field. They can be divided into electronic and ionic electro-active polymers (EAPs) depending on their actuation mechanism based on their composition. We consider electronic EAPs, for which attractive Coulomb forces or local re-orientation of polar groups cause a bulk deformation. Many of these materials exhibit pronounced visco-elastic behavior. Here we show the development and implementation of a constitutive model, which captures the influence of the electric field on the visco-elastic response within a geometrically non-linear finite element framework. The electric field affects not only the equilibrium part of the strain energy function, but also the viscous part. To adopt the familiar additive split of the strain from the small strain setting, we formulate the governing equations in the logarithmic strain space and additively decompose the logarithmic strain into elastic and viscous parts. We show that the incorporation of the electric field in the viscous response significantly alters the relaxation and hysteresis behavior of the model. Our parametric study demonstrates that the model is sensitive to the choice of the electro-viscous coupling parameters. We simulate several actuator structures to illustrate the performance of the method in typical relaxation and creep scenarios. Our model could serve as a design tool for micro-electro-mechanical systems, microfluidic devices, and stimuli-responsive gels such as artificial skin, tactile displays, or artificial muscle. © 2014 Elsevier Masson SAS. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2014.tech.FT.FT-TM.modeli
Keywords: Electroactivity; Electroelasticity; Electrostatics; Viscoelasticity

Modeling crystallization kinetics for selective laser sintering of polyamide 12 - Soldner, Dominic; Steinmann, Paul; Mergheim, Julia (GAMM-Mitteilungen, 2021)
Selective laser sintering (SLS) of polymers represents a widely used additive manufacturing process, where the part quality depends highly on the present thermal conditions. One distinct feature of SLS is the existence of separate temperature regions for melting and crystallization (solidification) and that the process optimally operates within said regions. Typically a crystallization model, such as the Nakamura model, is used to predict the degree of crystallization as a function of temperature and time. One limitation of this model is the inability to compute negative rates of the crystallization degree during remelting. As we will show in this work, such an extension is necessary, considering the varying temperature fields appearing in SLS. To this end, an extension is proposed and analyzed in detail. Furthermore, a dependency of the temperature and crystallization fields on the size of geometrical features is presente

Modeling of additively manufactured materials using gradient-enhanced crystal plasticity - Kergaßner, Andreas; Mergheim, Julia; Steinmann, Paul (Computers & Mathematics with Applications, 2018)
Additively manufactured metals possess a particular grain structure – ranging from equiaxed grains to columnar grains – which is strongly influenced by the manufacturing process. The grain structure determines the material behavior and therefore influences the mechanical behavior of additively manufactured parts. In the present contribution a mesoscopic model, based on gradient-enhanced crystal plasticity, is developed and used to simulate the behavior of additively manufactured Inconel 718. The gradient-enhanced crystal plasticity model is extended to account for relative misorientations of the grain boundaries. Representative Volume Elements of the material are generated using a Voronoi tessellation based method. Computational homogenization is used to identify the macroscopic elastic and plastic mechanical behavior, such as the anisotropic Young’s moduli and the yield locus diagram. The numerical results are validated against experimental data.<br
Keywords: Single crystal plasticityGradient plasticityGrain boundariesComputational homogenizationInconel 718

Modeling of jointed structures using zero thickness interface elements - Geisler, Johannes; Willner, Kai (Proceedings of 6th International Congress on Industrial Applied Mathematics and the 78th Annual Meeting of the International Association of Applied Mathematics and Mechanics, 2007)
UnivIS-Import:2015-04-16:Pub.2007.tech.FT.FT-TM.modeli_3

Modeling steady state rate- and temperature-dependent strain hardening behavior of glassy polymers - Zhao, Wuyang; Steinmann, Paul; Pfaller, Sebastian (Mechanics of Materials, 2024)
In this paper, we use molecular dynamics (MD) simulations to investigate the origin of strain hardening in glassy polymers, with a particular focus on the influences of strain rate and temperature. We demonstrate that strain hardening in uniaxial tension arises from bond stretching and is relaxed by bond rotation, characterized by the evolution of dihedral angles. Based on this rotational relaxation, strain rate plays a role analogous to temperature, resulting in a steady state behavior in the hardening region identifiable by strain rate and temperature. Following these observations, we propose a constitutive model to describe the rate- and temperature-dependent strain hardening behavior of glassy polymers using a viscous potential as a function of strain rate. To capture the elastic and yield behavior at small strains, we integrate this viscous potential with a conventional elasto-viscoplastic (EVP) model, giving rise to our V-EVP model. The V-EVP model is shown to be thermodynamically consistent and is validated by comparison to MD simulation results of glassy polymers undergoing uniaxial tension tests across a broad range of temperatures and strain rates.<br

Modeling the dynamic magneto-mechanical response of magnetic shape memory alloys based on Hamilton's principle: The governing equation system - Wang, Jiong; Fan, Chengkai; Steinmann, Paul (Journal of the Mechanics and Physics of Solids, 2022)
The governing equation system for modeling the high-frequency dynamic magneto-mechanical response of magnetic shape memory alloys (MSMAs) is formulated based on Hamilton's principle. First, by taking the single-crystalline Ni-Mn-Ga alloy as a representative member of MSMAs, we introduce some constitutive assumptions and material constants. Then, Hamilton's action integral is established for a MSMA sample subject to coupled magnetic and mechanical loads. By calculating the variation of Hamilton's action integral with respect to the independent variables, we derive the Maxwell's equations, the mechanical dynamic equations and some evolution laws for the internal variables in the effective magnetization. Furthermore, by studying the variation of Hamilton's action integral with respect to the path of the variant state distribution, the criteria for predicting the motion of twin interfaces in the sample are established. Combining the above equations and the twin interface motion criteria, the governing equation system for modeling the high-frequency dynamic magneto-mechanical response of the MSMA sample is formulated, which lays the foundation for future numerical simulations and underlying mechanism analyses. For convenience of practical application of the current model, we further adopt some simplifications and derive some analytical formulas from the governing equation system, which provide good predictions for the response of the MSMA sample subject to some typical loading conditions.
CRIS-Team Scopus Importer:2022-01-21
Keywords: Constitutive modeling; Dynamic response; Hamilton's principle; Magnetic shape memory alloys; Variant reorientation

Modeling the finite viscoelasticity of human brain tissue based on microstructural information - Reiter, Nina; Schäfer, Anne-Mareike; Auer, Sophia; Paulsen, Friedrich; Budday, Silvia (Proceedings in Applied Mathematics and Mechanics, 2023)
Continuum-mechanics-based computational models are a valuable tool to advance our understanding of mechanics-related physiological and pathological processes in the brain. Current numerical predictions of brain tissue behavior are mainly based on phenomenological material models. Such models rely on parameters that often lack physical interpretation and only provide adequate estimates for brain regions with a similar microstructure as those used for calibration. These issues can be overcome by establishing advanced constitutive models that are microstructurally motivated and account for regional and temporal changes through microstructural parameters. In a previous study, we have proposed a microstructure-informed finite viscoelastic constitutive model for porcine brain tissue based on experimental insights into the link between macroscopic deformations and cell displacements during compression tests. Here, we test whether the model can be applied to the material response of human brain tissue from different brain regions during compression and tension tests. We calibrate the model using a combination of cyclic loadings in compression and tension as well as stress relaxation experiments in compression. Furthermore, we include cell densities and the percentage area covered by cell nuclei from microstructural analyses of the tested samples into the model. While it was not possible to identify one set of material parameters for all four considered brain regions, we successfully applied the model to tissue from the cerebellar white matter. Our results show that the microstructure-based time constant that we had determined based on experiments on porcine brain tissue is also valid for human tissue. Furthermore, the microstructure-informed material model is capable of capturing the pronounced compression-tension asymmetry of brain tissue.<br

Modeling the life cycle of the human brain - Budday, Silvia; Kuhl, Ellen (Current Opinion in Biomedical Engineering, 2020)
In recent years, computational mechanics have become a powerful tool to study and predict the behavior of the human brain. Yet, an important challenge that remains unaddressed is that brain tissue is not a constant uniform material. Throughout its life time, our brain’s microstructure, mechanical properties, and macroscopic shape keep changing in close relation to brain function. In this review, we summarize the evolution of various microscopic and macroscopic features during brain development and aging. We discuss how to use mechanical models to translate processes on the microscopic scale into the evolution of mechanical properties and brain shape on the macroscopic scale. In addition, we propose how to incorporate additional coupling effects that arise from the ‘mechanosensitivity’ of brain cells. Considering the entire life cycle of the human brain will be critical to refine existing brain models towards personalized simulations of brain injury, brain damage, and brain protectio
Keywords: brain development; brain aging; nonlinear continuum mechanics; mechanosensing; growth; coupled problems

Modeling the porous and viscous responses of human brain tissue behavior - Comellas Sanfeliu, Ester; Budday, Silvia; Pelteret, Jean-Paul; Holzapfel, Gerhard A.; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2020)
The biomechanical characterization of human brain tissue and the development of appropriate mechanical models is crucial to provide realistic computational predictions that can assist personalized treatment of neurological disorders with a strong biomechanical component. Here, we present a novel material model that combines finite viscoelasticity with a nonlinear biphasic poroelastic formulation, developed within the context of the Theory of Porous Media. Embedded in a finite element framework, our model is capable of predicting the brain tissue response under multiple loading conditions. We show that our model can cap- ture both experimentally observed fluid flow and conditioning aspects of brain tissue behavior in addition to its well-established nonlinear and compression–tension asymmetric characteristics. Our results support the notion that porous and viscous effects are highly interrelated and that additional experimental data are required to reliably identify the model parameters. The modular and object-oriented design with automatic differentiation makes our open-source code easily amendable to future extensions. We provide a solid foundation towards the development of a reliable and comprehensive biomechanical model for brain tissue, which will be a versatile and useful tool in elucidating the rheology of brain tissue behavior to help the biomedical and clinical communities in the future study, prevention and treatment of brain injury and disease.
Keywords: Theory of porous media; Finite viscoelasticity; Finite element method; Material modeling; Brain mechanics; Mechanical testing

Modelling additive manufactured materials using a crystal plasticity model - Kergaßner, Andreas; Mergheim, Julia; Steinmann, Paul (Proceedings in Applied Mathematics and Mechanics, 2016)
In additive manufacturing complex parts are built from thin layers of powder material. In the process called selective electron beam melting (SEBM), the powder is fused by the energy of an electron beam. The electron beam is guided by electromagnetic fields which allows a very fast deection, opening the way to various scan strategies. By using these scan strategies it is possible to control the resulting mesostructure in the material, which may range from a columnar to an equiaxed grain structure. With dierent grain structures, dierent macroscopic properties are expected. Long and oriented grains cause highly anisotropic behaviour and a uniform grain stucture will result in isotropic mechanical behaviour. In this contribution the macroscopic behaviour of additively manufactured Inconel 718 will be identified using a crystal plasticity model on the meso-level. The experimentally observed grain structures will be used to generate a representative volume element. Based on this RVE and computational homogenization, macroscopic mechanical param-eters will be identified and compared with experimental results.
Keywords: Crystal plasticity; Inconel 718; Columnar grains

Modelling and Computation of 3D Discontinuities in Solids - Mergheim, Julia; Steinmann, Paul; Kuhl, Ellen; Jäger, Philippe (Proceedings GAMM'06, 2007)
UnivIS-Import:2015-04-16:Pub.2007.tech.FT.FT-TM.modell

Modelling and computation of curing and damage of thermosets - Mergheim, Julia; Possart, Gunnar; Steinmann, Paul (Computational Materials Science, 2012)
The curing of thermosets is a complex process involving the transition from a fluid into a (visco-) elastic solid. This phase transition comes along with an increase in stiffness and a volume shrinkage of the polymer. The latter may lead to severe residual strains and stresses, which in turn can cause damage in the final, usually quasi-brittle material. In this contribution a constitutive model is developed which takes into account the curing of a thermosetting material together with the process-induced damage as resulting from curing shrinkage. The curing of the material is governed by a phenomenological hypoelastic constitutive equation which includes temporal evolutions for stiffness and volume shrinkage. Thermal and viscous effects are neglected in the present study. An isotropic gradient-enhanced damage model is adapted to describe the damage evolution. The curing-damage model is implemented into a finite element code and numerical examples for thermosetting materials demonstrate that the proposed model is capable to predict cure-induced damage in thermosets. © 2011 Elsevier B.V. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2012.tech.FT.FT-TM.modell
Keywords: Damage; Finite elements; Material modelling; Polymer curing; Shrinkage

Modelling and Simulation of First and Second Sound in Solids - Steinmann, Paul; Bargmann, Swantje (International Journal of Solids and Structures, 2008)
We investigate the propagation of mechanical and thermal waves in solids at cryogenic temperatures. The latter are known as the second sound phenomenon. It occurs, e.g., in dielectric solids and differs greatly from the classical case in which the heat transport proceeds by diffusion. Since Fourier's law of heat conduction fails for modeling second sound, we apply a non-classical one. During the last two decades, the non-classical thermoelastodynamic theory of Green and Naghdi enjoys steadily growing research activities. © 2008 Elsevier Ltd. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2008.tech.FT.FT-TM.modell_3
Keywords: Green-Naghdi; Second sound; Thermal wave propagation; Thermoelasticity

Modelling and Simulation of Polymer Curing. - Steinmann, Paul; Possart, Gunnar; Mokarram, Hossain (Proceedings of the 7th EUROMECH Solid Mechanics Conference, 2009)
UnivIS-Import:2015-04-16:Pub.2009.tech.FT.FT-TM.modell_5

Modelling and simulation of the curing process of polymers by a modified formulation of the Arruda-Boyce model - Mokarram, Hossain; Steinmann, Paul (Archives of Mechanics, 2011)
A phenomenologically motivated small strain model and a finite strain general framework to simulate the curing process of polymer have been developed and discussed in our recently published papers [1, 2, 3, 4]. In order to illustrate the capability of the finite strain framework proposed earlier, only the micromechanicallyinspired 21-chain model and the phenomenologically motivated Neo-Hookean model (energy function) have been demonstrated so far. The Arruda-Boyce model (wellknown as the 8-chain model in the elastic case and Bergström-Boyce model [5, 14] in the viscoelastic case) is a prototype hyperelastic model for polymeric materials. This follow-up contribution presents an extension of the Arruda-Boyce model [6] towards modelling the curing process of polymers. The necessary details, i.e. the stress tensor and the tangent operator, for the numerical implementation within the finite element method, are derived. The curing process of polymers is a complicated process where a series of chemical reactions have been activated, which will convert low molecular weight monomer solutions into more or less cross-linked solid macromolecular structures via the chemical conversion. This paper will model the elastic behaviour and shrinkage effects of the polymer curing process in the isothermal case using the Arruda-Boyce model. Several numerical examples have been demonstrated to verify our newly proposed, modified approach in case of curing process. Copyright © 2011 by IPPT PAN.
UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.modell
Keywords: Arruda-Boyce model; Curing; Elasticity; Finite strain; Polymer

Modelling cardiac mechanics and electrophysiology of a rat left ventricle: A case study. - Duong, Minh Tuan; Wenger, Theresa; Herrnböck, Ludwig; Ach, Theresa; Holz, David; Kreipp, Anika; Binnewitt, Svea Vanessa; Stegmann, Hedwig; Dittrich, Sven; Alkassar, Muhannad; Leyendecker, Sigrid (International Conference on Biomedical Technology, 2017)
Keywords: mechanics; electrophysiology; rat left ventricle; fibres; FEM.

Modelling electro-active polymers with a dispersion-type anisotropy - Hossain, Mokarram; Steinmann, Paul (Smart Materials and Structures, 2018)
We propose a novel constitutive framework for electro-active polymers (EAPs) that can take into account anisotropy with a chain dispersion. To enhance actuation behaviour, particle-filled EAPs become promising candidates nowadays. Recent studies suggest that particle-filled EAPs, which can be cured under an electric field during the manufacturing time, do not necessarily form perfect anisotropic composites, rather they create composites with dispersed chains. Hence in this contribution, an electro-mechanically coupled constitutive model is devised that considers the chain dispersion with a probability distribution function in an integral form. To obtain relevant quantities in discrete form, numerical integration over the unit sphere is utilized. Necessary constitutive equations are derived exploiting the basic laws of thermodynamics that result in a thermodynamically consistent formulation. To demonstrate the performance of the proposed electro-mechanically coupled framework, we analytically solve a non-homogeneous boundary value problem, the extension and inflation of an axisymmetric cylindrical tube under electro-mechanically coupled load. The results capture various electro-mechanical couplings with the formulation proposed for EAP composites.
CRIS-Team Scopus Importer:2022-08-05
Keywords: electro-active polymers; electro-elasticity; electro-mechanical coupled problem; micro-sphere model; numerical integration

Modelling of failure with a hybrid dG/ interface approach - Mergheim, Julia; Kuhl, Ellen; Steinmann, Paul (Proceedings GAMM'03, 2003)
UnivIS-Import:2015-04-16:Pub.2003.tech.FT.FT-TM.comput_6

Modelling of iron-filled magneto-active polymers with a dispersed chain-like microstructure - Saxena, Prashant; Pelteret, Jean-Paul; Steinmann, Paul (European Journal of Mechanics A-Solids, 2015)
Magneto-active polymers are a class of smart materials commonly manufactured by mixing micron-sized iron particles in a rubber-like matrix. When cured in the presence of an externally applied magnetic field, the iron particles arrange themselves into chain-like structures that lend an overall anisotropy to the material. It has been observed through electron micrographs and X-ray tomographs that these chains are not always perfect in structure, and may have dispersion due to the conditions present during manufacturing or some undesirable material properties. We model the response of these materials to coupled magneto-mechanical loading in this paper using a probability based structure tensor that accounts for this imperfect anisotropy. The response of the matrix material is decoupled from the chain phase, though still being connected through kinematic constraints. The latter is based on the definition of a 'chain deformation gradient' and a 'chain magnetic field'. We conclude with numerical examples that demonstrate the effect of chain dispersion on the response of the material to magnetoelastic loading.
UnivIS-Import:2015-07-08:Pub.2015.tech.FT.FT-TM.modell_4
Keywords: Anisotropy; Chain dispersion; Nonlinear magnetoelasticity

Modelling, simulation and experimental validation of heat transfer in selective laser melting of the polymeric material PA12 - Riedlbauer, Daniel-Rouven; Drexler, Maximilian; Drummer, Dietmar; Steinmann, Paul; Mergheim, Julia (Computational Materials Science, 2014)
One of the most promising additive manufacturing techniques is selective laser melting of semi-crystalline thermoplastic powders. In this process the powder is fused in defined, locally-restricted points in the current powder layer by the energy input of a laser beam and, thereby, bonded to the already fused material of previous layers. In this way geometrically complex parts are constructed layer-by-layer. The accuracy of the process and the properties of the resulting parts depend on numerous process parameters and their interactions. To improve the process strategy and to reduce, e.g. eigenstresses and warpage a thorough understanding of the influence of various process parameters is required. In the present contribution one step in this direction is done by analysing the laser energy input into a powder bulk for different process parameters by comparing temperature distributions and the size of melting pools. Experiments with single-line specimens are conducted, analysed and compared to numerical results from finite element simulations of the highly nonlinear thermal problem. © 2014 Elsevier B.V. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2014.tech.FT.FT-TM.modell_2
Keywords: Additive manufacturing; Heat transfer simulation; Selective laser melting

Modelling the curing process in magneto-sensitive polymers: Rate-dependence and shrinkage - Mokarram, Hossain; Saxena, Prashant; Steinmann, Paul (International Journal of Non-Linear Mechanics, 2015)
This paper deals with a phenomenologically motivated magneto-viscoelastic coupled finite strain framework for simulating the curing process of polymers under the application of a coupled magneto-mechanical load. Magneto-sensitive polymers are prepared by mixing micron-sized ferromagnetic particles in uncured polymers. Application of a magnetic field during the curing process causes the particles to align and form chain-like structures lending an overall anisotropy to the material. The polymer curing is a viscoelastic complex process where a transformation from fluid to solid occurs in the course of time. During curing, volume shrinkage also occurs due to the packing of polymer chains by chemical reactions. Such reactions impart a continuous change of magneto-mechanical properties that can be modelled by an appropriate constitutive relation where the temporal evolution of material parameters is considered. To model the shrinkage during curing, a magnetic-induction-dependent approach is proposed which is based on a multiplicative decomposition of the deformation gradient into a mechanical and a magnetic-induction-dependent volume shrinkage part. The proposed model obeys the relevant laws of thermodynamics. Numerical examples, based on a generalised Mooney–Rivlin energy function, are presented to demonstrate the model capacity in the case of a magneto-viscoelastically coupled loa
UnivIS-Import:2015-03-09:Pub.2015.tech.FT.FT-TM.modell
Keywords: Magneto-sensitive polymers; Polymer curing; Magneto-mechanical coupled problem; Magneto-viscoelasticity; Curing shrinkage

Modelling the flexoelectric effect in solids: A micromorphic approach - McBride, A. T.; Davydov, Denis; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2020)
Flexoelectricity is characterised by the coupling of the second gradient of the motion and the electrical field in a dielectric material. The presence of the second gradient is a significant obstacle to obtaining the approximate solution using conventional numerical methods, such as the finite element method, that typically require a C1-continuous approximation of the motion. A novel micromorphic approach is presented to accommodate the resulting higher-order gradient contributions arising in this highly-nonlinear and coupled problem within a classical finite element setting. Our formulation accounts for all material and geometric nonlinearities, as well as the coupling between the mechanical, electrical and micromorphic fields. The highly-nonlinear system of governing equations is derived using the Dirichlet principle and approximately solved using the finite element method. A series of numerical examples serve to elucidate the theory and to provide insight into this intriguing effect that underpins or influences many important scientific and technical applications.
CRIS-Team Scopus Importer:2020-08-28
Keywords: Finite element method; Flexoelectricity; Micromorphic continua

Modelling the flexoelectric effect in solids - Mcbride, A.; Davydov, Denis; Steinmann, Paul (ADVANCES IN ENGINEERING MATERIALS, STRUCTURES AND SYSTEMS: INNOVATIONS, MECHANICS AND APPLICATIONS, 2019)
CRIS-Team WoS Importer:2020-01-10

Modelling the mechanical aspects of the curing process of magneto-sensitive elastomeric materials - Mokarram, Hossain; Saxena, Prashant; Steinmann, Paul (International Journal of Solids and Structures, 2015)
In this paper, a phenomenologically motivated magneto-mechanically coupled finite strain elastic framework for simulating the curing process of polymers in the presence of a magnetic load is proposed. This approach is in line with previous works by Hossain and co-workers on finite strain curing modelling framework for the purely mechanical polymer curing (Hossain et al., 2009b). The proposed thermodynamically consistent approach is independent of any particular free energy function that may be used for the fully-cured magneto-sensitive polymer modelling, i.e. any phenomenological or micromechanical-inspired free energy can be inserted into the main modelling framework. For the fabrication of magneto-sensitive polymers, micron-size ferromagnetic particles are mixed with the liquid matrix material in the uncured stage. The particles align in a preferred direction with the application of a magnetic field during the curing process. The polymer curing process is a complex (visco) elastic process that transforms a fluid to a solid with time. Such transformation process is modelled by an appropriate constitutive relation which takes into account the temporal evolution of the material parameters appearing in a particular energy function. For demonstration in this work, a frequently used energy function is chosen, i.e. the classical Mooney-Rivlin free energy enhanced by coupling terms. Several representative numerical examples are demonstrated that prove the capability of our approach to correctly capture common features in polymers undergoing curing processes in the presence of a magneto-mechanical coupled load.
UnivIS-Import:2015-03-09:Pub.2015.tech.FT.FT-TM.modell_2
Keywords: Finite strain; Magneto-mechanical coupled problem; Magneto-sensitive polymers; Polymer curing

Mode Lock-In and Friction Modeling - Allgaier, R.; Keiper, W.; Gaul, L.; Willner, Kai (Computational Methods in Contact Mechanics IV, 1999)
UnivIS-Import:2015-04-16:Pub.1999.tech.FT.FT-TM.modelo

Model reduction of gyroscopic systems in ALE formulation with and without non-linearities - Weidauer, Tim; Willner, Kai (PAMM, Volume 18, 2018)
Rotating systems are subject to gyroscopic inﬂuences which alter their dynamic behaviour. The Arbitrary Lagrangian Eulerian (ALE) formulation is a popular approach for related models, e.g. for the simulation of tire rolling contact. It allows for decoupling the rotational guiding motion from the relative deformation of the rotating structure. At the same time it complicates contact computations as the relative displacement between two material particles is not tracked naturally by the ALE observer. Model reduction techniques for (non-linear) systems face additional challenges in this context, of which a variety is discussed here for common approaches such as the Second order modal truncation, the Krylov subspace method or the Craig-Bampton method.<br
Keywords: ALE; Model reduction; gyroscopic system; contact

Models of Solvent Penetration in Glassy Polymers With an Emphasis on Case II Diffusion. A Comparative Review - Bargmann, Swantje; McBride, Andrew; Steinmann, Paul (Applied Mechanics Reviews, 2011)
The objective of this review is to provide an overview and a classification of the key literature on models of non-Fickian case II type diffusion. Several extensive review articles concerning non-Fickian diffusion exist in the literature; our objective is not to reproduce these worthy contributions. Rather, we focus on a limited number of, seemingly disparate, notable models and attempt to unify them using the language of thermodynamics and continuum mechanics. This attempted unification of selected models arising from various modeling communities serves to elucidate the key strengths and potential weaknesses of the model
UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.models
Keywords: Deformation; Diffusion (Physics); Polymers; Equations; Stress

Modified SFEM for computational homogenization of heterogeneous materials with microstructural geometric uncertainties - Pivovarov, Dmytro; Steinmann, Paul (Computational Mechanics, 2016)
In the current work we examine the application of the Stochastic Finite Element Method (SFEM) to the modeling of Representative Volume Elements for heterogeneous materials. Uncertainties in the geometry of the microstructure result in the random nature of the solution fields thus requiring use of the stochastic version of the Finite Element Method. For considering large differences in the material properties of matrix and inclusions a standard SFEM approach proves not stable and results in high numerical errors compared to a brute-force Monte-Carlo evaluation. Therefore in order to stabilize the SFEM we propose an alternative Gauss integration rule as resulting from a truncation of the probability density function for the random variable. In addition we propose new basis functions substituting the common Polynomial Chaos Expansion, resulting in higher accuracy for the standard deviation in the homogenized stress at the macro scale.
Keywords: Stochastic FEM; Computational Homogenization; Random Geometry

Molecular dynamics and finite elements: an approach to couple different worlds - Pfaller, Sebastian; Possart, Gunnar; Steinmann, Paul (PAMM, 2014)
The procedure proposed here couples a continuum with a particle region by introducing an overlapping bridging domain where both regions exchange information. Beyond existing methods, the particle region is computed by Molecular Dynamics (MD) at finite temperature, using a code that has been developed by our co-workers of the Theoretical Physical Chemistry Group at TU Darmstadt. It is also used in the wide field of physical chemistry for various approaches. In contrast to MD procedures employing periodic boundary conditions (PBC), stochastic boundary conditions (SBC) allow for the definition of static anchor points. These additional artificial particles are coupled to the continuum part and serve as information transmitter. The continuum is treated classically by the Finite Element Method (FEM) which has been adapted based on the Arlequin and the bridging domain method. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
UnivIS-Import:2015-07-08:Pub.2015.tech.FT.FT-TM.molecu_3

Molecular dynamics meets finite elements: An approach for coupled simulations of nanocomposites - Steinmann, Paul; Pfaller, Sebastian; Possart, Gunnar; Müller-Plathe, Florian; Rahimi, Mohammad; Böhm, Michael C. (NIC Series, 2013)
In contrast to field-based continuum mechanics, particle-based methods can take into account the specific atomistic structure of the material under consideration. In our approach the system consists of a particle region that is coupled to a continuum by introducing a bridging domain where both regions overlap. The particle domain is computed by Molecular Dynamics (MD) at finite temperature, while the continuum is discretized and solved using the Finite Element Method (FEM). In addition to existing coupling schemes, the particles are tethered to anchor points which transfer displacements and forces between the different domains.
UnivIS-Import:2015-04-16:Pub.2013.tech.FT.FT-TM.molecu
Keywords: Molecular Dynamics; Finite Element Method; Multiscale Simulation; Polymers

Molecular dynamics study of ferroelectric domain nucleation and domain switching dynamics - Boddu, Vishal; Endres, Florian; Steinmann, Paul (Scientific Reports, 2017)
Ferroelectric materials contain domains of ordered electric dipoles, separated by domain walls, that can undergo polarisation switching under externally applied electric fields. The domain switching dynamics in ferroelectric materials plays an essential role in their application to electronic and electro-optic de- vices. Previous studies suggest that the switching occurs largely through domain wall motion which is explained from the viewpoint of statistical physics on surface growth as the behaviour of a pinned elas- tic interface. We perform molecular dynamics simulations to investigate the domain switching process and quantitatively estimate the switching speed of anti-parallel 180° domains in ferroelectric, tetragonal BaTiO3 perfect single crystals at room temperature using the core-shell model. We observe an unprece- dented, non-linear increase in the domain switching speed caused by the nucleation of new domains within the switching domain. We determine the strength of the electric field to evoke nucleation of new domains and show that the nucleated domains diffuse into nearby favourable domains when the electric field is removed. Furthermore, we discuss the prominence of domain nucleations during ferroelectric switching.

Molecular static simulations of ferroelectric material hysteresis behaviour - Endres, Florian; Steinmann, Paul (PAMM, 2014)
The present contribution deals with molecular static modelling and the simulation of ferroelectric material hysteresis behaviour. Therefore the core-shell model is implemented in a molecular static algorithm. Moreover the algorithm is implemented as a finite element method for nonlinear trusses. Thereby the computational costs are reduced significantly compared to molecular dynamics. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
UnivIS-Import:2015-04-17:Pub.2015.tech.FT.FT-TM.molecu_5

Molecular statics simulations of ferroelectric barium titanate in the rhombohedral phase - Endres, Florian; Steinmann, Paul (GAMM-Mitteilungen, 2015)
Ferroelectric functional materials improved tremendously over the last decades. Therefore not only the material science regarding material manufacturing but also simulation models and algorithms have been developed further. There are two fundamentally different types of models available. Firstly, particle based models describe material as a discrete particle system. Secondly, continuum mechanics describe material as a continuum. Both continuum mechanics and the particle based methods have their benefits and disadvantages. Still the main disadvantage of particle based methods are the enormous computational costs. In this work the fundamentals of a molecular statics algorithm for the simulation of ferroelectric functional materials are elucidated in order to reduce the computational costs. Furthermore barium titanate has been simulated in order to demonstrate the applicability of the molecular statics algorithm. Since the computational costs of molecular statics are highly reduced compared to other atomistic algorithms larger systems can be calculated more efficiently.
Keywords: Molecular statics; barium titanate; core-shell model; ferroelectric materials

Molecular statics simulations of head to head and tail to tail nanodomains of rhombohedral barium titanate - Endres, Florian; Steinmann, Paul (Computational Materials Science, 2015)
Studies of head to head and tail to tail domain configurations of different sizes are performed in order to discover size effects in rhombohedral barium titanate. To this end, a molecular statics (MS) algorithm is applied to simulate ferroelectric barium titanate in the rhombohedral phase at 0 K (which is the standard restriction of MS). As a result the size effects on polarization patterns as well as the influence on the systems total energies are highlighted.
UnivIS-Import:2015-03-09:Pub.2014.tech.FT.FT-TM.molecu_8

More Hyperelastic models for rubber-like materials: Consistent tangent operators and Comparative Study - Mokarram, Hossain; Steinmann, Paul (Journal of the Mechanical Behavior of Materials, 2013)
Rubber-like materials can deform largely and nonlinearly upon loading, and they return to the initial configuration when the load is removed. Such rubber elasticity is achieved due to very flexible long-chain molecules and a three-dimensional network structure that is formed via cross-linking or entanglements between molecules. Over the years, to model the mechanical behavior of such randomly oriented microstructures, several phenomenological and micromechanically motivated network models for nearly incompressible hyperelastic polymeric materials have been proposed in the literature. To implement these models for polymeric material (undoubtedly with widespread engineering applications) in the finite element framework for solving a boundary value problem, one would require two important ingredients, i.e., the stress tensor and the consistent fourth-order tangent operator, where the latter is the result of linearization of the former. In our previous work, 14 such material models are reviewed by deriving the accurate stress tensors and tangent operators from a group of phenomenological and micromechanical models at large deformations. The current contribution will supplement some further important models that were not included in the previous work. For comparison of all selected models in reproducing the well-known Treloar data, the analytical expressions for the three homogeneous defomation modes, i.e., uniaxial tension, equibiaxial tension, and pure shear, have been derived and the performances of the models are analyzed.
UnivIS-Import:2015-03-09:Pub.2012.tech.FT.FT-TM.morehy

MSSP Special Issue devoted to Prof. Lothar Gaul - Link, Michael; Rixen, Daniel; Schmidt, Andre; Willner, Kai (Mechanical Systems and Signal Processing, 2022)
CRIS-Team WoS Importer:2021-10-29

Multifield computational model for human brain development: Explicit numerical stabilization - Zarzor, Mohammad Saeed; Steinmann, Paul; Budday, Silvia (Proceedings in Applied Mathematics and Mechanics, 2023)
The morphological surface of the human brain is still puzzling to scientists. During the last few decades, studies have addressed different aspects of this phenomenon. The underlying cellular processes occurring at the microscopic scale are certainly important for the folding process. However, there is also an essential contribution from mechanical forces generated at the macroscopic scale during these processes. Many previous studies confirmed this fact, but still, most of them have not considered the link between cellular processes and mechanical forces. Recently, we have explained how the proliferation in different zones of the brain, cell migration, and neuronal connectivity affect the folding through a multifield computational model coupling an advection-diffusion model with the theory of finite growth. We mathematically describe the cellular behavior of cells to control mechanical growth in both radial and circumferential directions. To deal with issues regarding numerical stability of the advection-diffusion equation, which lead to temporal and spatial numerical oscillations, reduced efficiency of the numerical solver, and inaccurate results, we introduce an artificial diffusivity, which we apply only when the actual cell density does not satisfy the balance equation. The proposed method stabilizes the numerical solution and significantly improves the simulation results without additional numerical cost. It allows us to study brain development in 2D and 3D.<br

Multiharmonic Balance Analysis of a Jointed Friction Oscillator - Süß, Dominik; Willner, Kai (Proceedings of the ECCOMAS, 2012)
This paper deals with the investigation of a jointed structure in the frequency domain. Because of the nonlinearity of most jointed systems an usual approach doing this is the usage of the Harmonic Balance Method (HBM), assuming that a harmonic excitation of the system is leading to a harmonic response. But for systems where the steady state response is not harmonic but periodic or systems which might be excited periodically, this assumption does no longer obtain satisfying results. So an advanced approach has to be used and the single-harmonic ansatz of the HBM to describe the response displacements of the system is extended to multiple harmonic parts. This leads to the so called Multi Harmonic Balance Method (MHBM) which represents a Fourier-type approximation of the periodic quantities of a system. The MHBM is presented for a friction oscillator containing a bolted joint. Furthermore the method is utilized for a parameter identification in the frequency domain using FRF measurements.
UnivIS-Import:2015-04-16:Pub.2012.tech.FT.FT-TM.multih_1
Keywords: Harmonic balance; Jointed structures; Structural dynamics

Multilayer 3D bioprinting and complex mechanical properties of alginate-gelatin mesostructures - Ahmadi Soufivand, Anahita; Faber, Jessica; Hinrichsen, Jan; Budday, Silvia (Scientific Reports, 2023)
In the biomedical field, extrusion-based 3D bioprinting has emerged as a promising technique to fabricate tissue replacements. However, a main challenge is to find suitable bioinks and reproducible procedures that ensure good printability and generate final printed constructs with high shape fidelity, similarity to the designed model, and controllable mechanical properties. In this study, our main goal is to 3D print multilayered structures from alginate-gelatin (AG) hydrogels and to quantify their complex mechanical properties with particular focus on the effects of the extrusion process and geometrical parameters, i.e. different mesostructures and macroporosities. We first introduce a procedure including a pre-cooling step and optimized printing parameters to control and improve the printability of AG hydrogels based on rheological tests and printability studies. Through this procedure, we significantly improve the printability and flow stability of AG hydrogels and successfully fabricate well-defined constructs similar to our design models. Our subsequent complex mechanical analyses highlight that the extrusion process and the mesostructure, characterized by pore size, layer height and filament diameter, significantly change the complex mechanical response of printed constructs. The presented approach and the corresponding results have important implications for future 3D bioprinting applications when aiming to produce replacements with good structural integrity and defined mechanical properties similar to the native tissue, especially in soft tissue engineering. The approach is also applicable to the printing of gelatin-based hydrogels with different accompanying materials, concentrations, or cells.
CRIS-Team Scopus Importer:2023-07-21

Multiscale FE-MD Coupling: Influence of the Chain Length on the Mechanical Behavior of Coarse-Grained Polystyrene - Ries, Maximilian; Weber, Felix; Striegel, Maximilian; Steinmann, Paul; Pfaller, Sebastian (Multiscale and Multiphysics Systems, 2021, 2021)
Polymers have become increasingly essential to cope with modern engineering challenges. To better understand their microstructure's influence, multi-scale approaches that couple molecular dynamics and continuum mechanics are emerging progressively. However, these simulation techniques require detailed knowledge of the material behavior, which is commonly derived from molecular dynamics simulations. Reducing the degrees of freedom by coarse graining enables the investigation of sufficiently large samples and thus we focus on coarse-grained (CG) polystyrene as a model material. The goal of this contribution is two-fold: Firstly, we identify the minimum sample size necessary to analyze the mechanical properties. Secondly, we quantify the influence of chain length on the material behavior of polystyrene. To this end, we investigate density, end-to-end distance, stress-strain behavior, Young's modulus, and Poisson's ratio. In conclusion, we were able to verify that we can use significantly smaller samples for our investigations without affecting their structure or mechanical behavior. The chain length has a drastic influence on the mechanical properties, with a loss of stiffness in the range of 15 % for very short-chain specimens. <br
Keywords: Coarse graining; Multiscale-modeling; Mechanical behavior; Molecular dynamics

Multiscale modeling for composites with energetic interfaces at the micro or nanoscale - Chatzigeorgiou, Georgios; Javili, Ali; Steinmann, Paul (Mathematics and Mechanics of Solids, 2013)
A homogenization framework is developed that accounts for the effect of size at the micro- or nanoscale. This is achieved by endowing the interfaces of the micro- or nanoscopic features with their own independent structure, using the theory of surface elasticity. Following a standard small-strain approach for the microscopic deformation in terms of the macroscopic strain tensor, a Hill-type averaging condition is used to link the two scales. A procedure for determining overall effective properties in the case of composites with elastic components and elastic material interfaces is presented. A special example of multilayered composites demonstrates the correlation between a material interface and a very thin interphase layer.
UnivIS-Import:2015-04-14:Pub.2013.tech.FT.FT-TM.multis

Multi-Scale Modelling of Plastic Deformation, Damage and Relaxation in Epoxy Resins - Konrad, Julian; Pfaller, Sebastian; Zahn, Dirk (Polymers, 2022)
Epoxy resin plasticity and damage was studied from molecular dynamic simulations and interpreted by the help of constitutive modelling. For the latter, we suggested a physically motivated approach that aims at interpolating two well-defined limiting cases; namely, pulling at the vanishing strain rate and very rapid deformation; here, taken as 50% of the speed of sound of the material. In turn, to consider 0.1-10-m/s-scale deformation rates, we employed a simple relaxation model featuring exponential stress decay with a relaxation time of 1.5 ns. As benchmarks, deformation and strain reversal runs were performed by molecular dynamic simulations using two different strain rates. Our analyses show the importance of molecular rearrangements within the epoxy network loops for rationalizing the strain-rate dependence of plasticity and residual stress upon strain reversal. To this end, our constitutive model reasonably reproduced experimental data of elastic and visco-elastic epoxy deformation, along with the maximum stress experienced before fracturing. Moreover, we show the importance of introducing damage elements for mimicking the mechanical behavior of epoxy resins.
CRIS-Team WoS Importer:2022-09-09

Multi-Scale Parameter Identification - Schmidt, Ulrike; Mergheim, Julia; Steinmann, Paul (International Journal For Multiscale Computational Engineering, 2010)
In this work a multiscale approach is introduced which allows for the identification of small scale mechanical properties by means of large scale test data. The proposed scheme is based on the computational homogenization method in which a small scale representative volume element is related to each large scale material point and the large scale material response is directly obtained via homogenization of the small scale field variables. Application of this computational homogenization method usually requires that the microstructure of the material be well characterized, i.e., that the constitutive behavior of all constituents of the heterogeneous material is known. This condition is circumvented here by the solution of an inverse optimization problem, which provides the fine scale material properties as a result. Therefore the objective function compares large scale experimental results to field values, simulated with the computational homogenization method. Discrete analytical expressions for the sensitivities are derived, and the performance of different gradient-based optimization algorithms is compared for linear elastic problems with various microstructures.
UnivIS-Import:2015-03-09:Pub.2010.tech.FT.FT-TM.multis_5
Keywords: multiscale; homogenization; parameter identification

Multiscale Simulation of Polymers - Coupling of Continuum Mechanics and Particle-Based Modelling - Pfaller, Sebastian (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2015)
In modern engineering applications, plastics play an important role for instance in the field of lightweight constructions or as substitutes for classical materials like wood, metal, or glass. Typically, they consist of organic polymers, which are long-chained molecules comprising numerous monomers as repeat units. In addition, polymers frequently contain fillers, plasticisers, or colourants to achieve and to adjust specific properties. In recent years, new techniques have been established to produce and to disperse filler particles in the range of nanometres, which corresponds to the typical dimensions of the monomers. Experiments reveal that these so-called “nanofillers” may significantly toughen polymers, improve their fatigue lifetime, and enhance control of their thermodynamical properties, even for low filler contents in terms of mass or volume. This cannot be explained by a simple rule of mixture, but is traced back to the very large ratio of surface to volume in case of nanofillers and to the associated processes at the molecular level. The effective design of such “nanocomposites” is demanding and often requires timeconsuming mechanical testing. For a better understanding of the relevant parameters and in order to improve the process of material development, it is beneficial to substitute “real” experiments by numerical simulations. To this end, sophisticated computation techniques are required that account for the specific processes taking place at the level of atoms and molecules. Particle-based strategies, as for instance employed in physical chemistry, are able to consider the atomistic structure in detail and thus permit to simulate material behaviour at atomistic length scales. However, it is still not possible to apply these techniques to large-scale systems relevant in engineering. There, the material behaviour of structures is typically described by continuum approaches, which, on the other hand, cannot account explicitly for the processes at the atomistic level. To overcome this, the present thesis proposes a novel coupling scheme to incorporate particle-based simulations into continuum-based methods. In particular, it links molecular dynamics as a standard tool in physical chemistry with the finite element method, which is nowadays widely used in engineering applications. This multiscale simulation approach has been developed jointly by the Theoretical Physical Chemistry Group at the Technische Universität Darmstadt and the Chair of Applied Mechanics at the Friedrich-Alexander-Universität Erlangen-Nürnberg. Thus, it bases upon expertise in atomistic simulation as well as continuum mechanics, whereby crucial modifications of established techniques in both fields had to be developed. Two sample systems, modelling pure polystyrene and a polystyrene-silica nanocomposite, are studied numerically and prove the suitability of the new approach. In this context, various parameters of the proposed method and its implementation are investigated. Based on this, a number of options to improve this multiscale technique are discussed and relevant issues for future research are summarise
UnivIS-Import:2016-07-26:Pub.2015.tech.FT.FT-TM.multis
Keywords: continuum mechanics; domain decomposition; molecular dynamics; multiscale simulation; particle-continuum coupling; polymer simulation

Natural element analysis of the Cahn-Hilliard phase-field model - Rajagopal, Amirtham; Fischer, Peter; Kuhl, Ellen; Steinmann, Paul (Computational Mechanics, 2010)
We present a natural element method to treat higher-order spatial derivatives in the Cahn–Hilliard equation. The Cahn–Hilliard equation is a fourth-order nonlinear partial differential equation that allows to model phase separation in binary mixtures. Standard classical C0-continuous finite element solutions are not suitable because primal variational formulations of fourth-order operators are well-defined and integrable only if the finite element basis functions are piecewise smooth and globally C1-continuous. To ensure C1-continuity, we develop a natural-element-based spatial discretization scheme. The C1-continuous natural element shape functions are achieved by a transformation of the classical Farin interpolant, which is basically obtained by embedding Sibsons natural element coordinates in a Bernstein–Bézier surface representation of a cubic simplex. For the temporal discretization, we apply the (second-order accurate) trapezoidal time integration scheme supplemented with an adaptively adjustable time step size. Numerical examples are presented to demonstrate the efficiency of the computational algorithm in two dimensions. Both periodic Dirichlet and homogeneous Neumann boundary conditions are applied. Also constant and degenerate mobilities are considered. We demonstrate that the use of C1-continuous natural element shape functions enables the computation of topologically correct solutions on arbitrarily shaped domains.
UnivIS-Import:2015-04-14:Pub.2010.tech.FT.FT-TM.natura

Neocortical development and epilepsy: insights from focal cortical dysplasia and brain tumours - Blümcke, Ingmar; Budday, Silvia; Poduri, Annapurna; Lal, Dennis; Kobow, Katja; Baulac, Stephanie (Lancet Neurology, 2021)
During the past decade, there have been considerable advances in understanding of the genetic and morphogenic processes underlying cortical malformations and developmental brain tumours. Focal malformations are caused by somatic (postzygotic) variants in genes related to cell growth (ie, in the mTOR pathway in focal cortical dysplasia type 2), which are acquired in neuronal progenitors during neurodevelopment. In comparison, developmental brain tumours result from somatic variants in genes related to cell proliferation (eg, in the MAP-kinase pathway in ganglioglioma), which affect proliferating glioneuronal precursors. The timing of the genetic event and the specific gene involved during neurodevelopment will drive the nature and size of the lesion, whether it is a developmental malformation or a brain tumour. There is also emerging evidence that epigenetic processes underlie a molecular memory in epileptogenesis. This knowledge will together facilitate understanding of why and how patients with these lesions have epilepsy, and could form a basis for a move towards precision medicine for this challenging cohort of patients.
CRIS-Team Scopus Importer:2021-10-29

Neuartige Studien zu Silikon-Brustimplantaten - Walter, Bastian; Daenicke, Jonas; Horch, Raymund E.; Kaschta, Joachim; Schubert, Dirk W. (Würzburger Tage 2012, 2014)

New experimental insights into magneto-mechanical rate dependences of magnetorheological elastomers - Moreno Mateos, Miguel Angel; Gonzalez-Rico, Jorge; Lopez-Donaire, Maria Luisa; Arias, Angel; Garcia-Gonzalez, Daniel (Composites Part B-Engineering, 2021)
Magnetorheological elastomers (MREs), consisting of an elastomeric matrix filled with magnetic particles, are one of the most promising multifunctional composites. The main advantage of these materials is their response to external magnetic fields by mechanically deforming and/or changing their magnetorheological properties. This multi-physical nature makes them ideal candidates for timely applications in soft robotics and bioengineering. Although several works have addressed the magneto-mechanical coupling in these composites from both experimental and modelling approaches, there is still a big gap of knowledge preventing the full understanding of their underlying physics. In this regard, there is no experimental work addressing a comprehensive magneto-mechanical characterisation combining different MRE configurations, mechanical deformation modes and magnetic conditions. Furthermore, the interplays of rate dependences into such magnetorheological behaviour still remain elusive. In this work, we provide an unprecedented experimental characterisation of a soft MRE considering more than 100 different experimental conditions involving more than 600 tests. The experiments include monotonous uniaxial compression at different deformation rates and magnetic conditions, magneto-mechanical DMA tests, relaxation tests, oscillatory shear tests at different deformation rates and magnetic conditions, magneto-mechanical shear frequency sweep tests, and novel magneto-mechanical experiments. The results obtained in this work provide full characterisation of soft MREs with a special focus on rate dependences, forming the basis to explain novel multifunctional mechanisms identified behind their coupled response. In addition, it opens the door to new constitutive and modelling approaches.
Created from Fastlane, Scopus look-up
Keywords: Experimental mechanics; Magneto-mechanical rheology; Magneto-rheological elastomers (MREs); Multifunctional composites; Smart materials; Viscoelasticity

Non-coherent energetic interfaces accounting for degradation - Esmaeili, Ali; Javili, Ali; Steinmann, Paul (Computational Mechanics, 2016)

Nonlinear finite element system simulation of piezoelectric vibration-based energy harvesters - Hegendörfer, Andreas; Steinmann, Paul; Mergheim, Julia (Journal of Intelligent Material Systems and Structures, 2021)
Piezoelectric vibration-based energy harvesters consist of an electromechanical structure and an electric circuitry, influencing each other. We propose a novel approach that allows a finite element based system simulation of nonlinear electromechanical structures coupled to nonlinear electric circuitries. In the finite element simulation the influence of the electric circuit on the electromechanical structure is considered via the vector of external forces, using an implicit time integration scheme. To demonstrate the applicability of the new simulation method an active power circuit is considered. Several examples of piezoelectric vibration-based energy harvesters, connected to standard or synchronized switch harvesting on inductor (SSHI) circuits, showing linear or nonlinear mechanical behavior, are studied to validate the proposed simulation method against numerical results reported in the literature. The advocated method allows for consistent and efficient simulations of complete nonlinear energy harvesters using only one software tool.
CRIS-Team Scopus Importer:2021-10-22
Keywords: coupled problem; finite element method; multiphysics simulation; nonlinear analysis; numerical simulation; Piezoelectric energy harvesting

Nonlinear magneto-viscoelasticity of transversally isotropic magneto-active polymers - Saxena, Prashant; Mokarram, Hossain; Steinmann, Paul (Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2014)
Iron-filled magnetorheological polymers, when cured in the presence of a magnetic field, result in having a transversely isotropic structure with iron particles forming chains along the direction of applied magnetic induction. In this work, we model the magneto-viscoelastic deformation (and magnetization) process of such polymers. Components of the deformation gradient and the applied magnetic induction in the direction of anisotropy are considered to be additional arguments of the energy density function. The existence of internal damping mechanisms is considered by performing a multiplicative decomposition of the deformation gradient and an additive decomposition of the magnetic induction into equilibrium and non-equilibrium parts. Energy density functions and evolution laws of the internal variables are proposed that agree with the laws of thermodynamics. In the end, we present solutions of some standard deformation cases to illustrate the theory. In particular, it is shown that the orientation of resltant magnetic field and principal stress directions change with time owing to viscoelastic evolution. © 2014 The Author(s) Published by the Royal Society. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2014.tech.FT.FT-TM.nonlin
Keywords: Magneto-viscoelasticity; Magnetoelasticity; Nonlinear elasticity; Transverse isotropy; Viscoelasticity

Non-linear switching kinetics of ferroelectric mono-domain single crystals - Boddu, Vishal; Endres, Florian; Steinmann, Paul (8th ECCOMAS Thematic Conference on Smart Structures and the 6th International Conference on Smart Materials and Nanotechnology in Engineering, 2017)

Nonlinear Vibration Damping of Structures with Bolted Joints - Gaul, L.; Nackenhorst, U.; Willner, Kai; Lenz, J. (Proceedings of the 12th IMAC, 1994)
UnivIS-Import:2015-04-16:Pub.1994.tech.FT.FT-TM.nonlin

Nonlinear viscoelastic behavior or measuring artifact? On the wall slip of magnetorheological (MR) elastomers - Walter, Bastian; Pelteret, Jean-Paul; Kaschta, Joachim; Schubert, Dirk W.; Steinmann, Paul (17th International Congress on Rheology, 2016)

Nonlinear viscoelastic behavior or measuring artifact? On the wall slip of magneto-sensitive elastomers - Walter, Bastian; Pelteret, Jean-Paul; Kaschta, Joachim; Schubert, Dirk W.; Steinmann, Paul (10th Annual European Rheology Conference, 2015)

Nonlocal interfaces accounting for progressive damage within continuum-kinematics-inspired peridynamics - Laurien, Marie; Javili, Ali; Steinmann, Paul (International Journal of Solids and Structures, 2024)
In this work, we present a modeling approach to nonlocal material interfaces in the framework of continuum-kinematics-inspired peridynamics. The nonlocal model accounts for progressive damage within a finite-thickness interface, as opposed to the more common practice of abrupt bond breakage across a zero-thickness interface. Our approach is based on an overlap of the constituents within the interface. Interfacial bonds between initially overlapping partner points are governed by a constitutive law reminiscent of a traction-separation-law. The governing equations for continuum-kinematics-inspired peridynamics in the presence of an interface are derived using a rate-variational principle. The damage formulation is established using the classical concept of internal variables. Following the notion of a standard dissipative material, thermodynamic consistency of the constitutive laws and the evolution of the internal variables is ensured. The latter results in a straightforward evaluation of a damage function. We give details about the computational implementation comprising a peridynamic discretization and a Newton–Raphson scheme. A sound approach to approximate the interface normal during deformation is presented, which allows to penalize material penetration across the interface. The proposed model is explored in a series of numerical examples, i.e., classical peeling and shearing tests, for a variety of damage functions. A key feature of our interface model are the nonlocal characteristics that are assumed to play a role especially at small scales. We, first, observe that an increasing thickness of the nonlocal interface leads to stronger interfacial bonding and less damage. Second, an increase in horizon size results in stiffer material behavior. When studying the wrinkling and delamination behavior of a compressed bilayer, it is found that an increase in interface stiffness leads to a smaller wrinkling wavelength. Moreover, delamination due to progressive damage of interfacial bonds in the post-wrinkling regime is observed, which, to the best of our knowledge, has not been studied in a nonlocal model before.<br
Keywords: Peridynamics; Material interface; Damage; Nonlocality; Cohesive zone; Rate-variational principle

Nonlocal interfaces accounting for progressive damage within continuum-kinematics-inspired peridynamics - Laurien, Marie; Javili, Ali; Steinmann, Paul (International Journal of Solids and Structures, 2024)
In this work, we present a modeling approach to nonlocal material interfaces in the framework of continuum-kinematics-inspired peridynamics. The nonlocal model accounts for progressive damage within a finite-thickness interface, as opposed to the more common practice of abrupt bond breakage across a zero-thickness interface. Our approach is based on an overlap of the constituents within the interface. Interfacial bonds between initially overlapping partner points are governed by a constitutive law reminiscent of a traction-separation-law. The governing equations for continuum-kinematics-inspired peridynamics in the presence of an interface are derived using a rate-variational principle. The damage formulation is established using the classical concept of internal variables. Following the notion of a standard dissipative material, thermodynamic consistency of the constitutive laws and the evolution of the internal variables is ensured. The latter results in a straightforward evaluation of a damage function. We give details about the computational implementation comprising a peridynamic discretization and a Newton–Raphson scheme. A sound approach to approximate the interface normal during deformation is presented, which allows to penalize material penetration across the interface. The proposed model is explored in a series of numerical examples, i.e., classical peeling and shearing tests, for a variety of damage functions. A key feature of our interface model are the nonlocal characteristics that are assumed to play a role especially at small scales. We, first, observe that an increasing thickness of the nonlocal interface leads to stronger interfacial bonding and less damage. Second, an increase in horizon size results in stiffer material behavior. When studying the wrinkling and delamination behavior of a compressed bilayer, it is found that an increase in interface stiffness leads to a smaller wrinkling wavelength. Moreover, delamination due to progressive damage of interfacial bonds in the post-wrinkling regime is observed, which, to the best of our knowledge, has not been studied in a nonlocal model before.
CRIS-Team Scopus Importer:2024-02-02
Keywords: Cohesive zone; Damage; Material interface; Nonlocality; Peridynamics; Rate-variational principle

Nonlocal wrinkling instabilities in bilayered systems using peridynamics - Laurien, Marie; Javili, Ali; Steinmann, Paul (Computational Mechanics, 2021)
Wrinkling instabilities occur when a stiff thin film bonded to an elastic substrate undergoes compression. Regardless of the nature of compression, this phenomenon has been extensively studied through local models based on classical continuum mechanics. However, the experimental behavior is not yet fully understood and the influence of nonlocal effects remains largely unexplored. The objective of this paper is to fill this gap from a computational perspective by investigating nonlocal wrinkling instabilities in a bilayered system. Peridynamics (PD), a nonlocal continuum formulation, serves as a tool to model nonlocal material behavior. This manuscript presents a methodology to precisely predict the critical conditions by employing an eigenvalue analysis. Our results approach the local solution when the nonlocality parameter, the horizon size, approaches zero. An experimentally observed influence of the boundaries on the wave pattern is reproduced with PD simulations which suggests nonlocal material behavior as a physical origin. The results suggest that the level of nonlocality of a material model has quantitative influence on the main wrinkling characteristics, while most trends qualitatively coincide with predictions from the local analytical solution. However, a relation between the film thickness and the critical compression is revealed that is not existent in the local theory. Moreover, an approach to determine the peridynamic material parameters across a material interface is established by introducing an interface weighting factor. This paper, for the first time, shows that adding a nonlocal perspective to the analysis of bilayer wrinkling by using PD can significantly advance our understanding of the phenomenon.
CRIS-Team WoS Importer:2021-08-13

Nonperiodic stochastic boundary conditions for molecular dynamics simulations of materials embedded into a continuum mechanics domain - Rahimi, Mohammad; Karimi-Varzaneh, Hossein Ali; Böhm, Michael C.; Müller-Plathe, Florian; Pfaller, Sebastian; Possart, Gunnar; Steinmann, Paul (Journal of Chemical Physics, 2011)
A scheme is described for performing molecular dynamics simulations on polymers under nonperiodic, stochastic boundary conditions. It has been designed to allow later the embedding of a particle domain treated by molecular dynamics into a continuum environment treated by finite elements. It combines, in the boundary region, harmonically restrained particles to confine the system with dissipative particle dynamics to dissipate energy and to thermostat the simulation. The equilibrium position of the tethered particles, the so-called anchor points, are well suited for transmitting deformations, forces and force derivatives between the particle and continuum domains. In the present work the particle scheme is tested by comparing results for coarse-grained polystyrene melts under nonperiodic and regular periodic boundary conditions. Excellent agreement is found for thermodynamic, structural, and dynamic properties. © 2011 American Institute of Physics.
UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.nonper

Normal contact of fractal surfaces Experimental and numerical investigations - Görke, Daniel; Willner, Kai (Wear, 2008)
Describing rough surfaces as a fractal over several length scales enables the application of parameters which are independent of the measurement resolution. To generate a fractal surface the measured structure function of a real surface is approximated by three intrinsic parameters: the RMS value of the roughness, the fractal dimension and the transition length between fractal behaviour at high wavenumbers and stationary behaviour at low wavenumbers. A numerical model which allows to describe the elasto-plastic normal contact of isotropic fractal surfaces is tested against experimental data which are obtained from contact tests of several aluminum specimens. The numerical model and the contact tests are described. Furthermore, a review of influencing variables like hardness and geometrical deviations with larger wavelengths than the roughness is given. © 2007 Elsevier B.V. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2008.tech.FT.FT-TM.normal
Keywords: Experiment; Fractal; Hardness; Normal contact stiffness; Rough surfaces; Waviness

Normal contact simulation of non-Gaussian fractal surfaces - Hauer, Franz; Willner, Kai (Proceedings of the 81st Annual Meeting of the International Association of Applied Mathematics and Mechanics, 2010)
Friction forces between contact partners in dry friction are primarily caused by adhesion and ploughing. In adhesive contact, tangential loads are transferred by shear forces within the real contact area. The real contact area is usually smaller than the apparent contact area, because real surfaces are always rough and only the highest surface peaks are in contact for moderate loads. Thus the size of the real contact area is a suitable measurement for the behaviour in dry friction. The normal contact is simulated with a halfspace model. The contact surfaces are modelled numerically in order to enable the independent investigation of the influence of several surface properties, namely the fractal behaviour on small scales, non-Gaussian height distribution and anisotropy. Fractal behaviour means that asperities are covered with smaller asperities of the same shape. Surface anisotropy means that valleys and ridges are oriented in a certain direction.
UnivIS-Import:2015-04-16:Pub.2010.tech.FT.FT-TM.normal_8

Novel vistas on the foundations of peridynamics - Steinmann, Paul; Mcbride, A.; Javili, A. (ADVANCES IN ENGINEERING MATERIALS, STRUCTURES AND SYSTEMS: INNOVATIONS, MECHANICS AND APPLICATIONS, 2019)
CRIS-Team WoS Importer:2020-01-10

Numerical analysis of failure modeling in clinching process chain simulation - Bielak, Christian R.; Böhnke, Max; Friedlein, Johannes; Bobbert, Mathias; Mergheim, Julia; Steinmann, Paul; Meschut, Gerson (Materials Research Proceedings, 2023)
The application of the mechanical joining process clinching allows the assembly of different sheet metal materials with a wide range of material thickness configurations, which is of interest for lightweight multi-material structures. In order to be able to predict the clinched joint properties as a function of the individual manufacturing steps, current studies focus on numerical modeling of the entire clinching process chain. It is essential to be able to take into account the influence of the joining process-induced damage on the load-bearing capacity of the joint during the loading phase. This study presents a numerical damage accumulation in the clinching process based on an implemented Hosford-Coulomb failure model using a 3D clinching process model applied on the aluminum alloy EN AW-6014 in temper T4. A correspondence of the experimentally determined failure location with the element of the highest numerically determined damage accumulation is shown. Moreover, the experimentally determined failure behavior is predicted to be in agreement in the numerical loading simulation with transferred pre-damage from the process simulation.
CRIS-Team Scopus Importer:2023-04-28
Keywords: Damage; Finite Element Method; Joining

Numerical analysis of the influence of crack surface roughness on the crack path - Weber, Wilhelm; Willner, Kai; Kuhn, Günther (Engineering Fracture Mechanics, 2010)
The influence of the 3D frictional crack surface interaction on the fracture mechanical parameters as well as on the crack path is numerically investigated. For the solution of the boundary value problem the 3D dual boundary element method in terms of the discontinuous formulation is utilized. This method is especially suited for contact problems because it directly deals with the discontinuities at the crack surfaces. The contact problem is solved by the application of the penalty method. Coulomb's frictional law is utilized for the consideration of the dissipative nature of friction. For discrete steps within one load cycle the stress intensity factors are determined by an extrapolation procedure from the stress field. Based on the analysis of a load cycle, the cyclic stress intensity factors are obtained. For the simulation of crack propagation an implicit time integration scheme of a crack propagation law implemented in terms of a predictor-corrector scheme is applied. The influence of the crack surface roughness on the crack path is shown by numerical examples. © 2010 Elsevier Ltd.
UnivIS-Import:2015-03-09:Pub.2010.tech.FT.FT-TM.numeri
Keywords: 3D simulation; Crack surface interaction; Fatigue crack propagation

Numerical analysis of the maximum load level in lightweight metal/fibre-reinforced polymer structures - Konchakova, Natalia; Balle, Frank; Müller, Ralf; Steinmann, Paul; Eifler, Dietmar; Barth, Franz-Josef (Advanced Engineering Materials, 2012)
UnivIS-Import:2015-03-09:Pub.2012.tech.FT.FT-TM.numeri

Numerical analysis of the mechanical behavior of lightweight metal-CFRP joints - Konchakova, Natalia; Balle, Frank; Müller, Ralf; Steinmann, Paul; Eifler, Dietmar; Barth, Franz-Josef (Advanced Engineering Materials, 2013)
Influence of the welding geometry on the mechanical characteristics of light metal/carbon fiber reinforced polymer overlapped structures is analyzed. An elastoplastic model with Lemaitre-type damage is used for the simulation of the mechanical behavior of the interface material. An interfacial traction-separation law is applied. Finite element method is used for the simulation of force-displacement curves of ultrasonically welded AA5754/CF-PA66 joints. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.numeri_5

Numerical and experimental investigation of the isothermal assumption in selective laser sintering of PA12 - Soldner, Dominic; Greiner, Sandra; Burkhardt, Christian; Drummer, Dietmar; Steinmann, Paul; Mergheim, Julia (Additive Manufacturing, 2020)

Numerical and experimental investigations of dynamic contact phenomena in jointed structures - Süß, Dominik; Geisler, Johannes; Willner, Kai (Proceedings of the 81st Annual Meeting of the International Association of Applied Mathematics and Mechanics, 2010)
UnivIS-Import:2015-04-16:Pub.2010.tech.FT.FT-TM.numeri_9

Numerical and experimental investigations of joint deflections under normal load - Willner, Kai; Görke, Daniel (Experimentelle und Angewandte Mechanik Ein Querschnitt, 2006)
UnivIS-Import:2015-04-16:Pub.2006.tech.FT.FT-TM.numeri

Numerical and experimental modal analysis of structures under gyroscopic inﬂuence in ALE formulation - Weidauer, Tim; Willner, Kai (ISMA2018, 2018)
A test set-up for the modal analysis of gyroscopic, rotationally symmetric systems is presented. It employs laser Doppler vibrometry along with automatic impulse excitation installed on a rotary table and is applied to a glass structure rotating about its ﬁgure axis. The effects of gyroscopic inﬂuences on the modal behaviour such as the split of eigenfrequencies and the treatment of complex eigenmodes as travelling waves are deduced analytically and shown experimentally. Finally numerical computations using the Arbitrary-Lagrangian-Eulerian (ALE) ﬁnite element formulation separating the rigid body rotation from the mesh deformation are conducted. With the combination of analytical, experimental and numerical analysis a broad overview of modal characteristics of gyroscopic systems is given.<br

Numerical Continuation Methods for the Concept of Non-linear Normal Modes - Jerschl, Martin; Süß, Dominik; Willner, Kai; Jerschl, Martin (Dynamics of Civil Structures, 2014)
Non-linear normal modes (NNMs) can be considered as a non-linear analogon to the description of linear systems with linear normal modes (LNMs). The definition of NNMs can be found in Vakakis (Normal modes and localization in nonlinear systems, Wiley, New York, 1996). Small systems with a low number of degrees of freedom and non-linear couplings (cubic springs) are investigated here. With increasing energy in the system the progressive non-linearity leads to a hardening effect. One typical dynamical property of non-linear systems is the frequency-energy dependency of the resulting oscillations. A good graphic illustration is to plot such a dependency in a so called frequency-energy plot (FEP). A NNM branch can be calculated by a numerical continuation method with starting at low energy level in a quasi linear regime and increasing the energy and reducing the period of the oscillation iteratively. Thereby a branch is a family of NNM oscillations with qualitatively equal motion properties (Peeters et al., Mech Syst Signal Process 23:195–216, 2009). In non-linear systems internal resonances and other phenomena can occur. Several tongues can bifurcate from a NNM branch. Therefore ordinary continuation methods fail at such bifurcation points. Here a predictor-corrector-method is used and different corrector algorithms are discussed for the branch continuation.
UnivIS-Import:2015-10-26:Pub.2014.tech.FT.FT-TM.numeri_94
Keywords: Arclength continuation; Non-linear coupling; Non-linear dynamics; Non-linear normal modes (NNMs); Predictor-corrector

NUMERICAL DRAG AND LIFT PREDICTION FRAMEWORK FOR SUPERELLIPSOIDAL PARTICLES IN MULTIPHASE FLOWS - Štrakl, Mitja; Wedel, Jana; Steinmann, Paul; Hriberšek, Matjaž; Ravnik, Jure (International Journal of Computational Methods and Experimental Measurements, 2022)
The numerical treatment of industrial and environmental problems, involving multiphase flows with particles, has gained significant interest of researchers over the recent years. For large-scale problems, involving an increased number of particles, authors mostly rely on the Lagrangian particle tracking approach, where particle-fluid interaction is generally unresolved and has to be modelled. Significant research efforts have already been made in developing various models to predict particle-fluid interaction, where applications involving complex particle shapes are especially intriguing. In the majority of encountered problems, particle dynamics is primarily governed by drag forces exerted on the particle by the carrier fluid. Following from that it is unsurprising that precise particle trajectories can only be established from accurate particle drag prediction model. In this context, we present a steady-state particle-resolved numerical model, based on OpenFOAM, for numerical drag prediction of superellipsoidal particles in Stokesian flow regime. The idea behind particle-resolved model is to benefit from multi parameter drag prediction, which considers not only the flow regime and particle size but also detailed geometric features (expressed by four independent parameters) and particle orientation. The proposed numerical model will also benefit from a parametric geometry formulation, which will allow to evaluate the drag force for the entire range of particle shapes, offered by the superellipsoidal parametrization. For a vast amount of non-spherical particles, this significantly improves the accuracy of the predicted drag force in comparison to traditional drag models, which do not account for the entire range of influencing factors. The numerical model is further supported by an automated parametric mesh generation algorithm, which makes it possible to autonomously address the full range of particle orientations in parallel. The parametric algorithm also enables the specification of various flow regimes, which are captured in the analysis. Thus, with a single set of input parameters, one can quickly obtain the drag function for given particle shape, with respect to the entire range of orientations and flow regimes. The authors believe that the proposed solution will significantly reduce the effort to obtain an accurate drag model for a vast amount of non-spherical particle shapes.
CRIS-Team Scopus Importer:2022-04-01
Keywords: Computational fluid dynamics; Drag; Lagrangian particle tracking; Lift; Multiphase flow; Superellipsoid

Numerical homogenization and simulation of a lamination stack - Baloglu, Maximilian Volkan; Willner, Kai (2016 6th International Electric Drives Production Conference (EDPC), 2016)
Parts of electric motors and transformers are composed of sheet-layered lamination stacks, which heavily influence the mechanical properties of such devices. Especially the interaction of individual sheets by direct contact or the presence of bonding varnish may cause a nonlinear deformation behavior such that these effects have to be included in a FE-simulation. Here, homogenization techniques are presented to ensure computational efficiency by avoiding a full numerical simulation with every single sheet and to cover simultaneously the real physical behavior by identifying a linearized transversely isotropic surrogate material model. During this homogenization process, the interlayer between two sheets is incorporated by Zero-Thickness element
Keywords: Contact Mechanics; Lamination Stack; Numerical Homogenization; Material Modelling

Numerical homogenization of elastic and thermal material properties for metal matrix composites (MMC) - Schindler, Stefan; Mergheim, Julia; Zimmermann, Marco; Aurich, Jan C.; Steinmann, Paul (Continuum Mechanics and Thermodynamics, 2016)
A two-scale material modeling approach is adopted in order to determine macroscopic thermal and elastic constitutive laws and the respective parameters for metal matrix composite (MMC). Since the common homogenization framework violates the thermodynamical consistency for non-constant temperature fields, i.e., the dissipation is not conserved through the scale transition, the respective error is calculated numerically in order to prove the applicability of the homogenization method. The thermomechanical homogenization is applied to compute the macroscopic mass density, thermal expansion, elasticity, heat capacity and thermal conductivity for two specific MMCs, i.e., aluminum alloy Al2024 reinforced with 17 or 30% silicon carbide particles. The temperature dependency of the material properties has been considered in the range from 0 to 500°C, the melting temperature of the alloy. The numerically determined material properties are validated with experimental data from the literature as far as possible.
Keywords: Numerical homogenization; Metal matrix composites; Thermomechanical; Material modeling

Numerical Investigation of Jointed Oscillators using Harmonic Balance Techniques - Süß, Dominik; Jerschl, Martin; Willner, Kai; Jerschl, Martin (Proceedings of the International Conference on Noise and Vibration Engineering ISMA, 2014)
Joints play an important role in most mechanical applications and the prediction of the dynamical behavior of jointed structures is a challenging task in structural dynamics. Their inclusion leads to, for example, shifts of the resonance frequencies or of the maximal response amplitude within a resonance due to damping effects. In this paper, the focus is on investigating the behavior of a jointed structure over a broad range of excitation frequencies within the frequency domain corresponding to the stationary behavior in the time domain. Due to the nonlinear forces, it is not possible to directly perform an analytical transformation of the system equations into the frequency domain, so the Harmonic Balance Method (HBM) is applied here. In the framework of the HBM it is assumed that a harmonic excitation of the system leads to a harmonic response. The calculation procedure is applied to a friction oscillator containing a bolted lap joint, which is modeled via different Finite Element models with a corresponding three dimensional contact law. The calculation results are compared to each other.
UnivIS-Import:2015-10-26:Pub.2014.tech.FT.FT-TM.numeri

Numerical investigation of the transient charging behavior of a piezoelectric vibration-based energy harvester for different base excitations - Hegendörfer, Andreas; Mergheim, Julia (Proceedings of SPIE - The International Society for Optical Engineering, 2022)
A piezoelectric vibration-based energy harvester (PVEH) is a combined device, which consists of an electromechanical structure and an electric circuit. Typically, the energy output of a PVEH is too low to continuously supply electrical devices, thus, the harvested energy must be accumulated and stored. In the case of a strongly coupled PVEH, the electrical and mechanical behavior significantly influence each other resulting in complex coupling phenomena. Therefore, system simulations that accurately account for electromechanical coupling are valuable tools for understanding the behavior of PVEHs. In the present work a system simulation method based on the finite-element method (FEM) is applied to investigate the transient charging process of a storage capacitor. A strongly coupled bimorph PVEH with a standard and a synchronized switch harvesting on inductor (SSHI) circuit is considered and a harmonic and a shock-like triangular pulse excitation are applied. The FEM solves the complete set of piezoelectric equations while the electric circuit is considered via the boundary conditions. Therefore, all coupling effects between the mechanical and electrical behavior are precisely taken into account in the simulations. The simulation results show that the standard circuit is more efficient for the harmonic excitation, while the SSHI circuit is more efficient than the standard circuit for the shock-like triangular pulse excitation. Furthermore, the influence of different capacitors on the charging behavior of the standard and SSHI circuit for the harmonic and the shock-like triangular pulse excitation is discussed.
CRIS-Team Scopus Importer:2022-06-24
Keywords: energy harvesting; finite element method; storage capacitor; System simulation; transient charging process

Numerical microstructure prediction by a coupled finite element cellular automaton model for selective electron beam melting - Köpf, Johannes; Soldner, Dominic; Ramsperger, Markus; Mergheim, Julia; Markl, Matthias; Körner, Carolin (Computational Materials Science, 2019)
Selective Electron Beam Melting (SEBM) refers to an additive manufacturing process of building near net shaped components layer wise by iteratively melting of metal powder using an electron beam. Due to the preheating of the material and very high scan velocities of the electron beam, the process allows large processing windows defined by different process strategies. This variety enables the adjustment of part properties by, e.g., targeting certain microstructures. However, this variety has its disadvantage in the need for costly trial and error experiments. Therefore, numerical predictions are inevitable in locating promising process parameter combinations. We present the weak coupling of a Finite-Element (FE) model with a cellular automaton (CA) model to predict the microstructure evolution during SEBM. We use an FE model for the computation of the heat input, since the temperature history mainly influences the subsequent microstructure evolution. The FE model provides precomputed temperature fields for our sophisticated CA-based crystal growth model, which successfully predicts bulk material microstructures. The compound is validated by accurately reproducing the microstructure of an additively build cylinder from CMSX-4 powder, a nickel based superalloy. Special emphasize is laid on the accurate prediction of the microstructure both in the shell as well as the core of the cylinder.
Keywords: Crystal growth; Finite element method; Additive manufacturing; Cellular automata; Nickel-base superalloy; Numerical heat solver; High performance computing; Microstructure simulation; Powder bed fusion; Selective electron beam melting

Numerical modeling of nonlinear photoelasticity - Mehnert, Markus; Oates, William; Steinmann, Paul (International Journal for Numerical Methods in Engineering, 2022)
When molecular photo-switches, such as azobenzene or norbornadiene, are embedded into a sufficiently soft polymer matrix the resulting compound can undergo a mechanical deformation induced by light of a specific wavelength. These photo-sensitive compounds have the potential to be applied as soft actuators without the need for hard wired electronics or a separate energy source. Such characteristics are especially attractive in the design of micro-scale robots but also other applications such as high-speed data transfer or the conversion of photonic energy into a mechanical response holds great promise. Despite these almost futuristic possibilities, photo-sensitive polymers have not yet experienced a sufficient attention in industrial applications. One important factor to increase the acceptance of this group of soft smart materials is the formulation of a rigorous constitutive modeling approach in combination with numerical simulation methods. Thus, in this contribution we present a photo-mechanical modeling approach, departing from the fundamentals published previously. We briefly introduce the necessary constitutive equations which are subsequently utilized in combination with the respective balance laws into a finite element implementation. Finally, the capabilities of the numerical solution approach are illustrated by a simple two-dimensional bench-mark example and subsequently extended to a more complex three-dimensional problem.
CRIS-Team Scopus Importer:2022-12-23
Keywords: finite element methods; materials science; smart materials

Numerical Modelling of Nonlinear Electroelasticity - Steinmann, Paul; Possart, Gunnar; Vu, Duc Khoi (International Journal for Numerical Methods in Engineering, 2007)
UnivIS-Import:2015-04-14:Pub.2007.tech.FT.FT-TM.numeri

Numerical modelling of nonlinear thermo-electro-elasticity - Mehnert, Markus; Pelteret, Jean-Paul; Steinmann, Paul (Mathematics and Mechanics of Solids, 2017)
This work presents the numerical modelling of nonlinear thermo-electro-elasticity in the context of electro-active polymers (EAPs). EAPs are characterised by their electro-mechanical coupling behaviour that converts electrical into mechanical energy. As polymeric materials in general are sensitive to the influence of temperature, thermal effects play an important role in the material behaviour of EAPs. Based on a thermo-electro-mechanically coupled constitutive framework presented in an earlier contribution, a variational formulation is developed and the finite-element method is employed to solve the nonlinear thermo-electro-mechanical coupling problem. The numerical implementation is studied by means of several examples.
Keywords: Nonlinear electro-elasticity; Nonlinear thermo-elasticity; Electro-active polymer; Thermo-electro-mechanical coupling; Finite-element method

Numerical modelling of thermo-electro-viscoelasticity with field-dependent material parameters - Mehnert, Markus; Mokarram, Hossain; Steinmann, Paul (International Journal of Non-Linear Mechanics, 2018)

Numerical modelling of thermomechanical solids with highly conductive energetic interfaces - Javili, Ali; McBride, Andrew; Steinmann, Paul (International Journal for Numerical Methods in Engineering, 2013)
Interfaces within a solid can play a significant role in the overall response of a body. The influence of an interface increases as the scale of the problem decreases. Furthermore, the thermomechanical properties of the interface can differ significantly from those of the surrounding bulk. Such effects are described here using interface elasticity theory. The objective of this contribution is to detail the computational aspects of modelling thermomechanical solids with highly conductive energetic interfaces. The interface is termed energetic in the sense that it possesses its own energy, entropy, constitutive relations and dissipation. The equations governing the fully nonlinear, transient problem are given. They are then solved using an efficient finite element scheme. Full details of the consistent linearisation of the nonlinear governing equations are provided. Key features of highly conductive energetic interfaces are then elucidated via a series of three-dimensional numerical examples. In particular and in contrast to highly conductive thermal interfaces, it is clearly shown that a jump in the heat flux across the interface is possible even in the absence of a heat flux along the interface. © 2012 John Wiley & Sons, Ltd.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.numeri
Keywords: Energetic interfaces; Finite element method; Highly conductive interfaces; Nanomaterials; Thermomechanics

Numerical modelling of thermomechanical solids with mechanically energetic (generalised) Kapitza interfaces - Javili, Ali; McBride, Andrew; Steinmann, Paul (Computational Materials Science, 2012)
Interfaces within a solid can play a significant role in the overall response of the body. The influence of the interface increases as the scale of the problem decreases. Furthermore, the properties of the interface can differ significantly from those of the surrounding bulk. Such effects are described here using interface elasticity theory. The objective of this presentation is to detail the computational aspects of modelling thermomechanical solids with mechanically energetic interfaces. The interface is termed energetic in the sense that it possesses its own energy, entropy, constitutive relations, and dissipation. A mechanically energetic interface does not possess a thermal structure, and thus lacks its own heat capacity, heat conduction and heat expansion coefficient. For a mechanically energetic interface within a thermomechanical solid, the jump of the normal heat flux across the interface is zero while a temperature jump is allowed. In this sense, a mechanically energetic interface can be understood as a generalised Kapitza interface. Therefore the concept of Kapitza thermal resistance is used to control the temperature jump across the interface. The equations governing the fully-nonlinear, transient problem are given. They are then solved using an efficient finite element scheme. Key features of mechanically energetic interfaces are elucidated via a series of three-dimensional numerical examples. © 2012 Elsevier B.V. All rights reserved.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Finite element method; Kapitza interface; Nanomaterials; Thermoelasticity

Numerical Optimization of a Nonlinear Nonideal Piezoelectric Energy Harvester Using Deep Learning - Hegendörfer, Andreas; Steinmann, Paul; Mergheim, Julia (Journal of Low Power Electronics and Applications, 2023)
This contribution addresses the numerical optimization of the harvested energy of a mechanically and electrically nonlinear and nonideal piezoelectric energy harvester (PEH) under triangular shock-like excitation, taking into account a nonlinear stress constraint. In the optimization problem, a bimorph electromechanical structure equipped with the Greinacher circuit or the standard circuit is considered and different electrical and mechanical design variables are introduced. Using a very accurate coupled finite element-electronic circuit simulator method, deep neural network (DNN) training data are generated, allowing for a computationally efficient evaluation of the objective function. Subsequently, a genetic algorithm using the DNNs is applied to find the electrical and mechanical design variables that optimize the harvested energy. It is found that the maximum harvested energy is obtained at the maximum possible mechanical stresses and that the optimum storage capacitor for the Greinacher circuit is much smaller than that for the standard circuit, while the total harvested energy by both configurations is similar.
CRIS-Team Scopus Importer:2023-04-07
Keywords: coupled optimization; electronic circuit simulator; finite element method; multiphysics optimization; numerical optimization; piezoelectric energy harvesting

Numerical simulation of friction in metal forming using a halfspace model - Hauer, Franz; Vierzigmann, Ulrich; Willner, Kai; Engel, Ulf (AIP Conf. Proc. 1536, 2011)
Sheet and bulk metal forming are widely used manufacturing methods. The industrial trend towards function integration leads to a demand for workpieces having features of both methods. The new forming technology sheet-bulk metal forming is a promising approach to manufacture workpieces with functional elements. Tribological aspects generally play an important role in metal forming processes. Especially for the formability of functional elements friction is very important. The coexistence of low and high contact pressures is characteristic of sheet-bulk metal forming and presents a challenge for the friction modelling. The surfaces of tool and workpiece are always rough so that initial contact only occurs at the asperities of surface roughness. Consequently for small and moderate loads the real contact area is smaller than the apparent contact area. Surface traction can only occur in the real contact area so that it is necessary to determine the real contact area in order to study the tribological behaviour of contact pairs. In order to get an accurate determination of the real contact area it is necessary to calculate the surface deformation in a three-dimensional model and to validate the simulation model by measurements. The halfspace approach has the significant advantage that only the surface has to be discretised while in a Finite Element Analysis the whole bulk has to be discretised. Consequently the numerical effort and thus the calculation time in the halfspace model are much lower than in FE-modelling. The numerical solution scheme based on the halfspace theory is presented in this paper. Results of the calculation of the real contact area of rough surfaces are compared to experimental data from ultrasonic inspection. Friction coefficients calculated with the halfspace model are compared to results of strip drawing tests. © 2011 American Institute of Physics.
UnivIS-Import:2015-04-16:Pub.2011.tech.FT.FT-TM.numeri_9
Keywords: friction; halfspace model; metal forming; real contact area; Simulation; strip drawing; ultrasonic inspection

Numerical simulation of particles movement in cellular flows under the influence of magnetic forces - Hribersek, Matjaz; Steinmann, Paul; Ravnik, Jure; Vogel, Franziska Anna (Proceedings of the 82nd Annual Meeting of the International Association of Applied Mathematics and Mechanics, 2011)
A numerical model of particle motion in fluid flow under the influence of hydrodynamic and magnetic forces is presented. As computational tool, a flow  solver based on the Boundary Element Method is used. The Euler-Lagrange  formulation of multiphase flow is considered. In the case of a particle with a magnetic moment in a nonuniform external magnetic field, the Kelvin body force  acts on a single particle. The derived Lagrangian particle tracking algorithm is  used for simulation of dilute suspensions of particles in viscous flows taking into account gravity, buoyancy, drag, pressure gradient, added mass and magnetophoretic force. As a benchmark test case the magnetite particle motion in  cellular flow field of water is computed with and without the action of the magnetic  force. The effect of the Kelvin force on particle motion and separation from themain flow is studied for a predefined magnetic field and different values of  magnetic flux density.
UnivIS-Import:2015-04-16:Pub.2011.tech.FT.FT-TM.numeri_5

Numerical simulation of particles movement in cellular flows under the influence of magnetic forces - Ravnik, Jure; Hribersek, Matjaz; Vogel, Franziska Anna; Steinmann, Paul (International Journal of Simulation Modelling, 2014)
A numerical model of particle motion in fluid flow under the influence  of hydrodynamic and magnetic forces is presented. The  Lagrangian particle tracking algorithm was developed being capable  of simulating dilute suspensions of particles in viscous flows where  gravity, buoyancy, drag, pressure gradient, added mass and  magnetophoretic forces are taken into account. The method is used   to study the behaviour of magnetite particles in a periodic cellular  flow field under the influence of a magnetic field produced by electric  wires placed in cell centres. For such a flow field it is known  that particles in steady state merge into individual trajectories. The   influence of the magnetic field on the particle trajectories is examined  and an exponential model for the time evolution of the  fraction of adhered particles to the electric wires is proposed. Three  particle Stokes number values are considered: 0.01, 0.1 and 1. The   existence of a critical magnetic pressure coefficient was found, at  which all particles end up to be adhered to the wires. The critical  magnetic pressure coefficient was found to be proportional to the   Stokes number. For sub-critical magnetic pressure coefficient, the  particle trajectories are significantly altered by the magnetic field,   both in their shape and in their number. Furthermore, in the   sub-critical regime, the minimal distance of particles to the cell   centres is larger for particles with smaller Stokes numbers.
UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.numeri
Keywords: Dispersed Two Phase Flow; Lagrangian Particle Tracking; Magnetic Force; Hydrodynamic Forces; Cellular Flow

Numerical simulations of the flow and aerosol dispersion in a violent expiratory event: Outcomes of the "2022 International Computational Fluid Dynamics Challenge on violent expiratory events" - Pallares, Jordi; Fabregat, Alexandre; Lavrinenko, Akim; Bin Norshamsudin, Hadifathul Akmal; Janiga, Gabor; Fletcher, David F.; Inthavong, Kiao; Zasimova, Marina; Ris, Vladimir; Ivanov, Nikolay; Castilla, Robert; Gamez-Montero, Pedro Javier; et al. (Physics of Fluids, 2023)
This paper presents and discusses the results of the "2022 International Computational Fluid Dynamics Challenge on violent expiratory events"aimed at assessing the ability of different computational codes and turbulence models to reproduce the flow generated by a rapid prototypical exhalation and the dispersion of the aerosol cloud it produces. Given a common flow configuration, a total of 7 research teams from different countries have performed a total of 11 numerical simulations of the flow dispersion by solving the Unsteady Reynolds Averaged Navier-Stokes (URANS) or using the Large-Eddy Simulations (LES) or hybrid (URANS-LES) techniques. The results of each team have been compared with each other and assessed against a Direct Numerical Simulation (DNS) of the exact same flow. The DNS results are used as reference solution to determine the deviation of each modeling approach. The dispersion of both evaporative and non-evaporative particle clouds has been considered in 12 simulations using URANS and LES. Most of the models predict reasonably well the shape and the horizontal and vertical ranges of the buoyant thermal cloud generated by the warm exhalation into an initially quiescent colder ambient. However, the vertical turbulent mixing is generally underpredicted, especially by the URANS-based simulations, independently of the specific turbulence model used (and only to a lesser extent by LES). In comparison to DNS, both approaches are found to overpredict the horizontal range covered by the small particle cloud that tends to remain afloat within the thermal cloud well after the flow injection has ceased.
CRIS-Team Scopus Importer:2023-04-28

Numerical treatment of frictional contact in ALE formulation for disc brake assemblies - Weidauer, Tim; Willner, Kai (Mechanical Systems and Signal Processing, 2020)
The Arbitrary-LAGRANGIAN-EULERIAN (ALE) formulation is a popular approach for finite element (FE) models governed by large rigid body movement. It facilitates the decomposition of guiding motions and relative deformation inside the model by considering the main motion of the system in the form of a material flow inside the FE mesh. This way, similar to fluid dynamics, an observer focused on spatial positions rather than individual material particles is introduced. Among others, this approach serves as an established tool in the simulation of tire rolling contact and its dynamics. However, while allowing for specific mesh refinement and simplifying issues such as finite displacements due to rigid body motions, it complicates contact computations. The history of contacting particles is not inherently tracked, demanding a special treatment of their relative displacement for evaluating their frictional contact state. The handling of stationary problems in this context is well-studied for the examples of elastic-rigid rolling contact, including inelastic material properties and thermo-mechanical coupling. This work attends to the remaining area of frictional contact in transient ALE problems and extends the methods towards elastic-elastic contact coupling in a three dimensional framework. To this end, classic Zero-Thickness contact elements, whose application in these surroundings is enabled by the relative kinematic ALE framework in the first place, are extended towards ALE compatibility. The proposed approach involves a slip-based contact formulation including inelastic slip variables and is applied in the field of disc brake assemblies. In here, several stationary and transient studies of emerging contact patterns and limit cycles are accomplished, outlining the capabilities of the proposed implementation.
CRIS-Team Scopus Importer:2020-06-09
Keywords: Arbitrary-LAGRANGIAN-EULERIAN (ALE); Disc brake; Friction oscillator; Limit cycle; Transient frictional contact; Zero-Thickness element

Observations on additive plasticity in the logarithmic strain space at excessive strains - Friedlein, Johannes; Mergheim, Julia; Steinmann, Paul (International Journal of Solids and Structures, 2022)
Additive plasticity in the logarithmic strain space is compared to multiplicative plasticity for various loading cases including coaxial and non-coaxial plastic deformations. Even though both finite plasticity approaches are based on total Lagrangian descriptions, the former is popular due to its inherent similarity to the infinitesimal theory and its easy extensibility. However, since its introduction several limitations of additive plasticity in the logarithmic strain space have been discovered. In this study, these problems such as stress rotation and softening are considered, revealing that fundamental differences compared to multiplicative plasticity occur for non-coaxial plastic deformations. We focus in particular on the observed softer response of the additive based approach, which is analysed in depth using three numerical examples including two well-known benchmarks for finite plasticity. By means of these finite element simulations the softer and possibly even localising response of additive plasticity in the logarithmic strain space is confirmed.
CRIS-Team WoS Importer:2022-04-29

On 3-D coupled BEM-FEM simulation of nonlinear electro-elastostatics - Vu, Duc Khoi; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2012)
In this work the numerical simulation of nonlinear electro-elastostatics is considered with a special focus on the influence of the free space surrounding an electro-sensitive body. The influence of the free space on the electric field and on the deformation field inside an electro-sensitive body can become highly important for many materials and can change profoundly the simulation results. In order to take into account this influence, the free space must be simulated by using, for example, the finite element method (FEM) or the boundary element method (BEM). A coupled BEM-FEM approach is employed here to exploit the advantage of the finite element method in solving nonlinear problems and the advantage of the boundary element method in dealing with infinite domains. Numerical studies using this approach show that for materials with low electric permittivity, the free space can have a huge impact on the simulated electric and deformation fields. The same observation is expected for the general case of nonlinear electro-elasticity and nonlinear electro-viscoelasticity and constitutes the direction for future works. © 2011 Elsevier B.V.
UnivIS-Import:2015-04-14:Pub.2012.tech.FT.FT-TM.on3dco
Keywords: Coupled BEM-FEM analysis; Nonlinear coupling; Nonlinear elastostatics; Nonlinear electrostatics

On adaptive mesh coarsening procedures for the virtual element method for two-dimensional elastic problems - van Huyssteen, Daniel; Rivarola, Felipe Lopez; Etse, Guillermo; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2024)
In the context of adaptive remeshing, the virtual element method provides significant advantages over the finite element method. The attractive features of the virtual element method, such as the permission of arbitrary element geometries, and the seamless permission of ‘hanging’ nodes, have inspired many works concerning error estimation and adaptivity. However, these works have primarily focused on adaptive refinement techniques with little attention paid to adaptive coarsening (i.e. de-refinement) techniques that are required for the development of fully adaptive remeshing procedures. In this work novel indicators are proposed for the identification of patches/clusters of elements to be coarsened, along with a novel procedure to perform the coarsening. The indicators are computed over prospective patches of elements rather than on individual elements to identify the most suitable combinations of elements to coarsen. The coarsening procedure is robust and suitable for meshes of structured and unstructured/Voronoi elements. Numerical results demonstrate the high degree of efficacy of the proposed coarsening procedures and sensible mesh evolution during the coarsening process. It is demonstrated that critical mesh geometries, such as non-convex corners and holes, are preserved during coarsening, and that meshes remain fine in regions of interest to engineers, such as near singularities.
CRIS-Team Scopus Importer:2023-10-20
Keywords: De-refinement; Elasticity; Mesh adaptivity; Mesh coarsening; Virtual element method; Voronoi meshes

On age-dependent bone remodeling - Papastavrou, Areti; Schmidt, Ina; Deng, Kefu; Steinmann, Paul (Journal of Biomechanics, 2020)
A number of previous studies have investigated the possibilities of modelling the change in density of bones. Remodeling can be formulated at the constitutive or the kinematic level. In this work we introduce a formulation for the density growth process which takes not only the mechanical stimulus into account but also the influence of age on the evolution of growth. We demonstrate the implementation in the context of the finite element method. This novel approach is illustrated for a simple uniaxial extension test and is verified against previous numerical results. Moreover, two further physiologically motivated examples are performed. The results of the proposed modified model show excellent agreement with comparable results from literature and are promising for the application to real-life problems.
CRIS-Team Scopus Importer:2020-03-20
Keywords: Adaption; Bone remodeling; Density change; Finite element method; Growth

On an atomistic scale finite element method for the simulation of ferroelectric functional materials - Endres, Florian; Steinmann, Paul (Proceedings on 2nd SMMM Conference on Smart Materials, 2014)
Molecular dynamics (MD) simulations of ferroelectric materials improved over the last decades and are an indispensable tool in order to predict the behaviour of materials on an atomistic level. Especially the core-shell model has been used for the simulation of ferroelectric materials. However the computational costs of MD calculations are significant. In this work molecular statics has been implemented as a finite element method using the core-shell model. For validation of the molecular statics algorithm barium titanate has been simulated. Furthermore periodic boundary conditions have been applied in order to simulate bulk material.
UnivIS-Import:2015-04-16:Pub.2014.tech.FT.FT-TM.onanat

On Applying Fuzzy Arithmetic to Finite Element Problems - Willner, Kai; Hanss, M.; Guidati, S. (Proceedings of the 17th Annual Meeting of the North American Fuzzy Information Processing Society NAFIPS 98, 1998)
UnivIS-Import:2015-04-16:Pub.1998.tech.FT.FT-TM.onappl

On a recursive algorithm for avoiding mesh distortion in inverse form finding - Germain, Sandrine; Steinmann, Paul (Journal of the Serbian Society for Computational Mechanics, 2012)
A challenge in the design of functional parts is the determination of the initial, undeformed shape such that under a given load a part will obtain the desired deformed shape. A shape optimization formulation might be used to determine the initial shape in the sense of an inverse problem via successive iterations of a direct mechanical problem. In this paper, we present a shape optimization formulation for elastoplastic materials with a constitutive model for anisotropic additive elastoplasticity in the logarithmic strain space. A discrete sensitivity analysis is performed and gives the analytical gradient of the objective function needed in the optimization algorithm. We found that the use of the coordinates of the functional component as design variables led to mesh distortions. Without a split of the total force applied on the component and an update of the undeformed configuration between two steps the optimization algorithm is not able to find an appropriate minimum. Three numerical examples in isotropic and anisotropic elastoplasticity illustrate the structure of such a recursive algorithm for avoiding mesh distortions.
UnivIS-Import:2015-03-09:Pub.2012.tech.FT.FT-TM.onarec
Keywords: Anisotropy; Elastoplasticity; Inverse form finding; Large strain; Shape optimization

On a recursive formulation for solving inverse form finding problems in isotropic elastoplasticity - Germain, Sandrine; Landkammer, Philipp; Steinmann, Paul (Advanced Modeling and Simulation in Engineering Sciences, 2014)
UnivIS-Import:2015-03-09:Pub.2014.tech.FT.FT-TM.onarec

On a Solution Strategy for Energy-Based Mesh Optimization in Finite Hyperelastostatics - Scherer, Michael; Denzer, Ralf; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2008)
The objective of this work is the development of a numerical solution strategy for energy-based mesh optimization in finite hyperelastostatics. In finite element computations that rely on the principle of minimum potential energy, the variational principle itself provides the basis for r-adaptive methods. The numerical solution can be improved by further minimizing the discrete potential energy with respect to the material node point positions. In this paper, we regard the mesh optimization as a nonlinear minimization problem with equality and inequality constraints. The equality constraints correspond to the spatial equilibrium condition, whereas the inequality constraints are given by the natural restriction that material elements with a negative volume (Jacobian) are inadmissible. Based on this interpretation, we develop a stable numerical solution strategy in which two approaches of nonlinear programming are combined. Applying a barrier method, the minimization problem is transformed into a sequence of problems without inequality constraints. Each problem of the sequence is solved by means of a Newton scheme that operates on the constrained surface given by the spatial equilibrium condition. © 2007 Elsevier B.V. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2008.tech.FT.FT-TM.onasol
Keywords: Barrier method; Configurational forces; Energy minimization; Hyperelasticity; r-Adaptivity

On biological availability dependent bone remodeling - Papastavrou, Areti; Schmidt, Ina; Steinmann, Paul (Computer Methods in Biomechanics and Biomedical Engineering, 2020)
Modeling the evolution of bone density is relevant for understanding, simulation and possible prediction of bone response to external and internal influences. In this work we present a formulation for the bone density evolution process that takes into account not only the commonly considered mechanical stimulus, but, as novelty, also the influence of the availability of nutrients and hormones, with its implementation pursued within the finite element method. A simple uni-axial extension test is used to illustrate and compare our novel model against the classical approach. The results of the proposed modified model are promising for application to real-life problems.
CRIS-Team Scopus Importer:2020-03-17
Keywords: biological availability; Bone remodeling; density change; finite element method; growth

On bridging domain methods to couple particle- and finite-element-based simulations - Pfaller, Sebastian; Steinmann, Paul (Proceedings of the 80th Annual Meeting of the International Association of Applied Mathematics and Mechanics, 2010)
This contribution investigates schemes to couple domains of different resolutions in space, a problem frequently arising in multi-scale modelling of materials. To couple a standard finite element domain with a high resolution atomistic or molecular, i.e. particle-based domain, a so-called bridging domain is considered, e.g. Xu and Belytschko [1], Zhang, Khare, Lu and Belytschko [2] and Bauman et al. [3]. The main goal is to separate the computation of finite element and atomistic domains as much as possible, amongst others, to calculate the different domains on several CPUs.
UnivIS-Import:2015-04-16:Pub.2010.tech.FT.FT-TM.onbrid

On characterization of the electro-mechanically coupled properties of VHB polymer - Mokarram, Hossain; Vu, Duc Khoi; Steinmann, Paul (Proceedings on 2nd SMMM Conference on Smart Materials, 2014)
UnivIS-Import:2015-04-16:Pub.2014.tech.FT.FT-TM.onchar_9

On constitutive models for the momentum transfer to particles in fluid-dominated two-phase flows - Cui, Yan; Ravnik, Jure; Hribersek, Matjaz; Steinmann, Paul (Springer Verlag, 2018)

On continuum modeling of cell aggregation phenomena - Firooz, Soheil; Kaessmair, Stefan; Zaburdaev, Vasily; Javili, Ali; Steinmann, Paul (Journal of the Mechanics and Physics of Solids, 2022)
Cellular aggregates play a significant role in the evolution of biological systems such as tumor growth, tissue spreading, wound healing, and biofilm formation. Analysis of such biological systems, in principle, includes examining the interplay of cell–cell interactions together with the cell–matrix interaction. These two interaction types mainly drive the dynamics of cellular aggregates which is intrinsically out of equilibrium. Here we propose a non-linear continuum mechanics formulation and the corresponding finite element simulation framework to model the physics of cellular aggregate formation. As an example, we focus in particular on the process of bacterial colony formation as recently studied by Kuan et al. (2021). Thereby we describe the aggregation process as an active phase separation phenomenon. We develop a Lagrangian continuum description of the problem which yields a substantial simplification to the formulations of the governing equations. Due to the presence of spatial Hessian and Laplacian operators, a gradient-enhanced approach is required to incorporate C1 continuity. In addition, a robust and efficient finite element formulation of the problem is provided. Taylor–Hood finite elements are utilized for the implementation to avoid instabilities related to the LBB condition. Finally, through a set of numerical examples, the influence of various parameters on the dynamics of the cellular aggregate formation is investigated. Our proposed methodology furnishes a general framework for the investigation of the rheology and non-equilibrium dynamics of cellular aggregates.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Active phase separation; Cellular aggregates; Continuum model; Eulerian approach; Lagrangian approach

On curvature approximation in 2D and 3D parameter-free shape optimization - Schmitt, Oliver; Steinmann, Paul (Structural and Multidisciplinary Optimization, 2016)
Manufacturing constraints considered in shape optimization often need to be expressed in terms of curvature. Within the scope of a sensitivity-based parameter-free shape optimization approach, curvature constraints have to be formulated in terms of the FE node coordinates in order to derive the required first order gradients with respect to the design node coordinates. In this contribution we introduce approaches to approximate the curvature of a FE model using the coordinates of the FE nodes at the boundary of the geometry, as a smooth representation of the design boundary is not available. Therefore, in the 2D case we present two different smooth curves which represent the design boundary and for which the curvature can be computed analytically. In a third 2D, as well as in our 3D approach, we use geometric information of the discretization such as the distance to neighboring boundary nodes and edge normals to approximate the curvature at the respective boundary node under consideration.
Keywords: shape optimization; manufacturing constraints; parameter-free; curvature approximation; sensitivity analysis

On curvature control in node-based shape optimization - Schmitt, Oliver; Steinmann, Paul (PAMM, 2015)
We present and compare three approaches to control of the curvature of the domain boundary in two–dimensional shape optimization. Since the coordinates of the FE–nodes are used as design variables, objective and constraint functions have to be formulated in terms of the nodal coordinates. Therefore we investigate various formulations for the curvature of the domain boundary in terms of the coordinates of the boundary nodes. In addition, the sensitivities of these expressions with respect to the design nodes are required for the application of gradient–based optimization algorithms.
UnivIS-Import:2015-10-26:Pub.2015.tech.FT.FT-TM.oncurv_5
Keywords: node-based shape optimization; manufacturing constraint; curvature

On effective behavior of microstructures embedding general interfaces with damage - Saeb, Saba; Steinmann, Paul; Javili, A. (Computational Mechanics, 2019)
The interface between constituents of a multiphase material exhibits properties different from those of the bulk and can lead to major alternation of the material response. Interface effects are particularly important for multiphase nano-materials where the area-to-volume ratio is significantly large. In this contribution, we study the influence of a degrading general interface. That is, we allow for the initiation and accumulation of damage on a generalized interface accounting for both jumps of the displacement and the traction across the interface. The applicability of the proposed framework is demonstrated through several numerical examples. We present a parametric study on the influence of a broad range of interface material parameters on the overall behavior of various microstructures subject to volumetric loading and unloading. The numerical results illustrate that the resistance along the interface plays a key role in the resulting damage mechanism and could potentially prevent the detachment of the inclusion from the matrix regardless of the resistance across the interface or bulk material parameters. This behavior is observed and shown for both two- and three-dimensional examples. Moreover, the size-effect due to the general interface model is examined and compared against other interface models. Finally, the influence of the boundary conditions on the effective response and damage initiation of several microstructures is studied.
CRIS-Team Scopus Importer:2019-06-04
Keywords: Cohesive interface; Computational homogenization; Elastic interface; Finite deformation; General interface

On equilibrating non-periodic molecular dynamics samples for coupled particle-continuum simulations of amorphous polymers - Weber, Felix; Ries, Maximilian; Bauer, Christof; Wick, Christian; Pfaller, Sebastian (Forces in Mechanics, 2023)
In the context of fracture simulations of polymers, the molecular mechanisms in the vicinity of the crack tip are of particular interest. Nevertheless, to keep the computational cost to a minimum, a coarser resolution must be used in the remaining regions of the numerical sample. For the specific case of amorphous polymers, the Capriccio method bridges the gap between the length and time scales involved at the different levels of resolution by concurrently coupling molecular dynamics (MD) with the finite element method (FEM). Within the scope of the Capriccio approach, the coupling to the molecular MD region introduces non-periodic, so-called stochastic boundary conditions (SBC). In similarity to typical simulations under periodic boundary conditions (PBC), the SBC MD simulations must reach an equilibrium state before mechanical loads are exerted on the coupled systems. In this contribution, we hence extensively study the equilibration properties of non-periodic MD samples using the Capriccio method. We demonstrate that the relaxation behavior of an MD-FE coupled MD domain utilizing non-periodic boundary conditions is rather insensitive to the specific coupling parameters of the method chosen to implement the boundary conditions. The behavior of an exemplary system equilibrated with the parameter set considered as optimal is further studied under uniaxial tension and we observe some peculiarities in view of creep and relaxation phenomena. This raises important questions to be addressed in the further development of the Capriccio method.<br
Keywords: Molecular dynamics; Finite element method; Multiscale modeling; Particle-continuum coupling; Simulation of polymers

On finite strain models for nano-filled glassy polymers - Mokarram, Hossain; Steinmann, Paul (Proceedings of the 7th European Conference on Constitutive Models for Rubber, 2012)
The recently proposed constitutive framework based on logarithmic strain space by Miehe et al. (3) is a successful model for the modelling of amorphous glassy polymers. The modular structure of this model makes it attractive especially for the numerical implementation. In this contribution, the Miehe model will be adapted to model the influence of different types of nano-fillers mixed into bulk amorphous glassy polymers. Here, different types of amorphous glassy polymers with various filler content, orientation of nanofillers and loaded by different strain rates have been investigated experimentally. Then, the Miehe model will be extended towards modelling the nano-particle influence in the amorphous glassy polymer which can be conceptualized by adapting the appropriate material parameters. The proposed modified model will finally be validated with experimental data. © 2012 Taylor & Francis Group.
UnivIS-Import:2015-04-16:Pub.2012.tech.FT.FT-TM.onfini

On Frictionally Constrained Wing- Cracks - Willner, Kai; Selvadurai, A.P.S.; Gaul, L. (Archives of Mechanics, 2005)
This paper examines the mechanics of wing-cracks that are located at its extremities of an interface region with Coulomb friction. The region containing the interface and the wing-cracks is first subjected to an isotropic compression, which induces closure of the interface region. The region is then subjected to a uniaxial compression in an incremental fashion. Since the frictional effects are restricted to pre-defined surfaces, the boundary element technique can be applied quite successfully to determine the influence of Coulomb friction on the development of stress intensity factors at the tips of the wing-cracks.
UnivIS-Import:2015-03-09:Pub.2005.tech.FT.FT-TM.onfric

On generalized crystal-plasticity based on defect-densities in a second-order continuum - Steinmann, Paul (GAMM-Mitteilungen, 2013)
Single crystals display various defects that may potentially act as obstacles to further evolution of inelastic deformations, i.e. to further plastic flow. These are translational defects in terms of dislocations, rotational defects in terms of disclinations, and (dilatational) pointdefects in terms of lattice vacancies or interstitial atoms. A formulation of generalized crystalplasticity is proposed that incorporates the densities of these defects in order to capture the hardening of the material. In particular the inclusion of the defect densities other than the dislocation density requires to root the formulation in a second-order continuum description. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.ongene
Keywords: Disclinations; Dislocations; Point-Defects; Torsion

On gradient-based optimization strategies for inverse problems in metal forming - Landkammer, Philipp; Söhngen, Benjamin; Steinmann, Paul; Willner, Kai (GAMM-Mitteilungen, 2017)
In the context of metal forming, optimization issues typically lead to inverse problems with a least-squares minimization as the objective. Due to the nonlinearities in forming simulations, iterative optimization approaches have to be considered. Gradient-based solution strategies for two inverse problems are proposed and compared to each other. Firstly, the identification of elasto-plastic material parameters is regarded. Secondly, a recently developed approach for the determination of an optimal workpiece design is investigated. As a special feature, both approaches can be coupled in a non-invasive fashion to arbitrary external finite element software via subroutine
Keywords: Inverse problems; metal forming; nonlinear least-squares; parameter identification; shape optimization

On Inverse Form Finding for Anisotropic Elastoplastic Materials - Germain, Sandrine; Steinmann, Paul (AIP Conference Proceedings, 2011)
The goal of this contribution is to present an extension of the work of Germain et al. [1] on inverse form finding for anisotropic hyperelastic materials to the case of anisotropic elastoplastic materials formulated in the logarithmic strain space. A short review of the theoretical aspects is presented. Based on some numerical examples we show that our method for inverse form finding in elastoplasticity can be used if the plastic strains are previously given as it is the case when a desired hardening state is prescribed. © 2011 American Institute of Physics.
UnivIS-Import:2015-04-16:Pub.2011.tech.FT.FT-TM.oninve_3
Keywords: Anisotropy; Elastoplasticity; Inverse Form Finding; Large Strain; Logarithmic Strain

On inverse form finding for orthotropic plasticity - Landkammer, Philipp; Germain, Sandrine; Steinmann, Paul (Computer Assisted Mechanics and Engineering Sciences, 2014)
Inverse form finding aims to determine the optimum blank design of a workpiece whereby the desired spatial configuration that is obtained after a forming process, the boundary conditions and the applied loads are known. Inputting the optimal material configuration, a subsequent FEM computation then has to result exactly in the nodal coordinates of the desired deformed workpiece. Germain et al. [1] recently presented a new form finding strategy for isotropic elastoplasticity. Switching between the direct and the inverse mechanical formulation, while fixing the internal plastic variables in the inverse step, uniquely detects the undeformed configuration iteratively. In this contribution, the developed recursive algorithm is extended to anisotropic plasticity. In particular the orthotropic Hill yield function is considered. A load and a displacement-controlled example demonstrate that this new strategy requires only a few iterations to determine the optimal initial design whereby an almost linear convergence rate is obtained. Copyright © 2013 by Institute of Fundamental Technological Research, Polish Academy of Sciences.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.oninve
Keywords: Inverse FEM; Inverse form finding; Logarithmic strain space; Optimum blank design; Orthotropic Hill's yield criterion

On Language Varieties Without Boolean Operations - Birkmann, Fabian; Milius, Stefan; Urbat, Henning (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2021)
Eilenberg’s variety theorem marked a milestone in the algebraic theory of regular languages by establishing a formal correspondence between properties of regular languages and properties of finite monoids recognizing them. Motivated by classes of languages accepted by quantum finite automata, we introduce basic varieties of regular languages, a weakening of Eilenberg’s original concept that does not require closure under any boolean operations, and prove a variety theorem for them. To do so, we investigate the algebraic recognition of languages by lattice bimodules, generalizing Klíma and Polák’s lattice algebras, and we utilize the duality between algebraic completely distributive lattices and posets.
CRIS-Team Scopus Importer:2021-04-30

On mesh refinement procedures for the virtual element method for two-dimensional elastic problems - van Huyssteen, Daniel; Rivarola, Felipe Lopez; Etse, Guillermo; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2022)
The virtual element method is an extension of the finite element method permitting arbitrary polygonal/polyhedral element geometry. The method's mesh flexibility is well-known and is beginning to be exploited in the context of mesh adaptivity. In this work a variety of novel approaches to the computation of isotropic and anisotropic mesh refinement indicators suited to the VEM are presented and comparatively assessed for the case of two-dimensional linear elasticity on structured meshes. Additionally, a novel investigation of the contributions of the two distinctive terms of the VE matrix, the consistency and stabilization terms, in the context of mesh adaptivity is performed. The results demonstrate that the best performance is achieved using combination of refinement procedures based on the displacement and strain fields. Furthermore, the results indicate that the stabilization term can be exploited to enhance adaptive refinement procedures.
CRIS-Team Scopus Importer:2022-04-08
Keywords: Anisotropic adaptivity; Elasticity; Mesh adaptivity; Mesh refinement procedure; Refinement indicators; Virtual element method

On molecular static and surface-enhanced continuum modeling of nano-structures - Davydov, Denis; Javili, Ali; Steinmann, Paul (Computational Materials Science, 2013)
Possible links between discrete and continuum formulations have been discussed in the scientific community since several decades. Different atomistic expressions for the continuum fields (most importantly stresses) were proposed. As an example, it is possible to link discrete models to a continuum formulation based on spatial averaging in the Eulerian configuration followed by probability (statistical) averaging. As an alternative to Eulerian averaging, Lagrangian averaging has been recently proposed. Both approaches allow calculation of the local continuum fields from atomistic simulations. From the continuum formulation perspective, the behavior of solids at the nanoscale can be captured based on a surface-enhanced continuum (SEC) theory whereby the surface is equipped with its own constitutive structure. A distinct advantage of continuum models over their atomistic counterparts is the increased computational efficiency. In this contribution we compare atomistic fields obtained from molecular statics (MS) simulations to their counterpart, obtained from numerical approximations to the SEC theory. Bulk elastic parameters for the continuum constitutive model are obtained directly from the atomistic model. A representative numerical simulation of face-centered-cubic (FCC) copper is used to compare the two approaches. The ability of the continuum formulation enhanced with a surface energy to model size effects, as observed in the atomistic simulations, is shown. The local fields evaluated using both the continuum and discrete approach are in a good agreement. The dependence of the results obtained from the atomistic-to-continuum procedure on both the averaging radius and the proximity of the free surface is studied. Eulerian and Lagrangian averaging approaches are shown to give comparable results for the here considered FCC crystal.
UnivIS-Import:2015-03-09:Pub.2012.tech.FT.FT-TM.onmole
Keywords: Atomistic to continuum; Surface elasticity; Nano-materials; Surface-enhanced continuum theory

On molecular statics simulation of ferroelectric barium titanate - Endres, Florian; Steinmann, Paul (Special Issue: 84th Annual Meeting of the International Association of Applied Mathematics and Mechanics, 2013)
The present contribution deals with the atomistic modelling of ferroelectric barium titanate. In this context a core-shell model is implemented in a Molecular Static algorithm. Furthermore, Coulomb forces are simulated by the Wolf summation method in order to allow for a small cut off radius. We discuss the core-shell model, molecular statics as a finite elements approach and present some numerical results.

On molecular statics simulations of ferroelectric functional materials - Steinmann, Paul; Endres, Florian (Proceedings in Applied Mathematics and Mechanics, 2015)
The simulation of ferroelectric materials on the atomistic length scale is getting more and more important due to recent advancements in related manufacturing technologies. Therefore, we present an extended molecular statics algorithm in order to not only compute equilibrium configurations efficiently but also to consider the deformation of a discrete particle system due to macroscopic stress. Furthermore, we discuss the impact of mechanical stress and strain on the spontaneous polarization and the magnitude of the coercive field of a ferroelectric barium titanate system.

On nonlinear thermo-electro-elasticity - Mehnert, Markus; Mokarram, Hossain; Steinmann, Paul (Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2016)
Electro-active polymers (EAPs) for large actuations are nowadays well-known and promising candidates for producing sensors, actuators and generators. In general, polymeric materials are sensitive to differential temperature histories. During experimental characterizations of EAPs under electro-mechanically coupled loads, it is difficult to maintain constant temperature not only because of an external differential temperature history but also because of the changes in internal temperature caused by the application of high electric loads. In this contribution, a thermo-electro-mechanically coupled constitutive framework is proposed based on the total energy approach. Departing from relevant laws of thermodynamics, thermodynamically consistent constitutive equations are formulated. To demonstrate the performance of the proposed thermo-electro-mechanically coupled framework, a frequently used non-homogeneous boundary-value problem, i.e. the extension and inflation of a cylindrical tube, is solved analytically. The results illustrate the influence of various thermo-electro-mechanical couplings.
Keywords: electro-mechanical problem; thermo-mechanical problem; nonlinear elasticity; electro-active polymers; thermo-electro-mechanical coupling

On optimization of heterogeneous materials for enhanced resistance to bulk fracture - Singh, Sukhminder; Pflug, Lukas; Mergheim, Julia; Stingl, Michael (Forces in Mechanics, 2023)
We propose a novel approach to optimize the design of heterogeneous materials, with the goal of enhancing their effective fracture toughness under mode-I loading. The method employs a Gaussian processes-based Bayesian optimization framework to determine the optimal shapes and locations of stiff elliptical inclusions within a periodic microstructure in two dimensions. To model crack propagation, the phase-field fracture method with an efficient interior-point monolithic solver and adaptive mesh refinement, is used. To account for the high sensitivity of fracture properties to initial crack location with respect to heterogeneities, we consider multiple cases of initial crack and optimize the material for the worst-case scenario. We also impose a minimum clearance constraint between the inclusions to ensure design feasibility. Numerical experiments demonstrate that the method significantly improves the fracture toughness of the material compared to the homogeneous case.
CRIS-Team Scopus Importer:2023-07-07
Keywords: Bayesian optimization; Fracture toughness; Heterogeneous materials; Phase-field method

On Optimization Strategies for Inverse Problems in Metalforming - Söhngen, Benjamin; Caspari, Michael; Willner, Kai; Steinmann, Paul (Sheet Bulk Metal Forming - Research Results of the TCRC73, 2020)
In this contribution we consider inverse mechanical problems in terms of parameter identification and shape optimization. The fundamental material behavior is thereby modelled with an elasto-plastic constitutive law based on the logarithmic strain space, considering anisotropic yield and kinematic hardening. The identification of the constitutive material parameters is based on the virtual fields method (VFM) minimizing the gap between external and internal virtual work. By using a strategy with relation to a stress sensitivity analysis, the virtual fields can be obtained automatically. A specifically designed cruciform specimen, which produces heterogeneous deformation states, is used with a biaxial testing machine. For the shape optimization, a Newton iteration step is deduced to iteratively minimize the differences between desired and deformed shape of a forming simulation. The presented inverse, node-based algorithm covers a wide range of applications, since all requirements of a forming process are fulfilled. The method is demonstrated by means of a backward extrusion process.<br

On periodic boundary conditions and ergodicity in computational homogenization of heterogeneous materials with random microstructure - Pivovarov, Dmytro; Zabihyan, Reza; Mergheim, Julia; Willner, Kai; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2019)
Due to high computational costs associated with stochastic computational homogenization, a highly complex random material microstructure is often replaced by simplified, parametric, ergodic, and sometimes periodic models. This replacement is often criticized in the literature due to unclear error resulting from the periodicity and ergodicity assumptions. In the current contribution we perform a validation of both assumptions through various numerical examples. To this end we compare large-scale non-simplified and non-ergodic models with simplified, ergodic, and periodic solutions. In addition we analyze the Hill-Mandel condition for stochastic homogenization problems and demonstrate that for a stochastic problem there are more than three classical types of boundary conditions. As an example, we propose two novel stochastic periodic boundary conditions which possess a clear physical meaning. The effect of these novel periodic boundary conditions is also analyzed by comparing with non-ergodic simulation results. (C) 2019 Elsevier B.V. All rights reserved.
CRIS-Team WoS Importer:2019-10-25

On phenomenological and micro-mechanical models in finite elasticity and viscoelasticity for rubber-like materials - Mokarram, Hossain; Possart, Gunnar; Steinmann, Paul; Denzer, Ralf (Proceedings of sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, 2008)
UnivIS-Import:2015-04-16:Pub.2008.tech.FT.FT-TM.onphen

On rate-dependent dissipation effects in electro-elasticity - Saxena, Prashant; Vu, Duc Khoi; Steinmann, Paul (International Journal of Non-Linear Mechanics, 2014)
This paper deals with the mathematical modelling of large strain electro-viscoelastic deformations in electro-active polymers. Energy dissipation is assumed to occur due to mechanical viscoelasticity of the polymer as well as due to time-dependent effective polarisation of the material. Additive decomposition of the electric field E=Ee+Ev and multiplicative decomposition of the deformation gradient F=Fe Fv are proposed to model the internal dissipation mechanisms. The theory is illustrated with some numerical examples in the end. © 2014 Elsevier Ltd.
UnivIS-Import:2015-04-14:Pub.2014.tech.FT.FT-TM.onrate
Keywords: Electromechanical coupling; Non-linear electroelasticity; Rate dependence; Viscoelasticity

On regularization in parameter-free shape optimization - Riehl, Stefan; Friederich, Jan; Steinmann, Paul (Proc. Appl. Math. Mech., 2014)
UnivIS-Import:2015-04-16:Pub.2014.tech.FT.FT-TM.onregu

On Simulation Knowledge Acquisition Using Gaussian Processes for the Design of Electric Motors - Dworschak, Fabian; Tüchsen, Johann; Pinto, Diogo; Pop, Adrian-Cornel; Schleich, Benjamin; Wartzack, Sandro (Procedia CIRP Volume 84, 2019)
In the automotive industry, high efforts are made to design high-efficiency, low-cost, requirement-optimized electric drives. Traditionally, time-consuming and expensive 3D finite element analyses are used to assess the effects of different design parameters from various engineering disciplines such as the electromagnetics, heat transfer, and mechanics. Often, to decrease the calculation efforts, scalable, physics-based reduced order models are used. For setting up and interpreting such reduced order models, simulation experts employ implicit knowledge by applying heuristic correction factors. This paper proposes a novel method to formalizing such implicit simulation knowledge using Gaussian Processes. Furthermore, the successful application of the method to a case study of electric motors is reported by validating the aforementioned correction factors for different motor designs.<br
Keywords: Knowledge Acquisition; Meta-Modelling; Gaussian Process; Electric Motor; Case Study

On some mixed variational principles in electro-elastostatics - Vogel, Franziska Anna; Bustamante, Roger A.; Steinmann, Paul (International Journal of Non-Linear Mechanics, 2012)
Some mixed variational principles are presented for problems involving electro-elastic interactions, whereby the electric field follows from a scalar potential. Firstly, in order to set the stage, we consider the basic case of merely free space. Secondly, to increase the complexity, we immerse an electro-active but mechanically rigid body into vacuum. As our final goal we thirdly treat a geometrically non-linear deformable electro-elastic body that is surrounded by free space. Electro-elastic bodies are of particular interest since they can develop large elastic deformations as a response to the presence of electric fields. © 2011 Elsevier Ltd. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2012.tech.FT.FT-TM.onsome_9
Keywords: Continuum mechanics; Electrostatics; Mixed principles

On spectral fuzzy–stochastic FEM for problems involving polymorphic geometrical uncertainties - Pivovarov, Dmytro; Willner, Kai; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2019)
In this work we review a unified formulation for spectral fuzzy, spectral stochastic, and spectral fuzzy–stochastic FEM. We propose some modifications for the fuzzy and fuzzy–stochastic FEM involving local bases in the non-deterministic dimensions and the incorporation of extended FEM into the non-deterministic FEM. These modifications were previously used for stochastic FEM only. We discuss advantages of the proposed techniques for problems with uncertainties in the geometry and demonstrate their application to computational homogenization of heterogeneous materials with geometrical uncertainties in the microstructure. We address also some theoretical aspects of fuzzy FEM, that have not been tackled in the literature, namely the inner product of fuzzy variables. We address also another important problem, which becomes often the target of criticism of fuzzy approach. The membership function of the fuzzy input has often some degree of arbitrariness: it is known only approximately or it is constructed based on some assumptions. Here we propose a fuzzy FEM representation, which requires only the modal value and support of the fuzzy input parameters and is completely independent of the membership function's shape. We also discuss the case of imprecise probabilities which allows for severe dimension reduction of the non-deterministic problem if the accurate spectral simulation technique is used. Application of dimension reduction is also demonstrated on the example of computational homogenization.
CRIS-Team Scopus Importer:2019-05-09
Keywords: eXtended FEM; Fuzzy FEM; Imprecise probability; Polymorphic uncertainties; Random geometry; Stochastic FEM

On stochastic FEM based computational homogenization of magneto-active heterogeneous materials with random microstructure - Pivovarov, Dmytro; Steinmann, Paul (Computational Mechanics, 2016)
In the current work we apply the stochastic version of the FEM to the homogenization of magneto-elastic heterogeneous materials with random microstructure. The main aim of this study is to capture accurately the discontinuities appearing at matrix-inclusion interfaces. We demonstrate and compare three different techniques proposed in the literature for the purely mechanical problem, i.e. global, local and enriched stochastic basis functions. Moreover, we demonstrate the implementation of the isoparametric concept in the enlarged physical-stochastic product space. The Gauss integration rule in this multidimensional space is discussed. In order to design a realistic stochastic Representative Volume Element we analyze actual scans obtained by electron microscopy and provide numerical studies of the micro particle distribution. The SFEM framework described in our previous work (Pivovarov and Steinmann in Comput Mech 57(1): 123–147, 2016) is extended to the case of the magneto-elastic materials. To this end, the magneto-elastic energy function is used, and the corresponding hyper-tensors of the magneto-elastic problem are introduced. In order to estimate the methods' accuracy we performed a set of simulations for elastic and magneto-elastic problems using three different SFEM modifications. All results are compared with ``brute-force'' Monte-Carlo simulations used as reference solution.
Keywords: Stochastic FEM; eXtended FEM; Computational homogenization; Random geometry; Nonlinear magneto-elasticity

On structural shape optimization using an embedding domain discretization technique - Riehl, Stefan; Steinmann, Paul (International Journal for Numerical Methods in Engineering, 2017)

On the adaptive finite element analysis of the Kohn-Sham equations: Methods, algorithms, and implementation. - Davydov, Denis; Young, Toby; Steinmann, Paul (International Journal for Numerical Methods in Engineering, 2015)
In this paper, details of an implementation of a numerical code for computing the Kohn–Sham equations are presented and discussed. A fully self-consistent method of solving the quantum many-body problem within the context of density functional theory using a real-space method based on finite element discretisation of realspace is considered. Various numerical issues are explored such as (i) initial mesh motion aimed at co-aligning ions and vertices; (ii) a priori and a posteriori optimization of the mesh based on Kelly's error estimate; (iii) the influence of the quadrature rule and variation of the polynomial degree of interpolation in the finite element discretisation on the resulting total energy. Additionally, (iv) explicit, implicit and Gaussian approaches to treat the ionic potential are compared. A quadrupole expansion is employed to provide boundary conditions for the Poisson problem. To exemplify the soundness of our method, accurate computations are performed for hydrogen, helium, lithium, carbon, oxygen, neon, the hydrogen molecule ion and the carbon-monoxide molecule. Our methods, algorithms and implementation are shown to be stable with respect to convergence of the total energy in a parallel computational environment.

On the Application of Hansbo's Method for Interface Problems - Kuhl, Ellen; Jäger, Philippe; Mergheim, Julia; Steinmann, Paul (Proceedings of IUTAM Symposium on Discretization Methods for Evolving Discontinuities, 2006)
UnivIS-Import:2015-04-16:Pub.2006.tech.FT.FT-TM.onthea

On the C1 continuous discretization of nonlinear gradient elasticity: a comparison of NEM and FEM based on Bernstein-Bézier patches - Fischer, Paul; Mergheim, Julia; Steinmann, Paul (International Journal for Numerical Methods in Engineering, 2010)
UnivIS-Import:2015-04-14:Pub.2010.tech.FT.FT-TM.onthec

On the discrete variant of the traction method in parameter-free shape optimization - Riehl, Stefan; Friederich, Jan; Scherer, Michael; Meske, Ralf; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2014)
UnivIS-Import:2015-03-09:Pub.2014.tech.FT.FT-TM.onthed

On the effects of roughness on the nonlinear dynamics of a bolted joint: A multiscale analysis - Armand, J.; Salles, Loic; Schwingshackl, C. W.; Süß, Dominik; Willner, Kai (European Journal of Mechanics A-Solids, 2018)
Accurate prediction of the vibration response of friction joints is of great importance when estimating both the performance and the life of build-up structures. The contact conditions at the joint interface, including local normal load distribution and contact stiffness, play a critical role in the nonlinear dynamic response. These parameters strongly depend on the mating surfaces, where the surface roughness is well known to have a significant impact on the contact conditions in the static case. In contrast, its effects on the global and local nonlinear dynamic response of a build-up structure is not as well understood due to the complexity of the involved mechanisms. To obtain a better understanding of the dependence of the nonlinear dynamic response on surface roughness, a newly proposed multiscale approach has been developed. It links the surface roughness to the contact pressure and contact stiffness, and in combination with a multiharmonic balance solver, allows to compute the nonlinear dynamic response for different interface roughness. An application of the technique to a single bolted lap joint highlighted a strong impact of larger roughness values on the pressure distribution and local contact stiffness and in turn on the nonlinear dynamic response.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Bolted joint; Elastic rough contact; Nonlinear dynamics

On the emergence of out-of-plane ferroelectricity in ultrathin films - Boddu, Vishal; Steinmann, Paul (Archive of Applied Mechanics, 2019)
The presence of a spontaneous and switchable polarization is the defining property of a ferroelectric material. Such materials are indispensable in a countless number of industrial and scientific applications. Furthermore, the enhancement of ferroelectric property at reduced dimensions is crucial for continuous advancement in nanoelectronic applications. In this work, we investigate the onset of out-of-plane ferroelectricity in open-circuited stress-free BaTiO3 ultrathin films by performing molecular dynamics simulations using the core–shell model potential. In doing so, we try to obtain electric polarization hysteresis loops using an appropriate range of external electric loading. It is found that out-of-plane ferroelectricity is suppressed in ultrathin films with thickness 10 or less than 10 unit cells, indicating that there exists a critical thickness for the emergence of out-of-plane ferroelectricity in ultrathin films. It is also found that the ultrathin films exhibit asymmetrical hysteresis loops slightly above the critical thickness.
CRIS-Team Scopus Importer:2019-06-04
Keywords: Atomistic simulations; Ferroelectric hysteresis; Thin films

On the equivalence of the two foundational formulations for atomistic flux in inhomogeneous transport processes - Diaz, Adrian; Davydov, Denis; Chen, Youping (Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2019)
Although there are numerous formulae for atomic-level fluxes, they are expressed either in terms of a singlet density, resulting from Irving and Kirkwood's statistical mechanics formulation of hydrodynamical equations, or a pair density, proposed in kinetic theories of transport processes. Flux formulae using singlet density have been further developed and widely implemented in molecular dynamics (MD) simulations by either replacing the Dirac delta with a volumetric averaging function or performing a surface average of the flux operators. Pair density-based flux formulae have also been further developed by using spatial-averaging kernels; these formulae, however, have rarely been implemented or used in modern MD. In this work, distributional calculus is used to reformulate the fluxes in momentum and energy transport processes. The formulation results demonstrate that these two types of existing flux formulae are mathematically equivalent when expressed with the Dirac delta. The lasting confusion regarding these two different types of flux formulae from two different formalisms is thus resolved.
CRIS-Team Scopus Importer:2019-05-02
Keywords: Atomistic flux; Dirac delta distribution; Irving-Kirkwood procedure; Local stress and heat flux; Statistical mechanics formalism; Transient transport fluxes

On the failure of silicone breast implants: New insights by mapping the mechanical properties of implant shells - Schubert, Dirk W.; Kaschta, Joachim; Horch, Raymund E.; Walter, Bastian; Daenicke, Jonas (Polymer International, 2014)
This review summarizes the knowledge on rupture (in vivo as well as under laboratory conditions) of gel-filled silicone breast implants, which has been an open question since the first implantation in 1962. We present recent progress which has been made by a mapping of the mechanical properties of the shell material together with a statistical failure analysis by means of a Weibull fit. Reference implants and intact as well as ruptured explants are tested after several years in vivo using tensile tests. Up to 110 dumbbell-shaped specimens per implant are measured allowing a detailed mapping of the mechanical properties of the silicone shell. Therefore, it is possible to illustrate the results of the tensile tests by mapping the measured values of the implants in the form of a contour plot revealing novel insights. The contour plots clearly display that the mechanical behaviour (e.g. stress at break) varies significantly over the shell. Additionally, a map is proposed which clearly shows separated clusters for different manufacturers and product categories. © 2013 Society of Chemical Industry
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.onthef

On the formulation and implementation of geometric and manufacturing constraints in node-based shape optimization - Schmitt, Oliver; Friederich, Jan; Riehl, Stefan; Steinmann, Paul (Structural and Multidisciplinary Optimization, 2016)
We introduce a novel method to handle geometrical and manufacturing constraints in  parameter-free shape optimization. Therefore the design node coordinates are split in two sets where one set is declared as new design variables and the other set is coupled to the new design variables such that the geometrical constraint is fulfilled. Thereby no additional equations are appended to the optimization problem. In contrast the implementation of a demolding constraint is presented by formulating inequality constraints which indeed have to be attached to the optimization problem. In the context of a sensitivity–based shape optimization approach all manufacturing constraints have to be formulated in terms of the finite element node coordinates such that first order gradients with respect to the design node coordinates can be derived.
Keywords: shape optimization; manufacturing constraints; geometrical constraints; symmetry; parameter-free; sensitivity analysis

On the homogenization of technical textiles - Fillep, Sebastian; Mergheim, Julia; Steinmann, Paul (Bytes and science, 2012)
UnivIS-Import:2015-10-26:Pub.2012.tech.FT.FT-TM.ontheh

On the identification of an effective cross section for a cruciform specimen - Härtel, Markus; Pfeiffer, Stefan; Schmaltz, Stefan; Söhngen, Benjamin; Kulawinski, Dirk; Willner, Kai; Henkel, Sebastian; Biermann, Horst; Wagner, Martin F.-X. (Strain, 2018)
Biaxial tensile testing of sheet metals is becoming increasingly popular for sheet metal forming. Determining equivalent stresses in biaxial tensile specimens is more complicated than in conventional uniaxial tensile specimens. In the present study, we compare four different approaches to calculate effective stresses during biaxial tensile loading of a cruciform specimen: (i) partial unloading method, where stresses are determined based on force-strain curves; (ii) identification with uniaxial tensile testing; (iii) an analysis of equivalent biaxial tests; (iv) numerical simulations. Considering experimental results for an AA1050 aluminum alloy and for a low-carbon steel DC06, we show that, for the cruciform sample studied here, two methods do not yield physically reasonable results: the uniaxial approach does not properly take into account the effect of transverse loading, and the equivalent biaxial approach exhibits uncertainties in strain measurement data. The most comprehensible approach is the numerical method; because it also yields detailed information about the local stress and strain states. The numerical results are in excellent agreement with the partial unloading method in terms of the initial flow stress and of effective stress-strain curves for strains up to 0.02, with both methods predicting a similar effective cross section of 18.0 mm2 for the considered specimen.
Keywords: biaxial tensile testing; cruciform specimen; effective cross section; FEM simulation; sheet metals

On the importance of using region-dependent material parameters for full-scale human brain simulations - Griffiths, Emma; Hinrichsen, Jan; Reiter, Nina; Budday, Silvia (European Journal of Mechanics A-Solids, 2023)
An accurate finite element (FE) model of the human brain reliably predicting its response to loading offers great possibilities for brain injury prevention, disease prediction, and surgical guidance. However, the brain is a very complex organ. One important aspect is the structural heterogeneity, both on a macroscopic and microscopic level. This also results in heterogeneous mechanical properties, which highly depend on the brain regions. The extent to which this heterogeneity affects the mechanical response of an FE simulated full brain remains largely unexplored. In this work, we investigate the importance of using region-specific material parameters when modelling the full human brain. Additionally, we assess how a prefixed Poisson's ratio used for the determination of regional parameters affects the response of the full brain under loading. Finally, we compare the simulation results when using parameter sets that have been determined from the unconditioned and preconditioned behaviour of human brain tissue. Our results show that accounting for region-dependent properties leads to significant differences in the predicted strain state compared to simulations assuming homogeneous material properties. Also the Poisson's ratio and using unconditioned or preconditioned data sets significantly affects the results of full-scale brain simulations, highlighting the importance of carefully selecting the material parameters used. The presented analyses have important implications for choosing appropriate region-dependent material parameters for full-scale FE human brain simulations in the future to ensure reliable predictions.
CRIS-Team Scopus Importer:2023-03-08
Keywords: Finite element method; Human brain; Material modelling; Material parameters; Regional heterogeneity

On the Indentation of a Membrane Reinforced Elastic Halfspace: Analytical and Computational Approaches - Selvadurai, A.P.S.; Willner, Kai; Gaul, L. (Computational Methods in Contact Mechanics V, 2001)
This paper examines the problem of the surface indentation of an isotropic elastic halfspace, which is reinforced by an inextensible membrane and subjected to indentation by a rigid circular punch with a smooth flat base. The inextensibility constraint is assumed to be applicable over the entire region of the membrane of infinite extent, which is located at a finite depth below the surface of the elastic halfspace. The paper presents the formal results that can be recovered as limiting cases of the analytical formulation and compares these with results obtained via a finite element modelling of the problem, which also accommodates for the elasticity of the membrane.
UnivIS-Import:2015-04-16:Pub.2001.tech.FT.FT-TM.onthei

On the influence of contact tribology on brake squeal - Hetzler, H.; Willner, Kai (Tribology International, 2012)
This contribution aims at introducing tribological contact properties into the stability analysis of macroscopic structural systems with focus on brake-squeal applications. First, the surfaces of several brake pads at different states of wear are analyzed experimentally. Based on these data a statistical contact model as well as a numerical simulation are presented. Using these models two constitutive contact laws are derived, which link contact pressure and stiffness. Second, a simple brake model incorporating these contact models is developed. Results of stability analyses are presented and the influence of the contact models on the steady state stability is discussed. © 2011 Elsevier Ltd.
Keywords: Brake squeal; Contact stiffness; Friction induced vibrations; Rough surface

On the influence of free space in topology optimization of electro-active polymers - Dev, Chaitanya; Stankiewicz, Gabriel; Steinmann, Paul (Structural and Multidisciplinary Optimization, 2023)
This study investigates the impact of the surrounding free space on the topology optimization (TO) of electro-active polymers (EAPs). It is well understood that, under the application of an electric field, the deformation of an EAP is not solely determined by the field distribution within the body, but also by the distribution in the free space surrounding it. This is particularly true for electronic EAP, which are emerging as leading candidates for developing artificial muscles. Our study specifically focuses on understanding the influence of the free space in the context of density-based TO. We model the free space as an extended void region around the design domain. Our numerical experiments focus on EAP actuators and take into account their geometrical nonlinear behavior. The results show that incorporating the surrounding free space has a significant impact on the performance of the optimized EAPs with low electric permittivity. This makes it essential to consider in real-world applications.
CRIS-Team Scopus Importer:2023-08-18
Keywords: Electro-active polymers; Free space; Topology optimization

On the influence of inhomogeneous stiffness and growth on mechanical instabilities in the developing brain - Budday, Silvia; Steinmann, Paul (International Journal of Solids and Structures, 2017)
The characteristic surface morphology of the mammalian brain is closely correlated with brain function and dysfunction. During development, the initially smooth surface evolves into an elaborately convoluted pattern. Growing evidence suggests that mechanical instabilities emerging from differential growth between a faster growing outer gray matter and a slower growing inner white matter play a major role in brain morphogenesis. Previous studies assume uniform growth and stiffness; yet, recent experiments indicate that the properties of brain tissue are highly inhomogeneous. Here, we hypothesize that regionally varying developmental pathways across the brain result in nonuniform material properties at the onset of cortical folding. We establish a computational model of brain growth to explore the effects of stiffness and growth variations in gray and white matter tissue to mimic cellular processes and evolving tissue microstructure. We present an effective approach to determine critical growth values from geometrical data and systematically study the effect of inhomogeneous material properties on growth-induced primary and secondary instabilities. Our results reveal that critical growth and wavelength strongly depend on the stiffness distribution in the developing brain. Regional variations in cortical growth affect secondary instabilities and evoke highly irregular folding patterns, but characteristic wavelength and critical growth remain relatively stable. The interplay of different influential factors including cortical thickness, brain geometry, stiffness, and growth explains how primary folds are highly preserved across individuals, whereas secondary and tertiary folds vary significantly. Our findings are directly applicable to imaging data of fetal brains and ultimately enable early diagnostics of cortical malformations to improve treatment of neurodevelopmental disorders including epilepsy, autism, spectrum disorders, and schizophrenia.
Keywords: Cortical folding; Growth; Instabilities; Period-doubling; Inhomogeneous properties

On the influence of the compliant electrodes on the mechanical behavior of VHB 4905 - Mehnert, Markus; Steinmann, Paul (Computational Materials Science, 2019)
The expression electro-active polymers (EAPs) is used to collectively describe polymeric materials that show the ability to undergo large deformations due to the excitation by an electric field. This ability makes them interesting candidates in the development of soft actuators that can be used for example in robotics. When using dielectric elastomers these types of actuators usually consist of a thin film of polymeric material sandwiched between a pair of compliant electrodes. However these electrodes influence the mechanical material response of the polymer. For this reason we demonstrate in this contribution the influence of the compliant electrodes on the viscoelastic material behavior of a polymeric material, i.e. VHB4905 (TM), using both experimental data and a modelling approach.
CRIS-Team WoS Importer:2019-03-12

On the Influence of the Coupled Invariant in Thermo-Electro-Elasticity - Mehnert, Markus; Mathieu-Pennober, Tiphaine; Steinmann, Paul (Generalized Models and Non-classical Approaches in Complex Materials, 2018)

On the mechanics of continua with boundary energies and growing surfaces - Steinmann, Paul; Papastavrou, Areti; Kuhl, Ellen (Journal of the Mechanics and Physics of Solids, 2013)
Many biological systems are coated by thin films for protection, selective absorption, or transmembrane transport. A typical example is the mucous membrane covering the airways, the esophagus, and the intestine. Biological surfaces typically display a distinct mechanical behavior from the bulk; in particular, they may grow at different rates. Growth, morphological instabilities, and buckling of biological surfaces have been studied intensely by approximating the surface as a layer of finite thickness; however, growth has never been attributed to the surface itself. Here, we establish a theory of continua with boundary energies and growing surfaces of zero thickness in which the surface is equipped with its own potential energy and is allowed to grow independently of the bulk. In complete analogy to the kinematic equations, the balance equations, and the constitutive equations of a growing solid body, we derive the governing equations for a growing surface. We illustrate their spatial discretization using the finite element method, and discuss their consistent algorithmic linearization. To demonstrate the conceptual differences between volume and surface growth, we simulate the constrained growth of the inner layer of a cylindrical tube. Our novel approach toward continua with growing surfaces is capable of predicting extreme growth of the inner cylindrical surface, which more than doubles its initial area. The underlying algorithmic framework is robust and stable; it allows to predict morphological changes due to surface growth during the onset of buckling and beyond. The modeling of surface growth has immediate biomedical applications in the diagnosis and treatment of asthma, gastritis, obstructive sleep apnoea, and tumor invasion. Beyond biomedical applications, the scientific understanding of growth-induced morphological instabilities and surface wrinkling has important implications in material sciences, manufacturing, and microfabrication, with applications in soft lithography, metrology, and flexible electronics. © 2013 Elsevier Ltd.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.onthem_8
Keywords: Airway wall remodeling; Boundary energy; Finite elements; Growth; Thin films

On the modeling of equilibrium twin interfaces in a single-crystalline magnetic shape-memory alloy sample—III: Magneto-mechanical behaviors - Wang, Jiong; Steinmann, Paul (Continuum Mechanics and Thermodynamics, 2016)
This is the concluding part III of a series of papers. The aim of the current paper is to simulate and analyze the procedure of variant reorientation in a magnetic shape-memory alloy (MSMA) sample and to predict the response of the sample subject to various loading conditions. The sample to be considered in this paper has a 3D cuboid shape and is subject to typical magneto-mechanical loading conditions. Variant reorientation in the sample is realized through twin interface movements. To investigate the key features of twin interface movements, the properties of configurational forces on the twin interfaces are analyzed. For both the stress-assisted MFIS tests and the field-assisted quasi-elasticity tests, the magneto-mechanical behavior of the MSMA sample during the whole loading procedure is simulated by using the finite element method. The influence of the initial variant distribution in the sample on its global response is discussed. The obtained numerical results are compared with the experimental results. It can be seen that the model predictions can fit the experimental results both at a qualitative as well as at a quantitative level.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Configurational force; Finite element method; Magnetic shape-memory alloys; Magneto-mechanical response; Twin interface

On the modeling of equilibrium twin interfaces in a single-crystalline magnetic shape memory alloy sample. II: numerical algorithm - Wang, Jiong; Steinmann, Paul (Continuum Mechanics and Thermodynamics, 2016)
This is part II of this series of papers. The aim of the current paper was to solve the governing PDE system derived in part I numerically, such that the procedure of variant reorientation in a magnetic shape memory alloy (MSMA) sample can be simulated. The sample to be considered in this paper has a 3D cuboid shape and is subject to typical magnetic and mechanical loading conditions. To investigate the demagnetization effect on the sample’s response, the surrounding space of the sample is taken into account. By considering the different properties of the independent variables, an iterative numerical algorithm is proposed to solve the governing system. The related mathematical formulas and some techniques facilitating the numerical calculations are introduced. Based on the results of numerical simulations, the distributions of some important physical quantities (e.g., magnetization, demagnetization field, and mechanical stress) in the sample can be determined. Furthermore, the properties of configurational force on the twin interfaces are investigated. By virtue of the twin interface movement criteria derived in part I, the whole procedure of magnetic field- or stress-induced variant reorientations in the MSMA sample can be properly simulated.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Configurational force; Finite element method; Iterative numerical algorithm; Magnetic shape memory alloys; Twin interface

On the modelling of equilibrium twin interfaces in a single-crystalline magnetic shape memory alloy sample. I: Theoretical formulation - Wang, Jiong; Steinmann, Paul (Continuum Mechanics and Thermodynamics, 2013)
In this paper, a variational approach is proposed to study the response of a single-crystalline magnetic shape memory alloy (MSMA) sample subject to external forces and magnetic fields. Especially, some criteria are derived to model the (quasi-static) movements of twin interfaces in the sample. By considering the compatibility condition, twin interfaces between two martensite variants are found to be flat planes with given normal vectors. To adopt the variational method, a total energy functional for the whole magneto-mechanical system is proposed. By calculating the variations of the total energy functional with respect to the independent variables, the equilibrium equations and the evolution laws for the internal variables can be derived. By further considering the variation of the total energy functional with respect to the variant distribution, some criteria for twin interface movements can be derived. The governing system of the current model is then formulated by composing the equilibrium equations, the evolution laws for the internal variables and the twin interface movement criteria. To show the validity of the governing system, some analytical results are constructed under certain simplified conditions, which can be used to simulate the magneto-mechanical response of the MSMA sample.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.onthem
Keywords: Single-crystalline; Magnetic shape memory alloys; Twin interface; Configurational force; Variational method

On the Multiscale Computation of Defect Driving Forces - Mergheim, Julia; Steinmann, Paul; Ricker, Sarah (International Journal For Multiscale Computational Engineering, 2009)
In the present contribution, the computational homogenization scheme is extended toward the homogenization of configurational quantities like the Eshelby stress and material node point forces. Configurational mechanics is concerned with changes of the material configuration of continuum bodies and has numerous applications in defect mechanics, as, e. g., it can be shown that the material force at a crack tip corresponds to the J-integral and thus yields a criterion for crack propagation. In the theoretical part of this work, the differences between the homogenization of the direct and the inverse motion problem are elaborated. Therefore focus is put onto the influence of microscopic material interfaces and material body forces on the averaged field values. The theoretical results are illustrated by various numerical examples, which on one hand compare the homogenized configurational quantities for different microstructures, and on the other hand, point out which features of the microstructure influence the macroscopic configurational quantities. © 2009 by Begell House, Inc.
UnivIS-Import:2015-03-09:Pub.2009.tech.FT.FT-TM.onthem_2
Keywords: Configurational forces; Homogenization; Multi-scale

On the Preparation, Characterisation, Modelling and Simulation of Magneto-Sensitive Elastomers - Walter, Bastian; Saxena, Prashant; Pelteret, Jean-Paul; Kaschta, Joachim; Schubert, Dirk W.; Steinmann, Paul (Proceedings of the Second Seminar on the Mechanics of Multifunctional Materials, 2014)
UnivIS-Import:2015-07-08:Pub.2014.tech.FT.FT-TM.onthep

On the Preparation, Characterization, Modeling and Simulation of Magneto-Sensitive Elastomers - Walter, Bastian; Saxena, Prashant; Pelteret, Jean-Paul; Kaschta, Joachim; Schubert, Dirk W.; Steinmann, Paul (14th International Conference on Electrorheological Fluids and Magnetorheological Suspensions, 2014)

On thermomechanical solids with boundary structures - Javili, Ali; Steinmann, Paul (International Journal of Solids and Structures, 2010)
This paper, in line with the previous works (Javili and Steinmann, 2009, 2010), is concerned with the thermomechanically consistent theory and formulation of boundary potential energies and the study of their impact on the deformations of solids. Thereby, the main thrust in this contribution is the extension to thermomechanical effects. Although boundary effects can play a dominant role in the material behavior, the common modelling in continuum mechanics takes exclusively the bulk into account, nevertheless, neglecting possible contributions from the boundary. In this approach the boundary is equipped with its own thermodynamic life, i.e. we assume separate boundary energy, entropy and the like. Afterwards, the derivations of generalized balance equations, including boundary potentials, completely based on a tensorial representation is carried out. The formulation is exemplified for the example of thermohyperelasticity. © 2010 Elsevier Ltd. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2010.tech.FT.FT-TM.onther
Keywords: Boundary potentials; Nanomaterials; Surface tension; Thermoelasticity

On thermo-viscoelastic experimental characterization and numerical modelling of VHB polymer - Liao, Zisheng; Hossain, Mokarram; Yao, Xiaohu; Mehnert, Markus; Steinmann, Paul (International Journal of Non-Linear Mechanics, 2020)
Recently, the so-called Very High Bond (VHB in short) tape has proven to be an ideal polymer for producing devices made of electric field-responsive functional materials, e.g., actuators in soft robotics, stretch sensors in wearable devices, and energy harvesters generating power from ambient motions. The VHB polymer is commercially available in several thicknesses. For this study, we have selected VHB 4905 due to its wide use as a common material for dielectric elastomers. The acrylic-based polymer is highly deformable, extremely viscoelastic, and highly sensitive to temperature fluctuations. Hence, in order to understand its mechanical and electro-mechanical behaviour, extensive experiments need to be conducted to unravel temperature dependencies in addition to strain-rate dependences. In this study, we present a wide variety of temperature experiments ranging from -30°C to 80°C at various strain rates and stretch levels under homogeneous deformation and temperature fields. The study demonstrates a pronounced influence of the temperature on the mechanical response of the VHB polymer. For VHB within the temperature range of our study, an increased temperature mechanically softens the material and vice-versa. After conducting a wide range of experiments, we propose a finite strain thermo-viscoelastic constitutive model that is an extension of a phenomenologically-motivated model where a non-linear evolution law is devised based on the classical concept of the multiplicative decomposition of the deformation gradient. Then, decoupled one-dimensional equations are derived and fitted to experimental data to identify relevant material parameters appearing in the model. The thermo-viscoelastic model validation shows its reasonably good capability to predict the experimental results.
CRIS-Team Scopus Importer:2019-09-27
Keywords: Dielectric elastomers; Temperature dependence; Thermo-viscoelasticity; VHB polymer

On the Roots of Continuum Mechanics in Differential Geometry: - A Review - - Steinmann, Paul (Springer International Publishing, 2013)
The aim of this contribution is to illustrate the roots of the geometrically nonlinear kinematics of (generalized) continuum mechanics in differential geometry. Firstly several relevant concepts from differential geometry, such as connection, parallel transport, torsion, curvature, and metric (in index notation) for holonomic and anholonomic coordinate transformations are reiterated. The notation and the selection of these topics are essentially motivated by their relation to the geometrically nonlinear kinematics of continuum mechanics. Then, secondly, the kinematics are considered from the point of view of nonlinear coordinate transformations and nonlinear point transformations, respectively. Together with the discussion on the integrability conditions for the (first-order) distortions, the concept of dislocation density tensors is introduced. After touching on the possible interpretations of nonlinear elasticity using concepts from differential geometry, a detailed discussion of the kinematics of multiplicative elastoplasticity is given. The discussion culminates in a comprehensive set of twelve different types of dislocation density tensors. Potentially, these can be used to model densities of geometrically necessary dislocations and the accompanying hardening in crystalline materials. Continuum elastoplasticity formulations of this kind fall into the class of generalized (gradient-type) plasticity models.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Covariant Derivative; Curvature Tensor; Deformation Gradient; Dislocation Density; Parallel Transport

On the Selection of Sensitivity Analysis Methods in the Context of Tolerance Management - Heling, Björn; Oberleiter, Thomas; Schleich, Benjamin; Willner, Kai; Wartzack, Sandro (Journal of Verification, Validation and Uncertainty Quantification, 2019)

On the solution of the 3D crack surface contact problem using the boundary element method - Weber, Wilhelm; Kolk, Karsten; Willner, Kai; Kuhn, Günther (Key Engineering Materials, 2011)
The efficient solution of the 3D crack surface contact problem utilizing the boundary element method (BEM) is presented. The dual discontinuity method (DDM), a special formulation of the BEM, is applied. This method deals directly with the relative displacements and the discontinuities of the tractions at the crack. For the normal behavior a unilateral contact is assumed and for the description of the tangential behavior Coulomb's frictional law is utilized. The hard contact formulation is regularized by the application of the penalty method. An incremental iterative procedure based on a radial return mapping algorithm is applied for the solution of this non-linear problem. Based on the stress field the fracture mechanical parameters are determined by an extrapolation method for all increments of a characteristic load cycle. By the analysis of this load cycle the cyclic fracture mechanics values are obtained. Due to the non-linear nature of crack growth the simulation is implemented in the framework of a predictor-corrector scheme. For the investigation of the influence of the crack surface roughness on the behavior of cracks two numerical examples are presented. © 2011 Trans Tech Publications.
UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.onthes
Keywords: Crack surface contact; Dual boundary element method; Dual discontinuity method; Fatigue crack propagation

On the spatial and material motion problems in nonlinear electro-elastostatics with consideration of free space - Vu, Duc Khoi; Steinmann, Paul (Mathematics and Mechanics of Solids, 2011)
In this work the formulation of spatial and material motion problems in nonlinear electro-elastostatics is considered using an energy approach, which takes into account the contribution of the free space surrounding a nonlinearly polarized body undergoing large deformation. The free space can have a huge impact on the electric field and on the deformation field inside a body made of materials with low electric permittivity such as the so-called electronic electroactive polymers (EEAPs). The contribution of the free space can be taken into account by using the electric flux and the Maxwell's traction acting on the boundary of the body. These two quantities can be expressed in terms of a stored energy density function. By using a stored energy density function for both the material body and the (finite or infinite) free space, the governing equations of both spatial and material motion problems are derived by considering the change of energy with respect to a change in the spatial or material configuration. In the spatial motion problem, well-known definitions for electric and mechanical quantities are derived. In the material motion problem, in addition to the derivation of configurational forces, this approach reveals the formulas for the part of energy that is released from the system material body, applied forces in response to a change in the material configuration, which are particularly useful in the study of defects such as crack propagation. The same approach can be used in the case of nonlinear electro-thermo-mechanical coupling and constitutes the direction for future works.
UnivIS-Import:2015-04-14:Pub.2011.tech.FT.FT-TM.onthes_6

On the wall slip of magnetorheological elastomers in parallel-plate rotational rheometry - Walter, Bastian; Pelteret, Jean-Paul; Kaschta, Joachim; Schubert, Dirk W.; Steinmann, Paul (7th ECCOMAS Thematic Conference on Smart Structures and Materials, 2015)

On the wall slip phenomenon of elastomers in oscillatory shear measurements using parallel-plate rotational rheometry: I. Detecting wall slip - Walter, Bastian; Pelteret, Jean-Paul; Kaschta, Joachim; Schubert, Dirk W.; Steinmann, Paul (Polymer Testing, 2017)
A systematic study is presented in order to reveal the occurrence of wall slip of pre-prepared elastomeric samples characterized with the use of rotational rheometry. To exclude effects that could be attributed to additional functional fillers, both an unfilled (primarily used) and lightly silica reinforced (complementary system) silicone rubber are evaluated. Cylindrical samples are prepared by casting using a standardized methodology and examined by means of a stress-controlled parallel-plate rotational rheometer. As a control test, samples are also cured within the rheometer (in situ), thereby fixing them to the measuring plates and firmly establishing their response in “no-slip” conditions. The experiments suggest that wall slip, postulated to be caused by an adhesive failure at the sample-plate interface, may occur if the deformation is sufficiently large and no cohesive failure is present. It is detected by an increase in the loss modulus that is related to the adhesive failure associated with local dynamic friction, resulting in increased dissipated energy. Direct (via raw waveform data and normalized Lissajous figures) and indirect (via fast-Fourier-transformation) analysis of the overall system response for a single steady state deformation cycle provided further insights into the mechanism of wall slip.
Keywords: Wall slip; Adhesive failure; Measuring artifact; Large amplitude oscillatory shear; Silicone rubber; Parallel-plate rotational rheometry

On the wall slip phenomenon of elastomers in oscillatory shear measurements using parallel-plate rotational rheometry: II. Influence of experimental conditions - Walter, Bastian; Pelteret, Jean-Paul; Kaschta, Joachim; Schubert, Dirk W.; Steinmann, Paul (Polymer Testing, 2017)
The use of parallel-plate rotational rheometry to characterize ex situ pre-prepared samples of rubber-like polymers is motivated by, for example, the investigation of magneto-rheological elastomers. When exceeding a critical excitation amplitude in oscillatory shear experiments, these elastomeric samples are prone to slip at the sample-plate contact interface. This phenomenon, known as wall slip, starts to occur at the sample's outer rim and leads to an imperfect force transfer onto the sample. This results in a systematic error of measured rheological material quantities. A thorough investigation is presented to reveal how this phenomenon is affected by selected experimental conditions, namely the static axial preload and measuring frequency. For this purpose disc-shaped samples composed of an unfilled silicone rubber are prepared by casting and examined by means +of a controlled stress rotational rheometer equipped with a serrated rotor configuration. The oscillatory strain sweep experiments suggest that wall slip, exclusively present at the serrated rotor surface, is significantly influenced by the static preload. In contrast, only a slight frequency dependence is observed within the examined experimental conditions. Further insights into the wall slip mechanism were attained by two novel methodologies. It is shown that it is possible to produce a master curve for the various applied preloads. This demonstrates that the physical mechanism behind wall slip is independent of the axial force. Furthermore, we derive an empirical model for the criterion governing the onset of wall slip. This links the critical stress at which wall slip is initiated to the static friction condition and geometrical aspects of the rotor configuration. From this it is anticipated that the conditions for reliable experiments involving ex situ pre-prepared samples composed of low damping elastomers can, in the future, be estimated a priori</em
Keywords: Wall slip; Adhesive failure; Measuring artifact; Large amplitude oscillatory shea; Silicone rubber; Parallel-plate rotational rheometry

On two different inverse form finding methods for hyperelastic and elastoplastic materials - Germain, Sandrine; Steinmann, Paul (PAMM, 2012)
This contribution focuses on two different developments of mechanical- computational methods for the optimal determination of the initial shape of formed functional components knowing the deformed configuration, the applied loads and the boundary conditions. The first method uses an inverse mechanical formulation and can be applied to materials with hyperelastic behaviors. For materials with elastoplastic properties this method is not advocated, without knowing the final plastic strains, due to the non uniqueness of the solution. The second method uses a shape optimization formulation in the sense of an inverse problem via successive iterations of the direct problem. For hyperelastic materials the inverse mechanical formulation is preferred for its velocity and the non exhibition of possible mesh distortions. In the shape optimization formulation mesh distortions can be avoided by an update of the reference configuration of the functional part. Both methods are using a formulation in the logarithmic strain space. A numerical example for materials with isotropic elastoplastic behaviors illustrates the shape  optimization formulation.
UnivIS-Import:2015-04-16:Pub.2012.tech.FT.FT-TM.ontwod

On Using Fuzzy Arithmetic to Solve Problems with Uncertain Parameters - Hanss, M.; Willner, Kai (Proceedings of Euromech 405 Colloquium, 1999)
UnivIS-Import:2015-04-16:Pub.1999.tech.FT.FT-TM.onusin

Open system peridynamics - Schaller, Emely; Javili, Ali; Steinmann, Paul (Continuum Mechanics and Thermodynamics, 2022)
We propose, for the first time, a thermodynamically consistent formulation for open system (continuum-kinematics-inspired) peridynamics. In contrast to closed system mechanics, in open system mechanics mass can no longer be considered a conservative property. In this contribution, we enhance the balance of mass by a (nonlocal) mass source. To elaborate a thermodynamically consistent formulation, the balances of momentum, energy and entropy need to be reconsidered as they are influenced by the additional mass source. Due to the nonlocal continuum formulation, we distinguish between local and nonlocal balance equations. We obtain the dissipation inequality via a Legendre transformation and derive the structure and constraints of the constitutive expressions based on the Coleman–Noll procedure. For the sake of demonstration, we present an example for a nonlocal mass source that can model the complex process of bone remodelling in peridynamics. In addition, we provide a numerical example to highlight the influence of nonlocality on the material density evolution.
CRIS-Team Scopus Importer:2022-05-20
Keywords: Mass change; Nonlocal material; Open system; Peridynamics

Optimal Design of Brittle Composite Materials: a Nonsmooth Approach - Prechtel, Marina; Leugering, Günter; Steinmann, Paul; Stingl, Michael (Journal of Optimization Theory and Applications, 2012)
Our goal is to design brittle composite materials yielding maximal energy dissipation for a given static load case. We focus on the effect of variation of fiber shapes on resulting crack paths and thus on the fracture energy. To this end, we formulate a shape optimization problem, in which the cost function is the fracture energy and the state problem consists in the determination of the potentially discontinuous displacement field in the two-dimensional domain. Thereby, the behavior at the crack surfaces is modeled by cohesive laws. We impose a nonpenetration condition to avoid interpenetration of opposite crack sides. Accordingly, the state problem is formulated as variational inequality. This leads to potential nondifferentiability of the shape-state mapping. For the numerical solution, we derive first-order information in the form of subgradients. We conclude the article by numerical results.
UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.optima
Keywords: Our goal is to design brittle composite materials yielding maximal energy dissipation for a given static load case. We focus on the effect of variation of fiber shapes on resulting crack paths and thus on the fracture energy. To this end; we formulate a shape optimization problem; in which the cost function is the fracture energy and the state problem consists in the determination of the potentially discontinuous displacement field in the two-dimensional domain. Thereby; the behavior at the crack surfaces is modeled by cohesive laws. We impose a nonpenetration condition to avoid interpenetration of opposite crack sides. Accordingly; the state problem is formulated as variational inequality. This leads to potential nondifferentiability of the shape-state mapping. For the numerical solution; we derive first-order information in the form of subgradients. We conclude the article by numerical results.

Optimal feedback control for constrained mechanical systems - Glaas, Daniel; Leyendecker, Sigrid (Proc. Appl. Math. Mech. (PAMM), 2016)
An approach to minimize the control costs and ensuring a stable deviation control is the Riccati controller and we want to use it to control constrained dynamical systems (differential algebraic equations of Index 3). To describe their discrete dynamics, a constrained variational integrators [1] is used. Using a discrete version of the Lagrange-d’Alembert principle yields a forced constrained discrete Euler-Lagrange equation in a position-momentum form that depends on the current and future time steps [2]. The desired optimal trajectory (qopt, popt) and according control input uopt is determined solving the discrete mechanics and optimal control (DMOC) algorithm [3] based on the variational integrator. Then, during time stepping of the perturbed system, the discrete Riccati equation yields the optimal deviation control input uR. Adding uopt and uR to the discrete Euler-Lagrange equation causes a structure preserving trajectory as both DMOC and Riccati equations are based on the same variational integrator. Furthermore, coordinate transformations are implemented (minimal, redundant and nullspace) enabling the choice of different coordinates in the feedback loop and in the optimal control problem. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinhei
Keywords: Variational integrator; feedback control; optimal control

Optimisation of the Capriccio Method to Couple Particle- and Continuum-Based Simulations of Polymers - Pfaller, Sebastian; Kergaßner, Andreas; Steinmann, Paul (Multiscale Science and Engineering, 2019)

Optimization of elastic material parameters of sheet metal with FEMU and DIC - Schmaltz, Stefan; Willner, Kai (PAMM 2011, 2011)
UnivIS-Import:2015-04-16:Pub.2011.tech.FT.FT-TM.optimi_2

Optimum blank design by using the inverse FEM in orthotropic elastoplasticity - Landkammer, Philipp; Germain, Sandrine; Steinmann, Paul (PAMM, 2014)
UnivIS-Import:2015-04-16:Pub.2014.tech.FT.FT-TM.optimu_1

Oxidized Hyaluronic Acid-Gelatin-Based Hydrogels for Tissue Engineering and Soft Tissue Mimicking - Kuth, Sonja; Karakaya, Emine; Reiter, Nina; Schmidt, Lorenz-Peter; Paulsen, Friedrich; Tessmar, Jorg; Budday, Silvia; Boccaccini, Aldo R. (Tissue Engineering - Part C: Methods, 2022)
Hydrogels are ideal materials for mimicking and engineering soft tissue. Hyaluronic acid is a linear polysaccharide native to the human extracellular matrix. In this study, we first develop and characterize two hydrogel compositions built from oxidized HA and gelatin with and without alginate-di-aldehyde (ADA) crosslinked by ionic and enzymatic agents with potential applications in soft tissue engineering and tissue mimicking structures. The stability under incubation conditions was improved by adjusting crosslinking times. Through large-strain mechanical measurements, the hydrogels' properties were compared to human brain tissue and the samples containing ADA revealed similar mechanical properties to the native tissue specimens in cyclic compression-tension. In vitro characterization demonstrated a high viability of encapsulated mouse embryonic fibroblasts and a spreading of the cells in case of ADA-free samples.
CRIS-Team WoS Importer:2022-05-20

Parameter identification for nonlinear dynamical systems using multiharmonic balance techniques - Süß, Dominik; Willner, Kai (Proceedings of Applied Mathematics and Mechanics (PAMM), 2011)
UnivIS-Import:2015-04-16:Pub.2011.tech.FT.FT-TM.parame_4

Parameter identification of strain rate dependent hardening for sheet metals - Söhngen, Benjamin; Willner, Kai (Proceedings in Applied Mathematics and Mechanics, 2019)
Abstract In this contribution we examine the influence of strain rate on the isotropic hardening of two sheet metals. The nominal strain rates vary between 0.0005 s−1 and 20 s−1 and the full field deformation is captured with the help of digital image correlation (DIC) technique. For modelling the strain rate dependent behaviour, we introduce a rate dependent part in the definition of the hardening stress, distinguishing between approaches that incorporate the rate dependency in an additive or multiplicative manner. The hardening laws are thereby embedded in a large strain plasticity framework based on the logarithmic strain space. The material parameters are identified both in a “direct” fashion, where the gap between constitutive equation and measured stress-strain curve is minimized and inverse, by using the finite element method (FEM) to generate force-displacement curves and the virtual fields method, which compares internal and external virtual work.

Parameter Identification over Multiple Scales - Schmidt, Ulrike; Mergheim, Julia; Steinmann, Paul (Proceedings of the 5th conference on Multiscale Materials Modelling, 2010)
UnivIS-Import:2015-04-16:Pub.2010.tech.FT.FT-TM.parame_1

Path continuation for the concept of non-linear normal modes using a normal flow algorithm - Jerschl, Martin; Süß, Dominik; Willner, Kai; Jerschl, Martin (Proceedings of the International Conference on Noise and Vibration Engineering ISMA, 2014)
Non-linear normal modes (NNMs) can be considered as a kind of parallel theory to the description of linear systems with linear normal modes (LNMs) but for non-linear ones. In this paper a NNM is not defined as harmonic or synchronous oscillation but as periodic one. Therefore one has to search for periodic solutions of the governing equations of the system to get an NNM. This periodicity condition leads to a mathematical formulation as a two-point-boundary-value problem. Small systems with a low number of degrees of freedom and non-linear couplings (cubic springs) are investigated. The approach is also adopted to a finite-element model with a cubic non-linearity. With increasing the energy in the system the progressive non-linearity leads to a hardening effect. One typical dynamical property of non-linear systems is the frequency-energy dependency of their oscillations. A good graphic illustration is to plot such dependency in a so called frequency-energy plot (FEP) because here this dependency of energy and eigenfrequency is given explicitly. Thereby the points on a branch in the FEP represent a family of NNM oscillations with qualitatively equal motion properties, quasi a family of periodic orbits. A NNM branch can be calculated by a numerical continuation method with starting at low energy level in a quasi linear regime and increasing the energy and reducing the period of the oscillation iteratively. In non-linear systems internal resonances and other phenomena can occur. Several tongues can bifurcate from a NNM branch. Therefore normal continuation methods fail at such bifurcation points. To overcome this problem a predictor-corrector-method is used. As correction a probability one homotopy algorithm is implemented, in particular the normal flow algorithm. The predicted solution point gets iterated by a Newton-Raphson approach. The gradual iteration steps to the solution of the periodicity condition are along a path which is normal to the so-called Davidenko flow. The Davidenko flow can be seen as family of solution curves around the periodic solution caused by small perturbations to the non-linear system equations and varying these perturbations. These correction steps are continued until convergence is achieved. Different corrector approaches are compared to the normal flow algorithm and the results are discussed.
UnivIS-Import:2015-10-26:Pub.2014.tech.FT.FT-TM.pathco

Patientenspezifische Modellierung des passiven Bewegungsapparates als Grundlage für die präoperative Abschätzung postoperativer Folgeerscheinungen des endoprothetischen Hüftgelenkersatzes - Scherb, David; Kurz, Marlene; Fleischmann, Christopher; Wolf, Alexander; Sesselmann, Stefan; Miehling, Jörg; Wartzack, Sandro (Proceedings of the 31st Symposium Design for X (DFX2020), 2020)
During preoperative planning of total hip arthroplasty, the patients’ biomechanics is widely reduced to geometrical parameters. To provide the orthopedist more functional biomechanical parameters, a method is shown to model a patient-specific musculoskeletal human model via CT-/MRI-images in OpenSim. Main focus of this contribution is the setup of the passive musculoskeletal system. A generic human model and a segmented dataset of bones from the hip area serve as the basis for the modelling process. During the method the generic model is processed by scaling it to the anthropometry of the patient and adjusting subject-specific kinematics and shapes gathered from the segmented data. Finally, to reach the patient-specific representation the segmented bones are integrated into the mode
Keywords: Patient-specific modeling; Image-based model; Musculoskeletal human model; OpenSim; Total Hip Arthroplasty

Percentage Comparison of Fuzzy Numbers Using a Newly Presented Method in the Context of Surrogate Modeling - Oberleiter, Thomas; Willner, Kai (International Journal of Fuzzy Systems, 2024)
The O-index presented here allows a statement about the percentage deviation between two fuzzy numbers. For this purpose, one fuzzy number is defined s the reference. This fuzzy number is described with the help of its core value and its support. The deviation of the other fuzzy number, which is defined as the comparison number, is then quantified via the area differences of the left and right limits of the two numbers. In addition, the case when decomposed fuzzy numbers are involved, which are given as α-cuts is taken into account. Thus, the O-index-α can be used to calculate a separate percentage deviation for each α-cut and thus generate additional knowledge. The O-index then allows a very detailed description of the deviation between two fuzzy numbers. One application of the O-index is the estimation of the accuracy of a surrogate model in relation to a reference model in the context of uncertainty quantification. This is illustrated by a mechanical example, a bending beam.
CRIS-Team Scopus Importer:2024-06-14
Keywords: Fuzzy number comparison; Fuzzy numbers; Surrogate modeling; Uncertainty

Peridynamic modeling of nonlocal degrading interfaces in composites - Laurien, Marie; Javili, Ali; Steinmann, Paul (Forces in Mechanics, 2022)
When modeling composite materials at small scales, the consideration of nonlocal effects is fundamental. In addition, the overall response of matrix-inclusion composites is strongly affected by the behavior of the interface between inclusion and matrix. This can be attributed to a possible detachment of the constituents as well as the high interface-to-volume ratio especially for nano-sized inclusions. Peridynamics is a nonlocal theory that is suitable to introduce a length-scale into a continuum description and take into account nonlocal interactions. Complex interface models within a peridynamic framework are, however, rarely studied. The objective of this work is to present a modeling approach to nonlocal interfaces accounting for opening and degradation within the framework of continuum-kinematics-inspired peridynamics (CPD). The proposed method is employed to study nonlocal effects in matrix-inclusion composites with focus on the effect of nonlocal interfaces. In our approach, the nonlocal interface is mdeled as a finite thickness interface, i.e. a region where the subdomains overlap. Within this region, the constituents are pair-wise connected through interface bonding forces that follow a characteristic force-opening law. In computational experiments, our model captures the influence of the strength and size of the interface as well as the inclusion volume fraction on the overall response. In particular, nonlocality manifests itself through a “smaller–stiffer” material behavior and an increased influence of the interface, which highlights the importance of an appropriate nonlocal interface model.<br

Peridynamic modeling of nonlocal degrading interfaces in composites - Laurien, Marie; Javili, Ali; Steinmann, Paul (Forces in Mechanics, 2023)
When modeling composite materials at small scales, the consideration of nonlocal effects is fundamental. In addition, the overall response of matrix-inclusion composites is strongly affected by the behavior of the interface between inclusion and matrix. This can be attributed to a possible detachment of the constituents as well as the high interface-to-volume ratio especially for nano- sized inclusions. Peridynamics is a nonlocal theory that is suitable to introduce a length-scale into a continuum description and take into account nonlocal interactions. Complex interface models within a peridynamic framework are, however, rarely studied. The objective of this work is to present a modeling approach to nonlocal interfaces accounting for opening and degradation within the framework of continuum-kinematics-inspired peridynamics (CPD). The proposed method is employed to study nonlocal effects in matrix-inclusion composites with focus on the effect of nonlocal interfaces. In our approach, the nonlocal interface is modeled as a finite thickness interface, i.e. a region where the subdomains overlap. Within this region, the constituents are pair-wise connected through interface bonding forces that follow a characteristic force-opening law. In computational experiments, our model captures the influence of the strength and size of the interface as well as the inclusion volume fraction on the overall response. In particular, nonlocality manifests itself through a “smaller–stiffer” material behavior and an increased influence of the interface, which highlights the importance of an appropriate nonlocal interface model.

Period-doubling and period-tripling in growing bilayered systems - Budday, Silvia; Kuhl, Ellen; Hutchinson, John W. (Philosophical Magazine, 2015)
Growing layers on elastic substrates are capable of creating a wide variety of surface morphologies. Moderate growth generates a regular pattern of sinusoidal wrinkles with a homogeneous energy distribution. While the critical conditions for periodic wrinkling have been extensively studied, the rich pattern formation beyond this first instability point remains poorly understood. Here, we show that upon continuing growth, the energy progressively localizes and new complex morphologies emerge. Previous studies have often overlooked these secondary bifurcations; they have focused on large stiffness ratios between layer and substrate, where primary instabilities occur early, long before secondary instabilities emerge. We demonstrate that secondary bifurcations are particularly critical in the low stiffness ratio regime, where the critical conditions for primary and secondary instabilities move closer together. Amongst all possible secondary bifurcations, the mode of period-doubling plays a central role – it is energetically favourable over all other modes. Yet, we can numerically suppress period-doubling, by choosing boundary conditions, which favour alternative higher order modes. Our results suggest that in the low stiffness regime, pattern formation is highly sensitive to small imperfections: surface morphologies emerge rapidly, change spontaneously and quickly become immensely complex. This is a common paradigm in developmental biology. Our results have significant applications in the morphogenesis of living systems where growth is progressive and stiffness ratios are low.
UnivIS-Import:2015-07-08:Pub.2015.tech.FT.FT-TM.period
Keywords: bifurcation; growth; instabilities; period-doubling; period-tripling; thin films

Phase field simulations of the poling behavior of BaTiO3 nano-scale thin films with SrRuO3 and Au electrodes - Schrade, D.; Mueller, R.; Gross, Dietmar; Steinmann, Paul (European Journal of Mechanics A-Solids, 2015)
A continuum phase field model is used to investigate the poling behavior of BaTiO3 (BTO) thin films with thicknesses ranging from 1 nm-80 nm. The finite element simulations focus on the influence of the electrode material on the electrical hysteresis curves. The 15 nm thick electrodes consist of either SrRuO3 (SRO) or Au and are explicitly included in the simulations. Experimental evidence suggests that there is a depolarization field in SRO-electroded BTO thin films. This depolarization field, which is due to an imperfect charge compensation by the electrodes, causes a suppression of ferroelectricity for film thicknesses of a few unit cells. The depolarization field and its effect on the electrical behavior is captured by a Robin type boundary condition for the order parameter of the phase field model. This boundary condition is applied at the interface between the thin film and the top and bottom electrode. The simulation results show that the overall poling behavior strongly depends on the lattice parameter of the electrode material. Films with SRO electrodes, which have a lattice parameter smaller than the a-parameter of tetragonal BTO, observe a switchable polarization larger than the spontaneous polarization. If Au is used (which has lattice parameter larger than the a-parameter of tetragonal BTO) then switching is inhibited for films which are less than 20 nm thick. It is also shown that the Robin boundary condition induces a depolarization field which has the effect of dramatically reducing the switchable polarization in ultrathin films.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Ferroelectrics; Phase field; Thin films

Phenomenological modelling of self-healing polymers - Mergheim, Julia; Steinmann, Paul (Computational Mechanics, 2013)
The present contribution introduces a phenomenological model for self-healing polymers. Self-healing polymers are a promising class of materials which mimic nature by their capability to autonomously heal micro-cracks. This self-healing is accomplished by the integration of microcapsules containing a healing agent and a dispersed catalyst into the matrix material. Propagating microcracks may then break the capsules which releases the healing agent into the microcracks where it polymerizes with the catalyst, closes the crack and ’heals’ the material. The present modelling approach treats these processes at the macroscopic scale, the microscopic details of crack propagation and healing are thus described by means of continuous damage and healing variables. The formulation of the healing model accounts for the fact that healing is directly associated with the curing process of healing agent and catalyst. The model is implemented and its capabilities are studied by means of numerical examples.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.phenom
Keywords: Self-healing polymers; Continuum damage model; Continuum healing model; Polymer curing

Phonon-based thermal configurational forces: Definitions and applications in rupture of semiconductors - Birang Oskouei, Seyedehelmira; Smith, Ana-Suncana; Steinmann, Paul (Engineering Fracture Mechanics, 2021)
A general framework encompassing spatial and material settings of atomistic crystalline systems is presented. Theoretical and computational analysis of configurational forces in the context of atomistic thermomechanics constitutes the central topic of the presented paper. We distinguish between atomistic configurational forces stemming from the changes in static energy density and the changes in vibrational energy density. To this end, we first propose a novel atomistic phonon-based thermal configurational forces rendering infinitesimal changes in vibrational energy density under configurational variations. Next, we employ pair and triplet configurational forces resulting from the changes in static energy density due to two-body stretch and three-body stretch-bending. Using thermal configurational forces, we study numerically the problem of temperature rise, bond stretching and bending occurring at the crack tip induced by brittle crack propagation in crystalline lattices. Energy release caused by large harmonic vibrations and deformations is estimated by the magnitude of configurational forces at the crack tip. The atomistic temperature is shown to be governed by atom-wise frequency through local entropy. Finally, we demonstrate suitability and versatility of atomistic configurational forces in analyzing fracture of silicon diamond lattice subjected to mode-I loading at different finite temperatures.
Created from Fastlane, Scopus look-up
Keywords: Atomistic configurational mechanics; Atomistic fracture mechanics; Configurational forces; Effective empirical potential; Spatial and material settings

Physical aspects of cortical folding - Greiner, Alexander; Käßmair, Stefan; Budday, Silvia (Soft Matter, 2021)
The characteristically folded surface of the human brain is critical for brain function and allows for higher cognitive abilities. Recent mostly computational research advances have shown that mechanical instabilities play a crucial role during early brain development and cortical folding. However, it is difficult to investigate such mechanisms in vivo. To experimentally gain deeper insights into the physical mechanisms that underlie the development of brain shape, we use a setup of swelling polymers. We investigate the influence of cortical thickness and the stiffness ratio between cortex and subcortex on the resulting surface pattern by taking the initially smooth fetal brain geometry at week 22 into consideration. The gel specimens possess a two-layered structure accounting for gray and white matter tissue and yield complex surface morphologies that well resemble patterns in the human brain. The results are in good agreement with analytical predictions. Through the variation of cortical thickness and stiffness, it is possible to reproduce cortical malformations such as polymicrogyria and lissencephaly. The results suggest that wrinkling with subsequent transition into folding is the driving instability mechanism during brain development. In addition, the experiments provide valuable insights towards the distinction between wrinkling and creasing instabilities. Taken together, the presented swelling experiments impressively demonstrate the purely physical aspects of brain shape and constitute a valuable tool to advance our understanding of human brain development.

Physical biology of human brain development - Budday, Silvia; Steinmann, Paul; Kuhl, Ellen (Frontiers in Cellular Neuroscience, 2015)
Neurodevelopment is a complex, dynamic process that involves a precisely orchestrated sequence of genetic, environmental, biochemical, and physical events. Developmental biology and genetics have shaped our understanding of the molecular and cellular mechanisms during neurodevelopment. Recent studies suggest that physical forces play a central role in translating these cellular mechanisms into the complex surface morphology of the human brain. However, the precise impact of neuronal differentiation, migration, and connection on the physical forces during cortical folding remains unknown. Here we review the cellular mechanisms of neurodevelopment with a view toward surface morphogenesis, pattern selection, and evolution of shape. We revisit cortical folding as the instability problem of constrained differential growth in a multi-layered system. To identify the contributing factors of differential growth, we map out the timeline of neurodevelopment in humans and highlight the cellular events associated with extreme radial and tangential expansion. We demonstrate how computational modeling of differential growth can bridge the scales-from phenomena on the cellular level toward form and function on the organ level-to make quantitative, personalized predictions. Physics-based models can quantify cortical stresses, identify critical folding conditions, rationalize pattern selection, and predict gyral wavelengths and gyrification indices. We illustrate that physical forces can explain cortical malformations as emergent properties of developmental disorders. Combining biology and physics holds promise to advance our understanding of human brain development and enable early diagnostics of cortical malformations with the ultimate goal to improve treatment of neurodevelopmental disorders including epilepsy, autism spectrum disorders, and schizophrenia.
UnivIS-Import:2015-10-26:Pub.2015.tech.FT.FT-TM.physic
Keywords: Connectivity; Cortical folding; Differential growth; Lissencephaly; Neurodevelopment; Polymicrogyria; Synaptogenesis

Plastic dislocation and incompatibility density as indicators for residual stresses - Landkammer, Philipp; Steinmann, Paul (15th International Conference on Computational Plasticity. Fundamentals and Applications, COMPLAS 2019, 2019)
Residual stresses in forming simulations are typically investigated by analyzing the remaining stress state after removing all external loadings. However, the generation of the stress state during forming remains unknown. As a remedy, we use the plastic and elastic dislocation and incompatibility densities - derived from continuum mechanical and differential geometrical considerations - as indicators to track the generation of residual stresses through out a forming operation. Theoretical backgrounds for small and large strain plasticity are highlighted and practical aspects regarding implementation are provided. Two examples demonstrate the functionality of the approach, whereby the plastic incompatibility density in phenomenological, multiplicative large strain plasticity serves as indicator.
CRIS-Team Scopus Importer:2021-04-20
Keywords: Differential Geometry; Incompatibility Density; Residual Stresses

Poro-Viscoelastic Effects During Biomechanical Testing of Human Brain Tissue - Greiner, Alexander; Reiter, Nina; Paulsen, Friedrich; Holzapfel, Gerhard A.; Steinmann, Paul; Comellas Sanfeliu, Ester; Budday, Silvia (Frontiers in Mechanical Engineering, 2021)
Brain tissue is one of the softest tissues in the human body and the quantification of its mechanical properties has challenged scientists over the past decades. Associated experimental results in the literature have been contradictory as characterizing the mechanical response of brain tissue not only requires well-designed experimental setups that can record the ultrasoft response, but also appropriate approaches to analyze the corresponding data. Due to the extreme complexity of brain tissue behavior, nonlinear continuum mechanics has proven an expedient tool to analyze testing data and predict the mechanical response using a combination of hyper-, visco-, or poro-elastic models. Such models can not only allow for personalized predictions through finite element simulations, but also help to comprehensively understand the physical mechanisms underlying the tissue response. Here, we use a nonlinear poro-viscoelastic computational model to evaluate the effect of different intrinsic material properties (permeability, shear moduli, nonlinearity, viscosity) on the tissue response during different quasi-static biomechanical measurements, i.e., large-strain compression and tension as well as indentation experiments. We show that not only the permeability but also the properties of the viscoelastic solid largely control the fluid flow within and out of the sample. This reveals the close coupling between viscous and porous effects in brain tissue behavior. Strikingly, our simulations can explain why indentation experiments yield that white matter tissue in the human brain is stiffer than gray matter, while large-strain compression experiments show the opposite trend. These observations can be attributed to different experimental loading and boundary conditions as well as assumptions made during data analysis. The present study provides an important step to better understand experimental data previously published in the literature and can help to improve experimental setups and data analysis for biomechanical testing of brain tissue in the future.
Keywords: human brain; viscoelasticity; poroelasticity; constitutive modeling; mechanical properties; biomechanical testing; indentation; finite element analysis

Poro-viscoelastic material parameter identification of brain tissue-mimicking hydrogels - Kainz, Manuel P.; Greiner, Alexander; Hinrichsen, Jan; Kolb, Dagmar; Comellas, Ester; Steinmann, Paul; Budday, Silvia; Terzano, Michele; Holzapfel, Gerhard A. (Frontiers in Bioengineering and Biotechnology, 2023)
Understanding and characterizing the mechanical and structural properties of brain tissue is essential for developing and calibrating reliable material models. Based on the Theory of Porous Media, a novel nonlinear poro-viscoelastic computational model was recently proposed to describe the mechanical response of the tissue under different loading conditions. The model contains parameters related to the time-dependent behavior arising from both the viscoelastic relaxation of the solid matrix and its interaction with the fluid phase. This study focuses on the characterization of these parameters through indentation experiments on a tailor-made polyvinyl alcohol-based hydrogel mimicking brain tissue. The material behavior is adjusted to ex vivo porcine brain tissue. An inverse parameter identification scheme using a trust region reflective algorithm is introduced and applied to match experimental data obtained from the indentation with the proposed computational model. By minimizing the error between experimental values and finite element simulation results, the optimal constitutive model parameters of the brain tissue-mimicking hydrogel are extracted. Finally, the model is validated using the derived material parameters in a finite element simulation.
CRIS-Team Scopus Importer:2023-05-05
Keywords: biomechanical testing; brain tissue; hydrogel; indentation; parameter identification; polyvinyl alcohol; poroelasticity; viscoelasticity

Potential and constraints for the application of CFD combined with Lagrangian particle tracking to dry powder inhalers - Sommerfeld, Martin; Cui, Yan; Schmalfuß, Silvio (European Journal of Pharmaceutical Sciences, 2019)
For about 15 years the performance of dry powder inhalers (DPIs) has been numerically analysed through CFD (computational fluid dynamics) approaches with the objective of understanding the evolving flow structures and the resulting transport of drug particles. Naturally the main interest is the numerical prediction of the emitted fine particle fraction (FPF) which is able to penetrate the lung airways. Due to the mostly used drug formulations (i.e. carrier-based or agglomerated drug powder) and the complex elementary processes occurring during the transport of such particles through inhalers this is not an easy task. Essential for a good and efficient performance of DPI is the drug particle detachment from a carrier or the aerosolisation of agglomerated drug powder. Mostly the motion of particulate matter through an inhaler is described in a Lagrangian way using either a discrete particle method (DPM) or a discrete element method (DEM). This paper reviews the major published contributions related to the numerical calculations of dry powder inhalers by considering particles which may be coarse carrier or fine drug particles or even clusters including agglomerated fine particles or carriers covered with many drug particles. This review also considers simulations on the behaviour of single clusters interacting with flows or colliding with rigid walls. Following that, the potentials and constraints of the DPM and DEM are critically assessed with regard to inhaler applications. As a result, the DPM is most suitable since the clusters (i.e. carrier with drug or agglomerated drugs) are considered and tracked as single entities. On the other hand, in DEM all individual primary particles within clusters are tracked accounting for the acting fluid forces and multiple contact interactions between particles. In most applications published so far, the fluid dynamic interactions between these primary particles are not adequately accounted for. Hence, both approaches need further modelling activities for realistically capturing all relevant elementary processes, such as, flow induced drug detachment from clusters, cluster-wall collisions and recollection of drug particles on clusters. Moreover, recent calculations on the motion of carrier particles through an inhaler for statistically analysing the experienced flow stresses are presented. Also, carrier-wall collisions were evaluated with regard to number and intensity. The flow simulations were conducted for steady-state conditions based on RANS (Reynolds-averaged Navier-Stokes) in connection with the k-ω-SST (shear-stress transport) turbulence model. Carrier particle tracking was done considering all relevant forces, especially transverse lift forces. Based on this information, fully resolved simulations of the flow over particle clusters (i.e. carrier particle coated with thousands of drug particles) using the Lattice-Boltzmann method (LBM) are introduced. Therefrom, the detachment probabilities by lift-off, as well as sliding and rolling stripping of fine drug particles are evaluated. For that purpose, laminar and turbulent plug flows, as well as shear flows, were assumed to interact with the fixed cluster in a cubic domain. Even at the highest relative velocities typically found in an inhaler, lift-off in a laminar flow was not possible when considering experimentally determined adhesion forces. However, turbulence is very effective in drug powder detachment from a carrier. Finally results are presented using a novel carrier-wall collision model for describing drug detachment in Euler/Lagrange simulations. The results for two inhalers (i.e. Cyclohaler and Unihaler, a modular inhaler developed at the University of Kiel) revealed that carrier-wall collisions are very effective for inertia-induced drug detachment. Hence, the predicted fine particle fraction was found to be close to 100% for both inhalers. As a conclusion of this study, it has become clear that the wall deposition of fine drug particles is an important mechanism during carrier or agglomerate wall collisions, which are responsible for the low emitted fine particle fraction (FPF) observed experimentally. It is hoped that this article provides requirements and guidelines for the further development of Euler/Lagrange simulations applied to dry powder inhaler device
Keywords: Drug formulations; Dry powder inhaler; Discrete particle method; Drug detachment; Euler/Lagrange approach; Numerical calculation CFD; Discrete element method

Preparation of magnetorheological elastomers and their slip-free characterization by means of parallel-plate rotational rheometry - Walter, Bastian; Pelteret, Jean-Paul; Kaschta, Joachim; Schubert, Dirk W.; Steinmann, Paul (Smart Materials and Structures, 2017)
A systematic study is presented to highlight a methodology of sample preparation and subsequent slip-free characterization of magnetorheological (MR) elastomers in parallel-plate rotational rheometry. Focusing on the magnetic field-dependent nonlinear viscoelastic behavior an array of oscillatory strain sweep measurements is conducted with samples cured within the rheometer. The examined nonlinear material response (i.e. the amplitude dependence of the storage and loss moduli) as a function of the applied magnetic field is found to be qualitatively similar to the amplitude dependence of particle reinforced elastomers (i.e. the Payne effect). Therefore, the experimental data (both moduli) is decomposed similar to that for reinforced elastomers and a phenomenological model is formulated for both the storage and loss modulus to account for the physical mechanisms governing the nonlinear material characteristics. Parameter identification suggests that the material response at low magnetic fields is dominated by the polymeric network whereas the strong magneto-reinforced microstructure governs the linear and nonlinear viscoelastic behavior at high magnetic fields. The overall experimental outcome further suggests that the underlying concept of the phenomenological model for particle reinforced elastomers (i.e. destruction and reformation of the filler network) can be transfered to magnetorheological materials. Consequently, the proposed phenomenological model can be applied to quantify and further analyze the nonlinear response characteristics of MR elastomers (i.e. the amplitude dependence of the storage and loss modulus as a function of the applied magnetic field) that is closely linked to microstructural changes of the magnetizable particle network.
Keywords: Magnetorheological Elastomers (MREs); Field-Responsive Materials; Large Amplitude Oscillatory Shear (LAOS); Magnetorheometry; Magneto-Induced Payne Effect

Primary and secondary instabilities in soft bilayered systems - Budday, Silvia; Steinmann, Paul; Kuhl, Ellen; Andres, Sebastian (PAMM, 2015)
Wrinkling phenomena emerging from mechanical instabilities in inhomogeneously compressed soft bilayered systems can evoke a wide variety of surface morphologies. Applications range from undesired instabilities in engineering structures such as sandwich panels, via fabricating surfaces with controlled buckling patterns of unique properties, to wrinkling phenomena in living matter such as lungs, mucosas, and brain convolutions. While moderate compression evokes periodic sinusoidal wrinkles, higher compression induces secondary instabilities - the surface bifurcates into increasingly complex morphologies. Periodic wrinkling has already been extensively studied, but the rich pattern formation in the highly nonlinear post-buckling regime remains poorly understood. Here, we establish a computational model of differential growth to explore the evolving buckling pattern of a growing layer bonded to a non-growing substrate. Our model provides a mechanistic understanding of growth-induced primary and secondary instabilities. We show that amongst all possible secondary bifurcations, the mode of period-doubling is energetically favorable. We experimentally validate our numerical results by examining buckling of a compressed polymer film on a soft foundation. Our computational studies have broad applications in the microfabrication of distinct surface patterns as well as in the morphogenesis of living systems, where growth is progressive and the formation of structural instabilities is critical to biological function.

Produktionsmanagement als effizientes Werkzeug zur Vernetzung von Forschungsprojekten - Ziegler, Christian; Stockinger, Andreas; Stoll, Tobias; Wittmann, Stefan; Weickmann, Johannes; Schmidt, Jürgen; Topic, Irena; Schuck, Marcus; Cojutti, Massimo; Al-Sheyyab, Ahmad (Zeitschrift für wirtschaftlichen Fabrikbetrieb, 2007)
LFT Import::2019-07-16 (1501)

Proposal for an Improved Engineering Fatigue Lifetime Assessment Concept - Rudolph, Jürgen; Wilhelm, Paul; Roth, Armin; Herbst, Matthias; Kammerer, Matthias; Schuler, Xaver; Herter, Karl-Heinz (Proceedings of the ASME 2016 Pressure Vessels & Piping Conference, 2016)

Quality of alveolar bone - Structure dependant material properties and design of a novel measurement technique - Winter, Werner; Steinmann, Paul; Wichmann, Manfred; et al. (IFMBE Proceedings 31, 2010)
In a first part, the aim of this paper is to describe the biomechanical background which can be used as a basis for determining bone quality by measuring elastic properties of bone. Applying material mechanical equations for porous and cellular structured models, the elastic material properties (modulus of elasticity) of cellular and cortical bone as porous structures were approximated over the whole range of relative bone mineral density 0
UnivIS-Import:2017-07-10:Pub.2010.tech.FT.FT-TM.qualit
Keywords: Bone density; bone quality; compressive testing; dental implant; elastic modulus

Rail Vibrations in the High Frequency Range - Knothe, Kl.; Strzyzakowski, Z.; Willner, Kai (Journal of Sound and Vibration, 1994)
Different models of rails for the high frequency range are compared. In addition to known models, a new model based entirely upon the finite element method is presented. The models are used to calculate the dispersion relations for wave propagation in free rails up to 15 kHz. The results for different models are compared. The deviations are explained and the validity ranges for the different models are given.
UnivIS-Import:2015-03-05:Pub.1994.tech.FT.FT-TM.railvi

Rate dependent deformations in magneto-rheological elastomers: Modelling and experiments - Saxena, Prashant; Mokarram, Hossain; Walter, Bastian; Pelteret, Jean-Paul; Steinmann, Paul (IUTAM Symposium on Thermomechanical-Electromagnetic coupling in solids: Microstructral and Stability Aspects, 2014)

Realization of multi-material polymer parts by simultaneous laser beam melting - Laumer, Tobias; Stichel, Thomas; Riedlbauer, Daniel-Rouven; Amend, Philipp; Mergheim, Julia; Schmidt, Michael (Journal of Laser Micro Nanoengineering, 2015)
In this paper, first results regarding the realization of multi-material parts by Simultaneous Laser Beam Melting (SLBM) of polymers are presented. This new approach allows the layerwise generation of parts consisting of different polymer materials within one building process. Besides the typical advantages of additive manufacturing technologies, such parts can fulfill different product requirements concomitant and therefore could enlarge the overall field of application. The powder materials used for this paper are polyethylene (PE) and a polyamide based thermoplastic elastomer (TPE). After depositing the powder materials next to each other, infrared-emitters heat the lower melting polymer and a CO2 laser provides the preheating temperature of the higher melting polymer. In the last step, a thulium fibre laser melts the two preheated powders simultaneously. The realized specimens are characterized by cross sections and their tensile strengths are determined. Additionally, the new approach of the simultaneous energy irradiation is investigated using a Finite Element Analysis in order to gain a more profound process understanding. In that sense, the influence of the size of the exposure area on the reachable maximum temperatures inside that area was analyzed by the simulation and compared to experimental studies.
UnivIS-Import:2015-07-08:Pub.2015.tech.FT.FT-TM.realiz
Keywords: Additive manufacturing; Multi-material parts; New materials; Simultaneous laser beam melting of polymers

Recent Amendments of EN13445-3, Clause 18 and Related Annexes: Detailed Assessment of Fatigue Life - Rudolph, Jürgen; Baylac, Guy; Wilhelm, Paul; Wintle, John; Buennagel, Emilie (Proceedings of the ASME 2014 Pressure Vessels & Piping Conference, 2014)

Reduced-Order Modelling and Homogenisation in Magneto-Mechanics: A Numerical Comparison of Established Hyper-Reduction Methods - Brands, Benjamin; Davydov, Denis; Mergheim, Julia; Steinmann, Paul (Mathematical and Computational Applications, 2019)
The simulation of complex engineering structures built from magneto-rheological elastomers is a computationally challenging task. Using the FE2 method, which is based on computational homogenisation, leads to the repetitive solution of micro-scale FE problems, causing excessive computational effort. In this paper, the micro-scale FE problems are replaced by POD reduced models of comparable accuracy. As these models do not deliver the required reductions in computational effort, they are combined with hyper-reduction methods like the Discrete Empirical Interpolation Method (DEIM), Gappy POD, Gauss-Newton Approximated Tensors (GNAT), Empirical Cubature (EC) and Reduced Integration Domain (RID). The goal of this work is the comparison of the aforementioned hyper-reduction techniques focusing on accuracy and robustness. For the application in the FE2 framework, EC and RID are favourable due to their robustness, whereas Gappy POD rendered both the most accurate and efficient reduced models. The well-known DEIM is discarded for this application as it suffers from serious robustness deficiencies.
CRIS-Team WoS Importer:2019-09-17

Reduced-order modelling for linear heat conduction with parametrised moving heat sources - Brands, Benjamin; Mergheim, Julia; Steinmann, Paul (GAMM-Mitteilungen, 2016)
<p style="margin: 0px 0px 0.938em; padding: 0px; border: 0px; outline: 0px; font-size: 1.6em; vertical-align: baseline; background: 0px 0px rgb(249, 249, 249); line-height: 1.5; color: rgb(51, 51, 51); font-family: "Open Sans", Arial, Helvetica, "Lucida Sans Unicode", sans-serif;"> The purpose of Reduced-Order Modelling (ROM) is to substantially lower the computational cost of numerical simulations. As an example proper orthogonal decomposition (POD), which is optimal in a least-square sense, is applied to compute basis functions using existing solutions, e.g. from previously computed simulations. These reduced basis functions are subsequently used for the Galerkin projection of the governing equations. <p style="margin: 0px 0px 0.938em; padding: 0px; border: 0px; outline: 0px; font-size: 1.6em; vertical-align: baseline; background: 0px 0px rgb(249, 249, 249); line-height: 1.5; color: rgb(51, 51, 51); font-family: "Open Sans", Arial, Helvetica, "Lucida Sans Unicode", sans-serif;"> There is intense research on the application of ROM to parametrised partial differential equations (pPDE). However, in the case of transient equations research on ROM is mainly focused on models with constant parameters. In this paper an approach to cope with the linear heat conduction problem with a moving heat source is introduced. Problems of such kind are encountered in the simulation of laser or electron beam melting processes in additive manufacturing. To construct the reduced basis a nested POD method is used to mitigate the com-putational costs of large-scale eigenproblems. To further gain computational efficiency the discrete empirical interpolation method (DEIM) is applied to deal with non-affine parameter dependencies.
Keywords: proper orthogonal decomposition; model reduction; parameter-dependent models; projection-based model reduction; heat conduction with moving sources

Reduced Order Modelling for Non-Linear Rotating Systems in ALE Formulation with Contact - Weidauer, Tim; Willner, Kai (Nonlinear Dynamics, Volume 1; Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics 2018, 2018)
One approach for the simulation of rotating systems is the Arbitrary-Lagrangian-Eulerian (ALE) finite element formulation, which is well-established in the field of rolling contact mechanics for tires. With this formulation the rotational motion is handled from an Eulerian viewpoint and thus can be separated from the occurring Lagrangian deformation of the finite element mesh. In this context of (non-linear) systems undergoing gyroscopic and/or contact forces, e.g. for tires or disc brakes, model reduction techniques such as the Second order modal truncation, the Krylov subspace technique and the Craig-Bampton method are employed and analysed in their applicability.
Keywords: Gyroscopic system; ALE; non-linear dynamics; model order reduction; contact

Reducing computational cost of the simulation of selective laser melting of PA12 - Soldner, Dominic; Steinmann, Paul; Mergheim, Julia (Proceedings of the 6th International Conference on Additive Technologies, 2016)
The simulation of powder bed based additive manufacturing processes is a computational expensive task, due to different time and length scales, highly nonlinear material behaviour and dynamic growth of the simulation domain. Hence, conventional Finite Element based simulation tools may lead to very large scale systems. Therefore techniques are desired that decrease the computational cost. One approach is given by model reduction. The Finite Element space is characterized by locally supported ansatz functions and may be of high dimension, i.e. a large number of unknowns have to be determined. Computed quantities such as the temperature field corresponding to certain parameters, e.g. laser power, often lie in a lower dimensional subspace. This possibly truncated subspace, represented by a basis with global ansatz functions, may then be used to solve problems for similar parameters with a lower number of unknowns. In the present contribution projection based reduced-order modelling is applied to decrease the computational effort of the three dimensional simulation of selective laser melting of PA12 at a macroscopic level, focusing on the thermal problem. The Proper Orthogonal Decomposition is used to compute appropriate bases along with so-called hyper-reduction techniques, leading to a considerable reduction of computational cost.
Keywords: Reduced-Order Modeling; Hyper-Reduction; Additive Manufacturing; Heat Transfer Simulation

Regional aerosol deposition in the human airways: The SimInhale benchmark case and a critical assessment of in silico methods - Koullapis, P.; Kassinos, S.C.; Muela, J.; Perez-Segarra, C.; Rigola, J.; Lehmkuhl, O.; Cui, Yan; Sommerfeld, Martin; Elcner, J.; Jicha, M.; Saveljic, I.; Filipovic, N.; et al. (European Journal of Pharmaceutical Sciences, 2018)
Regional deposition effects are important in the pulmonary delivery of drugs intended for the topical treatment of respiratory ailments. They also play a critical role in the systemic delivery of drugs with limited lung bioavailability. In recent years, significant improvements in the quality of pulmonary imaging have taken place, however the resolution of current imaging modalities remains inadequate for quantifying regional deposition. Computational Fluid-Particle Dynamics (CFPD) can fill this gap by providing detailed information about regional deposition in the extrathoracic and conducting airways. It is therefore not surprising that the last 15 years have seen an exponential growth in the application of CFPD methods in this area. Survey of the recent literature however, reveals a wide variability in the range of modelling approaches used and in the assumptions made about important physical processes taking place during aerosol inhalation. The purpose of this work is to provide a concise critical review of the computational approaches used to date, and to present a benchmark case for validation of future studies in the upper airways. In the spirit of providing the wider community with a reference for quality assurance of CFPD studies, in vitro deposition measurements have been conducted in a human-based model of the upper airways, and several groups within MP1404 SimInhale have computed the same case using a variety of simulation and discretization approaches. Here, we report the results of this collaborative effort and provide a critical discussion of the performance of the various simulation methods. The benchmark case, in vitro deposition data and in silico results will be published online and made available to the wider community. Particle image velocimetry measurements of the flow, as well as additional numerical results from the community, will be appended to the online database as they become available in the future.<br
Keywords: Inhaled drug delivery; Computational fluid particle dynamics; Benchmark case; Respiratory airways; Regional deposition

Region‐ and loading‐specific finite viscoelasticity of human brain tissue - Budday, Silvia; Sommer, Gerhard; Paulsen, Friedrich; Holzapfel, Gerhard A.; Steinmann, Paul; Kuhl, Ellen (Proceedings in Applied Mathematics and Mechanics, 2018)
Computational simulations are a powerful tool to understand the mechanical behavior of our brain in health and disease, with the ultimate goal to prevent pathological conditions. Accurate numerical predictions, however, require the development of appropriate constitutive models and, equally important, the careful calibration of the corresponding constitutive parameters. This has been exceptionally challenging due to the ultrasoft and heterogeneous nature of brain tissue, resulting in a distinctly nonlinear, rate‐dependent, compression‐tension asymmetric, and region‐dependent behavior. Previous constitutive models have been deduced from a single loading mode, but fail to predict the behavior under various loading conditions. Here, we developed a large strain, nonlinear, viscoelastic constitutive model for brain tissue on the basis of cyclic and relaxation experiments under multiple loading modes, simple shear, compression, and tension. We carefully calibrated individual parameter sets for four different regions of the human brain, the cortex, the basal ganglia, the corona radiata, and the corpus callosum. The model captures effects such as nonlinearity and compression‐tension asymmetry, but also time‐dependent effects with substantial pre‐conditionning during the first loading cycle, only minor conditioning effects during subsequent cycles, and successive softening when the applied strain is stepwise increased. With close consideration of the underlying microstructure, we evaluate the physical meaning of viscoelastic material parameters with rate‐dependent regional trends. Our results help to improve the accuracy of human brain simulations during development and disease or to predict outcomes of neurosurgical procedure

Reinforced Hyaluronic Acid-Based Matrices Promote 3D Neuronal Network Formation - Janzen, Dieter; Bakirci, Ezgi; Faber, Jessica; Mier, Mateo Andrade; Hauptstein, Julia; Pal, Arindam; Forster, Leonard; Hazur, Jonas; Boccaccini, Aldo R.; Detsch, Rainer; Tessmar, Joerg; Budday, Silvia; et al. (Advanced Healthcare Materials, 2022)
3D neuronal cultures attempt to better replicate the in vivo environment to study neurological/neurodegenerative diseases compared to 2D models. A challenge to establish 3D neuron culture models is the low elastic modulus (30-500 Pa) of the native brain. Here, an ultra-soft matrix based on thiolated hyaluronic acid (HA-SH) reinforced with a microfiber frame is formulated and used. Hyaluronic acid represents an essential component of the brain extracellular matrix (ECM). Box-shaped frames with a microfiber spacing of 200 mu m composed of 10-layers of poly(e-caprolactone) (PCL) microfibers (9.7 +/- 0.2 mu m) made via melt electrowriting (MEW) are used to reinforce the HA-SH matrix which has an elastic modulus of 95 Pa. The neuronal viability is low in pure HA-SH matrix, however, when astrocytes are pre-seeded below this reinforced construct, they significantly support neuronal survival, network formation quantified by neurite length, and neuronal firing shown by Ca2+ imaging. The astrocyte-seeded HA-SH matrix is able to match the neuronal viability to the level of Matrigel, a gold standard matrix for neuronal culture for over two decades. Thus, this 3D MEW frame reinforced HA-SH composite with neurons and astrocytes constitutes a reliable and reproducible system to further study brain diseases.
CRIS-Team WoS Importer:2022-09-09

Reinforcement Learning for Engineering Design Automation - Dworschak, Fabian; Dietze, Sebastian; Wittmann, Maximilian; Schleich, Benjamin; Wartzack, Sandro (Advanced Engineering Informatics, 2022)
Reinforcement Learning has proven to be capable of solving complex tasks like playing video games, robotics control, speech or image recognition and processing. Transferring Reinforcement Learning into engineering design helps to overcome two current issues of data-driven Design Automation in engineering design. First, dealing with sparse training data resulting from differing design samples. Second, overcoming the limited number of samples in the training data as consequence of short or insufficient product history. To introduce an alternative approach for Design Automation, this contribution studies feasiblity, training effort and transferability of Reinforcement Learning in engineering design. The presented method maps engineering requirements and parametric models into learning environments and provides a novel approach for design automation. In addition to that, the contribution summarises the hyperparameters, which design engineers have to set prior to training, and introduces a novel transfer learning concept for Reinforcement Learning in related design tasks. The support is probed by design tasks of performance-oriented bike parts. Case-independent indicators are presented to estimate the case-specific training effort, the effects of hyperparameter variation and the effects of transferring a pretrained agent to related design tasks. Finally, the findings are used to compare Reinforcement Learning to other data-independent Design Automation approaches to assess potential fields of application for Reinforcement Learning in engineering desig
Keywords: Reinforcement Learning; Design Automation; Deep Q-learning

Reinforcing Tissue-Engineered Cartilage: Nanofibrillated Cellulose Enhances Mechanical Properties of Alginate Dialdehyde–Gelatin Hydrogel - Chayanun, Slila; Ahmadi Soufivand, Anahita; Faber, Jessica; Budday, Silvia; Lohwongwatana, Boonrat; Boccaccini, Aldo R. (Advanced Engineering Materials, 2023)
Cartilage tissue engineering offers a promising option for treating osteochondral defects. Alginate dialdehyde–gelatin (ADA–GEL) hydrogel has been explored as promising material for soft tissue scaffolds; however, its low stiffness has posed a constraint to load bearing applications. Herein, this limitation is addressed by introducing nanofibrillated cellulose (NFC) into the ADA–GEL matrix. The effect of NFC on the physicochemical properties of hydrogels is evaluated. Fourier transform infrared spectra demonstrate no chemical interaction between NFC and ADA–GEL, while scanning electron microscopy pictures reveal NFC fibers embedded in the hydrogel matrix, thus confirming the fiber-reinforced composite hypothesis. NFC-reinforced ADA–GEL (AG-N) composite hydrogels exhibit increased stiffness, with a maximum compressive effective modulus of 19.6 ± 3.0 kPa at 25% w/w NFC content. ATDC5 cell viability and proliferation as well as chondrogenic differentiation are assessed using immunohistochemical staining for sulfated glycosaminoglycans and collagen type II. A possible application of AG-N hydrogels as an osteochondral plug is also proposed, with polyetheretherketone as the subchondral bone anchor part. The mechanical properties of the resulting osteochondral device highlight its potential as a promising biomaterial for treatment of osteochondral defects. These findings provide valuable insights into the development of AG-N hydrogels for load-bearing tissue engineering applications.
CRIS-Team Scopus Importer:2023-09-22
Keywords: alginate; alginate dialdehyde–gelatin; cartilage tissue engineering; nanofibrillated cellulose; osteochondral plugs

Relationships between the admissible range of surface material parameters and stability of linearly elastic bodies - Javili, Ali; McBride, Andrew; Steinmann, Paul; Reddy, Batmanathan Dayanand (Philosophical Magazine, 2012)
This work focuses on the problem of an elastic bulk encased by an energetic elastic surface. The key contribution of this work is a study of the admissible range for the surface material parameters. In particular, the validity of negative surface parameters, which have been reported in the literature, is assessed. The balance equations for a continuum with a coherent energetic surface are stated. The local bifurcation conditions for the system (i.e. the bulk and the surface) are analysed using a standard ansatz for stationary waves. Under the reasonable assumption that the bulk is pointwise stable, the analysis concludes that pointwise stability of the surface elasticity tensor excludes any possible bifurcations; the weaker condition of surface strong ellipticity does not. The stability of the approximation of the governing equations using the finite element method is shown to be mesh-dependent for the case where the surface elasticity tensor loses pointwise stability. This is clearly illustrated via a series of numerical examples. Critically, it appears that the admissible range for the surface material properties differs for inherently non-local atomistic models and classical continuum formulations, both of which are used to model surface effects at the nanometre-scale. A key conclusion based on this observation is that care should be taken when fitting material properties obtained from atomistic models to classical continuum formulations that inherently lack a length-scale. The length-scale provided by the spatial discretisation can add stability, albeit artificially. © 2012 Copyright Taylor and Francis Group, LLC.
UnivIS-Import:2015-03-09:Pub.2012.tech.FT.FT-TM.relati
Keywords: bifurcation; mesh dependency; stability; surface elasticity

Relationships between the material parameters of continuum-kinematics-inspired peridynamics and isotropic linear elasticity for two-dimensional problems - Ekiz, E.; Steinmann, Paul; Javili, A. (International Journal of Solids and Structures, 2022)
Continuum-kinematics-inspired Peridynamics (CPD) has been recently proposed as a geometrically exact formulation of peridynamics that is also thermodynamically and variationally consistent. CPD can capture the Poisson effect exactly, unlike the original formulation of peridynamics (PD). Due to its geometrically exact nature, CPD does not suffer from zero-energy modes and displacement oscillations that may be observed in state-based PD formulations. For a two-dimensional analysis, CPD builds upon one-neighbor and two-neighbor interactions. The one-neighbor interactions of CPD are equivalent to the bond-based interactions of the original PD formalism. Two-neighbor interactions, however, are key in CPD since the basic notions of classical continuum kinematics, namely length and area, are preserved exactly. The isotropic two-dimensional CPD formulation of non-local elasticity therefore involves two material constants, namely C1 and C2, associated with length and area, respectively. This manuscript aims to establish relationships between the material parameters of CPD and isotropic linear elasticity for an affine deformation in a two-dimensional setting. It is shown that each of the CPD material parameters can be expressed in terms of any pairs of isotropic linear elasticity constants, such as Lamé parameters. Finally, we establish the admissible ranges for CPD material parameters.
CRIS-Team Scopus Importer:2021-12-17
Keywords: Continuum-kinematics-inspired peridynamics; CPD; Elastic material parameters; Nonlocal elasticity; Peridynamics; Thermodynamic consistency

Resonance phenomena in oscillatory shear rheometry: Influence of material parameters - Redel, Michael; Walter, Bastian; Kaschta, Joachim; Steinmann, Paul; Schubert, Dirk W. (Nordic Polymer Days 2018, 2018)
Rheological measurements are an established method for the characterisation of dynamic mechanical polymer properties. In current literature, possible restrictions to thesemeasurements by the phenomenon of resonance were evaluated by Stettin [1]. However, this paper is quiet about the influence of material parameters like stiffness or damping on the resonance phenomenon Therefore, an unfilled silicone elastomer, free of material particle interactions, is used. The cylindrical specimen are cured in a rheometer binding them firmly to the rotor. This has proven to prevent occurrence of for example wall slip [2]. The experiments conducted are frequency sweeps by means of a parallel-plate rheometer with a smooth geometry surface. Consequently, the influence of the setup, which was detected by Stettin [1], can be neglected. Resulting resonance frequencies are analysed concerning the material's damping and stiffness. Change in these parameters is realised by variation of mixture as well as addition of an additive. The resulting resonance frequencies show an explicit dependency of complex shear modulus |G*| as a measure of the stiffness. The resulting dependence in double logarithmic plot is compared with resonance frequency calculations based on oscillatory theories. Contribution of varying damping, realised by changing loss factor tan(δ), is detectable as an additional shift in resonance frequency and also discussed. Intriguingly, the wavedata of the stress response after resonance, obtained via fast Fourier transformation, differs from the expected sinusoidal signal. The change in wavedata and aberration from the sinusoidal excitation is explained by the phenomenon of vibration isolation. Furthermore, it is correlated with the material’s parameters reasoning the different experimental outcomes caused by the change in composition. A guideline to avoid the influence of resonance on oscillatory measurements is lastly presented

Revealing the percolation–agglomeration transition in polymer nanocomposites via MD-informed continuum RVEs with elastoplastic interphases - Richter, Eva; Possart, Gunnar; Steinmann, Paul; Pfaller, Sebastian; Ries, Maximilian (Composites Part B-Engineering, 2024)
This contribution builds the concluding step of a multiscale approach to effectively capture the mechanical behavior of polymer nanocomposites (PNCs), in this case, silica-modified polystyrene. By introducing continuum-based representative volume elements (RVEs) that employ previously identified elastoplastic property gradients for the interphases surrounding the fillers, the effects of particle size, particle volume fraction, and agglomeration on the mechanical performance are investigated. Uniaxial tension tests are simulated with the respective finite-element RVEs, and stress–strain curves are derived. The elastic and plastic material properties of the RVE can then be extracted and analyzed quantitatively by fitting the stress–strain curves with a Voce-type elastoplasticity formulation. At small degrees of agglomeration, i.e., good particle dispersion, in combination with sufficiently large particle volume fraction, percolation bands form, leading to improved elastic and plastic properties. Higher degrees of agglomeration or particle clusters behave like large single particles, which has an adverse effect, i.e., the nanoscale size effect is thereby neutralized. Therefore, the precise MD-informed elastoplastic interphase representation of our RVEs enables the investigation of the transition from beneficial percolation to unfavorable agglomeration. Ultimately, this contribution establishes a link between the effects of particle size, particle volume fraction, agglomeration, and percolation, which have so far only been discussed separately in the literature. Our methodology offers new insights into the structure–property relations of PNCs and their resulting mechanical behavior. The underlying multiscale approach with a systematic transition from molecular to microscopic scales is required to complement experimental observations and exploit the full potential of PNCs.
CRIS-Team Scopus Importer:2024-05-17
Keywords: Agglomeration; Finite elements; Interphase; Mechanical properties; Modeling and simulation; Nanocomposites; Percolation bands; Polymer composites; Size effect

Reviewing the roots of continuum formulations in molecular systems. Part II: Energy and angular momentum balance equations - Davydov, Denis; Steinmann, Paul (Mathematics and Mechanics of Solids, 2013)
This paper is the second part of a series dedicated to reviewing the fundamental link between discrete and continuum formulations, which is established by space averaging followed by probability density averaging. On obtaining the continuum balance laws of mass and linear momentum in the part I, here the balance laws of angular momentum and energy are re-derived from a discrete (atomistic/molecular) description. Different approaches (explicit and implicit) for the consideration of the potential energy are reviewed. Thereby for the explicit approach ambiguous possibilities for the localization of the potential energy are briefly discussed. Thereby we conclude that the explicit approach is preferable from the practical application point of view, however it becomes cumbersome when applied to multi-body interactions systems, whereas the implicit approach has no ambiguity in the localization of the potential energy to each particle and is easily applicable to any multi-body potential. Possible solutions for continuum fluxes (couple stresses, heat flux) are postponed until part III of the series.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.review

Reviewing the roots of continuum formulations in molecular systems. Part III: Stresses, Couple Stresses, Heat Fluxes - Davydov, Denis; Steinmann, Paul (Mathematics and Mechanics of Solids, 2014)
This contribution is the third part in a series devoted to the fundamental link between discrete particle systems and continuum descriptions. The basis for such a link is the postulation of the primary continuum fields such as density and kinetic energy in terms of atomistic quantities using space and probability averaging. In this part, solutions to the flux quantities (stress, couple stress, and heat flux), which arise in the balance laws of linear and angular momentum, and energy are discussed based on the Noll’s lemma. We show especially that the expression for the stress is not unique. Integrals of all the fluxes over space are derived. It is shown that the integral of both the microscopic Noll–Murdoch and Hardy couple stresses (more precisely their potential part) equates to zero. Space integrals of the Hardy and the Noll–Murdoch Cauchy stress are equal and symmetric even though the local Noll–Murdoch Cauchy stress is not symmetric. Integral expression for the linear momentum flux and the explicit heat flux are compared to the virial pressure and the Green–Kubo expression for the heat flux, respectively. It is proven that in the case when the Dirac delta distribution is used as kernel for spatial averaging, the Hardy and the Noll–Murdoch solution for all fluxes coincide. The heat fluxes resulting from both the so-called explicit and implicit approaches are obtained and compared for the localized case. We demonstrate that the spatial averaging of the localized heat flux obtained from the implicit approach does not equate to the expression obtained using a general averaging kernel. In contrast this happens to be true for the linear momentum flux, i.e. the Cauchy stress.
UnivIS-Import:2015-03-09:Pub.2014.tech.FT.FT-TM.review

Reviewing the roots of continuum formulations in molecular systems. Part I: Particle dynamics, statistical physics, mass and linear momentum balance equations - Davydov, Denis; Steinmann, Paul (Mathematics and Mechanics of Solids, 2012)
The link between atomistic quantities and continuum fields has been the subject of research for at least half a century. Nevertheless, there are still many open questions and misleading discussions in the literature. Therefore, based on the fundamental principles of classical mechanics and statistical physics we construct the basic framework for the link between the atomistic and continuum worlds. In doing so, considerable attention is paid to the central force decomposition and multi-body potentials, balance of angular momentum for the system of particles and its relationship to the extended third Newton axiom and the difference between the theorem of change of kinetic energy and the energy balance law. A number of general theorems related to the convolution properties of statistically averaged quantities, as well as their rates are also proven. These theorems make the derivation of balance equations far simpler when compared to the approaches used by others. Such theorems also make the link between space–time averaging and space–probability averaging more transparent. In this contribution the balance laws of mass and linear momentum are derived. The remaining balance laws of angular momentum and energy as well as the particular forms of fluxes, such as the stress, are discussed in the follow-up contributions of this series.
UnivIS-Import:2015-03-09:Pub.2012.tech.FT.FT-TM.review

Revised Boundary Conditions for FE-MD Multiscale Coupling of Amorphous Polymers - Ries, Maximilian; Jain, Y.; Steinmann, Paul; Pfaller, Sebastian (VIII Conference on Mechanical Response of Composites, 2021)
Due to their versatility, polymer nanocomposites have become an indispensable class of materials in recent years. Classical simulation approaches like the Finite Element method (FE) often struggle to predict such composite materials' behavior since they cannot account for molecular effects taking place, particularly in the additives' vicinity. To incorporate these effects, many multiscale formulations coupling continuum mechanics with particle descriptions have been proposed. One promising candidate, focusing on amorphous polymers, is the Capriccio Method introduced by Pfaller et al. [1]. They implement a coupling of FE and molecular dynamics (MD) by introducing a handshake region, the so-called bridging domain where information is transferred via virtual particles. The method has proved its capabilities in various studies, e.g., deriving nanocomposites' interphase properties [2,3]. So far, the Capriccio method relies on stochastic boundary conditions (SBC) to confine the particles and create a thermodynamic state. However, these SBCs require cutting any protruding molecule and thus an unphysical change of the microstructure. To address this problem, we extend the SBCs by adding an outer layer of particles governed by the continuum deformation enabling us to generate coupled FE-MD samples whose density matches a periodic MD solution. Combining these new boundary conditions with the inelastic extension of the Capriccio method proposed in [4] allows us to predict amorphous polymers' stress-strain behavior under arbitrary loading accurately. This extension enhances the Capriccio method's performance and will be useful in future studies of polymer nanocomposites.
Keywords: multiscale simulation; amorphous polymers; FE-MD coupling

Rheological characterization of human brain tissue - Budday, Silvia; Sommer, Gerhard; Haybaeck, Johannes; Steinmann, Paul; Holzapfel, Gerhard A.; Kuhl, Ellen (Acta Biomaterialia, 2017)
The rheology of ultrasoft materials like the human brain is highly sensitive to regional and temporal variations and to the type of loading. While recent experiments have shaped our understanding of the time-independent, hyperelastic response of human brain tissue, its time-dependent behavior under various loading conditions remains insufficiently understood. Here we combine cyclic and relaxation testing under multiple loading conditions, shear, compression, and tension, to understand the rheology of four different regions of the human brain, the cortex, the basal ganglia, the corona radiata, and the corpus callosum. We establish a family of finite viscoelastic Ogden-type models and calibrate their parameters simultaneously for all loading conditions. We show that the model with only one viscoelastic mode and a constant viscosity captures the essential features of brain tissue: nonlinearity, pre-conditioning, hysteresis, and tension-compression asymmetry. With stiffnesses and time constants of μ∞=0.7 kPa, μ1=2.0 kPa, and τ1=9.7 s in the gray matter cortex and μ∞=0.3 kPa, μ1=0.9 kPa and τ1=14.9 s in the white matter corona radiata combined with negative parameters α∞ and α1, this five-parameter model naturally accounts for pre-conditioning and tissue softening. Increasing the number of viscoelastic modes improves the agreement between model and experiment, especially across the entire relaxation regime. Strikingly, two cycles of pre-conditioning decrease the gray matter stiffness by up to a factor three, while the white matter stiffness remains almost identical. These new insights allow us to better understand the rheology of different brain regions under mixed loading conditions. Our family of finite viscoelastic Ogden-type models for human brain tissue is simple to integrate into standard nonlinear finite element packages. Our simultaneous parameter identification of multiple loading modes can inform computational simulations under physiological conditions, especially at low to moderate strain rates. Understanding the rheology of the human brain will allow us to more accurately model the behavior of the brain during development and disease and predict outcomes of neurosurgical procedures.
Keywords: Human brain; Rheological testing; Finite viscoelasticity; Ogden model; Parameter identification

Risk Assessment of Infection by Airborne Droplets and Aerosols at Different Levels of Cardiovascular Activity - Wedel, Jana; Steinmann, Paul; Strakl, Mitja; Hribersek, Matjaz; Ravnik, Jure (Archives of Computational Methods in Engineering, 2021)
Since end of 2019 the COVID-19 pandemic, caused by the SARS-CoV-2 virus, is threatening humanity. Despite the fact that various scientists across the globe try to shed a light on this new respiratory disease, it is not yet fully understood. Unlike many studies on the geographical spread of the pandemic, including the study of external transmission routes, this work focuses on droplet and aerosol transport and their deposition inside the human airways. For this purpose, a digital replica of the human airways is used and particle transport under various levels of cardiovascular activity in enclosed spaces is studied by means of computational fluid dynamics. The influence of the room size, where the activity takes place, and the aerosol concentration is studied. The contribution aims to assess the risk of various levels of exercising while inhaling infectious pathogens to gain further insights in the deposition behavior of aerosols in the human airways. The size distribution of the expiratory droplets or aerosols plays a crucial role for the disease onset and progression. As the size of the expiratory droplets and aerosols differs for various exhaling scenarios, reported experimental particle size distributions are taken into account when setting up the environmental conditions. To model the aerosol deposition we employ OpenFOAM by using an Euler-Lagrangian frame including Reynolds-Averaged Navier-Stokes resolved turbulent flow. Within this study, the effects of different exercise levels and thus breathing rates as well as particle size distributions and room sizes are investigated to enable new insights into the local particle deposition in the human airway and virus loads. A general observation can be made that exercising at higher levels of activity is increasing the risk to develop a severe cause of the COVID-19 disease due to the increased aerosolized volume that reaches into the lower airways, thus the knowledge of the inhaled particle dynamics in the human airways at various exercising levels provides valuable information for infection control strategies.
CRIS-Team WoS Importer:2021-07-16

Robust design optimization for enhancing delamination resistance of composites - Singh, Sukhminder; Pflug, Lukas; Mergheim, Julia; Stingl, Michael (International Journal for Numerical Methods in Engineering, 2022)
Recent developments in the field of computational modeling of fracture have opened up possibilities for designing structures against failure. A special case, called interfacial fracture or delamination, can occur in loaded composite structures where two or more materials are bonded together at comparatively weak interfaces. Due to the potential crack growth along these interfaces, the structural problem suffers from snap-back/snap-through instabilities and bifurcations with respect to the model parameters, leading to noisy and discontinuous responses. For such a case, the design optimization problem for a selected quantity of interest is ill-posed, since small variations in the design parameters can lead to large jumps in the structural response. To this end, this article presents a stochastic optimization approach to maximize delamination resistance that is less sensitive to small perturbations of the design and thereby leads to a robust solution. To overcome the intractability of Monte Carlo methods for estimating the expected value of the expensive-to-evaluate response function, a global, piecewise-constant surrogate is constructed based on nearest-neighbor interpolation that is iteratively refined during the optimization run. We found that by taking a large stochastic region at the beginning of the optimization and gradually reducing it to the desired one can help overcome poor local optima. Our results demonstrate the effectiveness of the proposed framework using an example of shape optimization of hard inclusions embedded in a double-cantilever beam, which significantly enhances delamination resistance.
CRIS-Team WoS Importer:2022-12-16

Sampling strategy for fuzzy numbers in the context of surrogate models - Oberleiter, Thomas; Willner, Kai (SN Applied Sciences, 2021)
The paper presents an investigation of the accuracy of surrogate models for systems with uncertainties, where the uncertain parameters are represented by fuzzy numbers. Since the underlying fuzzy arithmetic using alpha-level optimisation requires a large number of system evaluations, the use of numerically expensive systems becomes prohibitive with a higher number of fuzzy parameters. However, this problem can be overcome by employing less expensive surrogate models, where the accuracy of the surrogate depends strongly on the choice of the sampling points. In order to fnd a sufciently accurate surrogate model with as few as possible sampling points, the infuence of various sampling strategies on the accuracy of the fuzzy evaluation is investigated. As well suited for fuzzy systems, the newly developed Fuzzy Oriented Sampling Shift method is presented and compared with established sampling strategies. For the surrogate models radial basis functions and a Kriging model are employed. As test cases, the Branin and the Camelback function with fuzzy parameters are used, which demonstrate the varying accuracy for diferent sampling strategies. A more application oriented example of a fnite element simulation of a deep drawing process is given in the e
Keywords: Surrogate modelling · Fuzzy numbers · Kriging · DACE · Radial basis function · Uncertainty

Scale-dependent modeling of joint behavior - Willner, Kai (Conference Proceedings of the Society for Experimental Mechanics Series, 2016)
An investigation of the influence of constitutive friction laws on the damping behavior of dry friction joints is presented. The modeling starts at the micro- scale of the surface roughness leading to constitutive laws with regard to both the normal and tangential contact. These laws are used in a 3D finite element simulation of a simplified model joint. Numerical simulations show the influence of various levels of sophistication of the used contact laws. Here, the influence of high level contact laws proves to be limited in a spatially resolved joint model.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Dissipation; Friction; Joint; Rough surface; Simulation

Secondary instabilities modulate cortical complexity in the mammalian brain - Budday, Silvia; Steinmann, Paul; Kuhl, Ellen (Philosophical Magazine, 2015)
UnivIS-Import:2015-07-08:Pub.2015.tech.FT.FT-TM.second

Selektives Laserstrahlschmelzen von Kunststoffen - Modellierung des Temperaturhaushaltes und Einfluss auf resultierende Bauteileigenschaften - Drexler, Maximilian; Drummer, Dietmar; Wudy, Katrin; Riedlbauer, Daniel-Rouven; Steinmann, Paul; Mergheim, Julia (2. Industriekolloquium des SFB 814, 2013)
UnivIS-Import:2015-04-16:Pub.2013.tech.FT.FT-KT.selekt

Self-healing of Bessel beams - Lindlein, Norbert; Merklein, Bastian; Aiello, Andrea (2016)

Sensitivitätsanalyse der tribologischen Eigenschaften gefräster Oberflächenstrukturen bei der Blechmassivumformung - Breitsprecher, Thilo; Hense, Rouven; Beyer, Florian; Biermann, Dirk; Wartzack, Sandro; Willner, Kai (Tagungsband zum 2. Erlanger Workshop Blechmassivumformung 2013, 2013)
Reibeigenschaften von Oberflächen für Umformwerkzeuge gezielt einzustellen (Tailored Friction) nimmt bei der Entwicklung moderner Umformprozesse in technischer und ökonomischer Hinsicht eine zentrale Rolle ein. Dies betrifft insbesondere die Blechmassivumformung, die im Rahmen des SFB Transregio 73 erforscht wird. Ein neues Verfahren, das im SFB entwickelt wird, ist die Strukturierung durch regenerative Werkzeugschwingungen beim Fräsen. Ziel dabei ist es, einen separaten Prozessschritt, in dem nur strukturiert wird, einzusparen. Beim Fräsen mit Werkzeugschwingungen ist aufgrund der hohen Komplexität eine simulationsgestützte Auslegung unentbehrlich. Realitätsnahe Ergebnisse können dabei nur durch eine hinreichend gute Parametrisierung der Simulation erzielt werden, was im Besonderen für die Zerspankraftparameter gilt. In diesem Artikel wird die Sensitivität von tribologisch relevanten Kenngrößen auf die Zerspankraftparameter mit dem Ziel diskutiert, eine Aussage über die notwendige Güte zu treffen, mit der diese ermittelt werden müssen, um die Reibeigenschaften gefräster Oberflächen zuverlässig vorhersagen zu können. Um aus den simulierten gefrästen Oberflächen tribologische Kennwerte zu ermitteln, die für die Blechmassivumformung mit ihren hohen Flächenpressungen realitätsnah sind, findet ein Halbraummodell Anwendung.
Keywords: Tailored Friction; Sensitivitätsanalyse; Knowledge Discovery in Databases

Sequential topology and shape optimization framework to design compliant mechanisms with boundary stress constraints - Dev, Chaitanya; Stankiewicz, Gabriel; Steinmann, Paul (Structural and Multidisciplinary Optimization, 2022)
We present a sequential topology and shape optimization framework to design compliant mechanisms with boundary stress constraints. In our approach, a density-based topology optimization method is used to generate the configuration of the mechanisms. Afterwards, a node-based shape optimization is invoked to obtain an exact boundary representation. A specialized, optimality criteria-based design update is formulated for the shape optimization. To avoid impractical hinges with point connections, stress constraints are imposed. The stress constraints are imposed using two strategies: Local stress constraints on the nodes of the boundary or global P-norm stress constraints in the domain. Further, an adaptive shape refinement strategy is adopted to increase the design space of shape optimization and to capture the fine-scale details of the geometry. Finally, numerical experiments are presented, showing that the proposed approach can be effectively applied to the design of compliant mechanisms with stress constraints.
CRIS-Team WoS Importer:2022-06-24

Settling characteristics of nonspherical porous sludge flocs with nonhomogeneous mass distribution - Cui, Yan; Ravnik, Jure; Steinmann, Paul; Hribersek, Matjaz (Water Research, 2019)
The paper reports on the development of an advanced Lagrangian particle tracking model of sludge flocs that takes into account its nonspherical shape, the internal porosity and permeability, as well as the nonhomogenous mass distribution. The floc shapes, sizes and free settling velocities are determined based on the experimental measurement of settling sludge flocs originating from a wastewater treatment plant. Based on the floc shape characterization, a prolate axisymmetric ellipsoid is selected as the modelled sludge particle. In order to determine the main particle characteristics, e.g. the internal porosity, the density and the flow permeability, a Lagrangian particle tracking model is developed based on Brenner's drag model for a prolate axisymmetric ellipsoid and a buoyancy force model for a porous particle. The model is implemented for numerical simulations of the free settling process. The obtained floc characteristics are presented in the form of a two-part polynomial fitting curve, which can be used to model floc characteristics. The values of settling velocities of flocs computed by the model show very good agreement with experimental results. Futhermore, as the internal structure of a floc is seldom uniform, the nonhomogeneous mass distribution is considered, influencing the rotational and translational motions of the settling flocs. The nonhomogeneous mass distribution is introduced into the floc settling model. The parametric analyses of different barycentre offsets and shear rates are performed, and their influences on the free settling velocity are evaluated. The presented modelling approach can also be applied to flocculent settling of alum and other flocs in drinking water treatment plants. The developed Lagrangian model is suitable for use as a point source within the framework of Eulerian flow computations, and is solved as a two-phase flow model with a suitable Computational Fluid Dynamics code.
CRIS-Team Scopus Importer:2019-05-02
Keywords: activated sludge; Floc settling velocity; Lagrangian particle tracking model; Non-homogenous porous floc; Prolate spheroidal floc

Shape matters: Lagrangian tracking of complex nonspherical microparticles in superellipsoidal approximation - Wedel, Jana; Steinmann, Paul; Štrakl, Mitja; Hriberšek, Matjaž; Ravnik, Jure (International Journal of Multiphase Flow, 2023)
Humans are constantly exposed to airborne pollutants such as pollen, exhaust residues, microplastics, fabrics, aerosols, or, as recently, ash particles from volcanic eruptions, which are rarely perfectly spherical. In order to reduce the impact of harmful particles or, on the contrary, to improve the targeted delivery of drugs, understanding the motion of complex shaped particles in fluid flows is of key interest. Common models mainly use shape factors to account for deviations from spherical shape, but these often fail to accurately predict particle motion. We advocate a more accurate modeling of complex particles by a superellipsoidal shape approximation, which allows covering a wide range of particle geometries. Superellipsoidal particle shapes allow for a novel approximation of translational and rotational resistance tensors, derived based on data from dedicated DNS computations. Our surrogate approach for convex bodies (ϵ1,ϵ2∈(0,2)), implemented in OpenFOAM® based on Lagrangian particle tracking, is first validated based on experimental and in-silico results from the literature, followed by a comparison of the effects of non-sphericity for some well known fluid flow cases, such as a lid-driven cavity (validated for Re=470, St=0.0023), pipe flow (validated for Re=137, St=0.01) and a simplified bifurcation (validated for Re=500, St=0.5×10−2−0.5). We show that using shape factor assisted spherical or ellipsoidal approximations of the particles leads to insufficient accuracy of computation of the particle's trajectory, whereas the newly derived superellipsoidal drag and torque models proved to provide a superior accuracy of the Lagrangian particle tracking over simplified non-spherical particle approximations.
CRIS-Team Scopus Importer:2022-11-25
Keywords: CFD; Non-spherical particles; OpenFOAM; Superellipsoids

Shape Optimization for Anisotropic Elastoplasticity in Logarithmic Strain Space - Germain, Sandrine; Steinmann, Paul (COMPLAS XI Proceeding (CD), 2011)
This paper deals with shape optimization for anisotropic elastoplasticity in logarithmic strain space. We aim to find an appropriate undeformed configuration of a workpiece knowing in advance its deformed configuration, the boundary conditions and the applied loads. The node coordinates of the finite element (FE) domain are chosen as design variables. A discrete sensitivity analysis is presented and analytical gradients are performed. A numerical example illustrates the theoretical aspects.
UnivIS-Import:2015-04-16:Pub.2011.tech.FT.FT-TM.shapeo
Keywords: Anisotropy; Elastoplasticity; Shape optimization

Shape Optimization of a Backward Extrusion Process Using a Non-Invasive Form Finding Algorithm - Caspari, Michael; Landkammer, Philipp; Steinmann, Paul (Procedia Manufacturing, 2020)
The objective of our algorithm is to optimize the material configuration of a forming workpiece to ensure that the spatial configuration corresponds to a given target shape. Hence, the preform of a forming process is optimized in order to satisfy the geometric requirements at the end of the forming process. The algorithm is non-invasive, which is a unique feature as it enables commercial solvers to be used to simulate the forming process. As a result, even complex forming processes can be considered. For most of these processes the material undergoes large deformations, which in turn requires the use of remeshing strategies to ensure a high quality mesh throughout the entire simulation. The global remeshing of the system poses a particular challenge to the form finding algorithm when using a node-based approach. This problem is explicitly addressed in this contribution. The implementation is highlighted for the example of a backward extrusion process.<br
Keywords: Non-Invasive; Optimization; Mesh Projection; Remeshing

Sheet steel material parameter identification utilizing a biaxial tensile test and optical full-field measurements - Schmaltz, Stefan; Willner, Kai (PhotoMechanics, 2013)
UnivIS-Import:2015-04-16:Pub.2013.tech.FT.FT-TM.sheets_4

Simulating the mechanical stimulation of cells on a porous hydrogel scaffold using an FSI model to predict cell differentiation - Azizi, Pedram; Drobek, Christoph; Budday, Silvia; Seitz, Hermann (Frontiers in Bioengineering and Biotechnology, 2023)
3D-structured hydrogel scaffolds are frequently used in tissue engineering applications as they can provide a supportive and biocompatible environment for the growth and regeneration of new tissue. Hydrogel scaffolds seeded with human mesenchymal stem cells (MSCs) can be mechanically stimulated in bioreactors to promote the formation of cartilage or bone tissue. Although in vitro and in vivo experiments are necessary to understand the biological response of cells and tissues to mechanical stimulation, in silico methods are cost-effective and powerful approaches that can support these experimental investigations. In this study, we simulated the fluid-structure interaction (FSI) to predict cell differentiation on the entire surface of a 3D-structured hydrogel scaffold seeded with cells due to dynamic compressive load stimulation. The computational FSI model made it possible to simultaneously investigate the influence of both mechanical deformation and flow of the culture medium on the cells on the scaffold surface during stimulation. The transient one-way FSI model thus opens up significantly more possibilities for predicting cell differentiation in mechanically stimulated scaffolds than previous static microscale computational approaches used in mechanobiology. In a first parameter study, the impact of the amplitude of a sinusoidal compression ranging from 1% to 10% on the phenotype of cells seeded on a porous hydrogel scaffold was analyzed. The simulation results show that the number of cells differentiating into bone tissue gradually decreases with increasing compression amplitude, while differentiation into cartilage cells initially multiplied with increasing compression amplitude in the range of 2% up to 7% and then decreased. Fibrous cell differentiation was predicted from a compression of 5% and increased moderately up to a compression of 10%. At high compression amplitudes of 9% and 10%, negligible areas on the scaffold surface experienced high stimuli where no cell differentiation could occur. In summary, this study shows that simulation of the FSI system is a versatile approach in computational mechanobiology that can be used to study the effects of, for example, different scaffold designs and stimulation parameters on cell differentiation in mechanically stimulated 3D-structured scaffolds.
CRIS-Team Scopus Importer:2023-10-20
Keywords: cell differentiation; computational fluid dynamic; finite element analysis; fluid-solid interaction; in silico; tissue engineering

Simulation-based development of Pareto-optimized tailored blanks for the use within sheet-bulk metal forming - Küstner, Christof; Beyer, Florian; Kumor, Dustin; Loderer, Andreas; Wartzack, Sandro; Willner, Kai; Blum, Heribert; Rademacher, Andreas; Hausotte, Tino (DS 84: Proceedings of the DESIGN 2016 14th International Design Conference, 2016)
In the context of lightweight design, the so-called tailored blanks are more frequently used to improve sheet-bulk metal forming process results. In order to meet the requirements of tailored blank designs for subsequent sheet-bulk metal forming process steps, design engineers can influence many process or geometry parameters. A crucial task for design engineers is to find the optimal process and geometry parameter setting that is an optimal design with respect to multiple design requirements. A simulation-based approach to face this challenge is presented in this pape
Keywords: pareto-optimized design; simulation study; friction law

Simulation of 3d Fatigue Crack Propagation Using an Implicit Time Integration Scheme - Weber, Wilhelm; Steinmann, Paul; Kuhn, Günther (International Journal of Fatigue, 2012)
Due to the non-linear behavior of fatigue crack growth an incremental numerical procedure has to be applied for the simulation. In the present work a new implicit time integration scheme for arbitrary loading conditions is presented ensuring accurate simulation results. Within this scheme special focus is on the evolution of the stress field between two successive discrete crack fronts of the incremental procedure. By the consideration of the changing stress field the numerically obtained crack fronts are optimized with respect to their shape and location. The whole procedure is implemented in the framework of a predictor–corrector scheme. Two examples are shown to demonstrate the benefit of the presented scheme.
UnivIS-Import:2015-03-09:Pub.2012.tech.FT.FT-TM.simula_0
Keywords: 3D crack growth simulation; 3D crack growth criterion; Predictor–corrector scheme

Simulation of adhesive joints by viscoelastic interface material model - Konchakova, Natalia; Müller, Ralf; Steinmann, Paul; Balle, Frank; Eifler, Dietmar; Barth, Franz-Josef (Advanced Engineering Materials, 2013)
Numerical results of lightweight metal/carbon fiber reinforced polymer (CFRP) overlapped structures modeling with different non-elastic interfaces are presented. The hybrid joints of metal and polymer composite can be produced by ultrasonic metal welding or by means of adhesive bonding. The simulation of both types of joints is the focus of this investigation. The difference in the numerical models of the ultrasonic welded and adhesively bonded specimens is elaborated. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.simula_8

Simulation of creep and cyclic viscoplastic strains in high-Cr steel components based on a modified becker-hackenberg model - Wang, J.; Steinmann, Paul; Rudolph, J.; Willuweit, A. (International Journal of Pressure Vessels and Piping, 2015)
A constitutive model is proposed to simulate the thermo-mechanical behavior of high-Cr steel components. In this model, the total inelastic strain is decomposed into the creep strain and the viscoplastic strain. For creep strain, two Larson-Miller parameters are adopted to evaluate the minimum creep rate and the average creep rupture time. The cyclic viscoplastic strain is predicted through the conventional Chaboche-type modeling approach with the viscoplastic strain rate. The cyclic softening effect, ratcheting effect, time recovery effect and temperature rate effect are taken into account in the kinematic and isotropic hardening rules. A strategy of stress-range separation is proposed to identify the involved material parameters. Some examples are presented to show that the current model can predict the response of high-Cr steels at a quantitative level. This model provides an opportunity to evaluate the remaining lifetimes of power plant components subject to long dwell time in combination with variable loading conditions.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Constitutive model; Creep; Cyclic viscoplasticity; Finite element simulation; High-Cr steel

Simulation of fracture in heterogeneous elastic materials with cohesive zone models - Prechtel, Marina; Ronda, Pavel Leiva; Janisch, Rebecca; Hartmaier, Alexander; Leugering, Günter; Steinmann, Paul; Stingl, Michael (International Journal of Fracture, 2010)
In brittle composite materials, failure mechanisms like debonding of the matrix-fiber interface or fiber breakage can result in crack deflection and hence in the improvement of the damage tolerance. More generally it is known that high values of fracture energy dissipation lead to toughening of the material.Ouraimis toinvestigate the influence of material parameters and geometrical aspects of fibers on the fracture energy as well as the crack growth for given load scenarios. Concerning simulations of crack growth the cohesive element method in combination with the Discontinuous Galerkin method provides a framework to model the fracture considering strength, stiffness and failure energy in an integrated manner. Cohesive parameters are directly determined by DFT supercell calculations.We perform studies with prescribed crack paths as well as free crack path simulations. In both cases computational results reveal that fracture energy depends on both the material parameters but also the geometry of the fibers. In particular it is shown that the dissipated energy can be increased by appropriate choices of cohesive parametersof the interface and geometrical aspects of the fiber. In conclusion, our results can help to guide themanufacturing process ofmaterials with a high fracture toughness.
UnivIS-Import:2015-03-09:Pub.2010.tech.FT.FT-TM.simula

Simulation of Sheet-Bulk Metal Forming Processes with Simufact.forming using User-Subroutines - Beese, Stefan; Beyer, Florian; Blum, Heribert; Isik, Kerim; Kumor, Dustin; Löhnert, Stefan; Rademacher, Andreas; Tekkaya, A. Erman; Willner, Kai; Wriggers, Peter; Zeller, Sebastian (19th ESAFORM Conference, 2016)
In this article, we consider the simulation of sheet-bulk metal forming processes, which makes high demands on the underlying models and on the simulation software.We present our approach to incorporate new modelling approaches from various fields in a commercial simulation software, in our case Simufact.forming. Here, we discuss material, damage, and friction models as well as model adaptive techniques.

Simulation of the creep and fatigue damages in high-Cr steel components based on a modified becker-hackenberg model - Wang, Jiong; Steinmann, Paul; Rudolph, Jürgen; Willuweit, Adrian (American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP, 2014)
Components of conventional power plants are subject to three potential damage mechanisms and their combination (accumulation) with impact on lifetime considerations: creep, fatigue and ratcheting. Currently, there is a growing need for advanced material models which are able to simulate these damage phenomena and can be implemented effectively within finite-element (FE) codes. This constitutes the basis of an advanced component design. In this work, a constitutive material model, named as the modified Becker-Hackenberg model, is proposed to simulate the thermo-mechanical behavior of high-Cr steel components subject to complex loading conditions. Both creep and viscoplasticity are taken into account in the model, which are viewed as two different kinds of inelastic mechanisms. The key features of the creep strain, i.e., the minimum creep rate and the average creep rupture time, are evaluated by using two Larson-Miller parameters. The cyclic viscoplastic strain is predicted through the conventional Chaboche-type modeling approach, where suitable constitutive evolution equations are adopted to capture the cyclic softening effect, ratcheting effect, time recovery effect and temperature rate effect. All the material parameters involved in this model are identified by using a strategy of stress-range separation. This constitutive model is further implemented in a commercial FE software to simulate the thermo-mechanical behaviors of high-Cr steel components with technologically relevant dimensions. The strain and stress evolution data obtained from the model can be further used for the fatigue damage assessment of high-Cr steel components subject to creep-fatigue interactions. Within an ongoing work, a multiaxial fatigue analyzer is developed to predict the fatigue lifetime of high-Cr steels subject to cyclic loading conditions respectively - in a further step - creep-fatigue interaction.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Constitutive model; Creep; Cyclic viscoplasticity; Finite element simulation; High-Cr steel

Simulation of the elastohydrodynamic contact with a piezo-viscous fluid - Leitz, Thomas; Willner, Kai (Proc. Appl. Math. Mech. (PAMM), 2012)

Simulation of the temperature distribution in the selective beam melting process for polymer material - Riedlbauer, Daniel-Rouven; Mergheim, Julia; Steinmann, Paul (29th International Conference of the Polymer Processing Society, 2014)
In the present contribution the temperature distribution in the selective beam melting process for polymer materials is simulated to better understand the influence of process parameters on the properties of the produced part. The basis for the developed simulation tool is the nonlinear heat equation including temperature dependent functions for the heat capacity and the heat conduction which were obtained by experimental measurements. The effect of latent heat occurring in the process is also taken into account. The heat equation is discretized in time and space where a Runge-Kutta method of Radau IIA type is used for time integration. An adaptive finite element method is applied for the discretization in space and the model is implemented into the finite element library deal.II. The heat and cooling rate as important process parameters are simulated for different beam velocities. The ability for computing these process parameters makes the simulation tool suited for optimizing the process management of selective beam melting plants. © 2014 American Institute of Physics.
UnivIS-Import:2015-04-16:Pub.2014.tech.FT.FT-TM.simula_3
Keywords: cooling rate; heat rate; numerical simulation; Selective beam melting; transient heat transfer

Simulation von Temperaturfeldern und mechanischen Materialverhalten in additiven Fertigungsprozessen - Riedlbauer, Daniel-Rouven; Steinmann, Paul; Mergheim, Julia (3. Industriekolloquium des Sonderforschungsbereichs 814 - Additive Fertigung, 2014)
UnivIS-Import:2015-04-16:Pub.2014.tech.FT.FT-TM.simula_9

Single crystal plasticity – A mesoscale based approach for modeling the mechanics of additively manufactured Inconel 718 - Kergaßner, Andreas; Mergheim, Julia; Steinmann, Paul (Proceedings in Applied Mathematics and Mechanics, 2018)
In this contribution the mesoscopic material behavior of columnar grained Inconel 718 is modeled with a gradient enhanced crystal plasticity formulation and simulated by means of Finite Elements. A Voronoi tessellation based method is used to model the grain structure. On the mesoscale, the thermo‐mechanical behavior is modeled using a thermal gradient‐crystal‐plasticity model, allowing for relative misorientations on the grain boundaries. Computational homogenization and macroscopic experimental data are used to inversely identify elastic and plastic mesoscopic mechanical parameters. With the homogenized RVE at hand the parameters of a general anisotropic yield criterion for the macro scale are identified.<br
Keywords: Crystal Plasticity; Material Modelling; Homogenization; Multi Surface Yield Criterion

Size and curvature regulate pattern selection in the mammalian brain - Budday, Silvia; Steinmann, Paul; Goriely, Alain; Kuhl, Ellen (Extreme Mechanics Letters, 2015)
Mammalian brains display a wide variety of shapes and surface morphologies. Their characteristically folded surface is closely correlated to neuronal activity and serves as a clinical indicator for physiological and pathological conditions. Yet, the regulators of pattern formation in evolution and development remain poorly understood. Here we show how brain size and curvature affect the folding pattern in the developing mammalian brain. We model cortical folding as the instability problem of a bilayered system subjected to growth-induced compression. Using analytical estimates and continuum models for finite growth, we systematically explore the effects of geometric factors on the evolution of surface shape. We demonstrate that extrinsic geometric features-including brain size, cortical thickness, and cortical curvature-tightly regulate pattern selection: The mammalian brain is extremely soft and even small environmental changes can create extremely large alterations in its surface morphology. Our simulations explain why gyrification increases with brain size and why longer brains tend to fold more longitudinally than radially. Our results suggest that brain folding is driven, at least in part, by extreme mechanics, rather than by phylogeny alone.
UnivIS-Import:2015-10-26:Pub.2015.tech.FT.FT-TM.sizean
Keywords: Brain mechanics; Cortical folding; Growth; Instabilities; Living matter; Soft matter; Thin films

Size effects in a silica-polystyrene nanocomposite: Molecular dynamics and surface-enhanced continuum approaches - Davydov, Denis; Voyiatzis, E; Chatzigeorgiou, Georgios; Liu, S; Steinmann, Paul; Böhm, M; Müller-Plathe, F. (Soft Materials, 2014)
Size effects in a system composed of a polymer matrix with a single silica nanoparticle are studied using molecular dynamics and surface-enhanced continuum approaches. The dependence of the composites mechanical properties on the nanoparticles radius was examined. Mean values of the elastic moduli obtained using molecular dynamics were found to be lower than those of the polystyrene matrix alone. The surface-enhanced continuum theory produced a satisfactory fit of macroscopic stresses developing during relaxation due to the interface tension and uniaxial deformation. Neither analytical nor finite-element solutions correlated well with the size-effect in elastic moduli predicted by the molecular dynamics simulations.
Keywords: Molecular dynamics; Nanocomposite; Size effect; Surface energy; Surface-enhanced continuum

Size Effects in Computational Homogenization of Polymer Nano-Composites - Kumar, Paras; Mergheim, Julia (Proceedings in Applied Mathematics & Mechanics, 2021)

Size effects of 109? domain walls in rhombohedral barium titanate single crystals–A molecular statics analysis - Endres, Florian; Steinmann, Paul (Journal of Applied Physics, 2016)
Ferroelectric functional materials are of great interest in science and technology due to their electromechanically coupled material properties. Therefore, ferroelectrics, such as bariumtitanate, are modeled and simulated at the continuum scale as well as at the atomistic scale. Due to recent advancements in related manufacturing technologies the modeling and simulation of smart materials at the nanometer length scale is getting more important not only to predict but also fundamentally understand the complex material behavior of such materials. In this study, we analyze the size effects of 109° nanodomain walls in ferroelectricbariumtitanate single crystals in the rhombohedral phase using a recently proposed extended molecular statics algorithm. We study the impact of domain thicknesses on the spontaneous polarization, the coercive field, and the lattice constants. Moreover, we discuss how the electromechanical coupling of an applied electric field and the introduced strain in the converse piezoelectric effect is affected by the thickness of nanodomains.
Keywords: Polarization; domain walls; ferroelectric materials; electrical hysteresis; barium titanate

Smooth conformal alpha-NEM for Gradient Elasticity - Rajagopal, Amirtham; Scherer, Michael; Steinmann, Paul; Sukumar, Natarajan (The International journal of structural changes in solids: mechanics and applications, 2009)
Strain gradient theory for continuum analysis has kinematic relations, which include terms from second gradients of the deformation map. This results in balance equations that have fourth order spatial derivatives, supplemented with higher order boundary conditions. The weak formulation of fourth order operators stipulate that the basis functions must be globally C 1 continuous; very few finite elements in two dimensions meet this requirement. In this paper, we propose a meshfree methodology for the analysis of gradient continua using a conformal alpha-shape based natural element method (NEM). The conformal alpha-NEM allows the construction of models entirely in terms of nodes, and ensures quadratic precision of the interpolant over convex and non-convex boundaries. Smooth natural neighbor interpolants are achieved by a transformation of Farin's C 1 interpolant, which are obtained by embedding Sibson's natural neighbor coordinates in the Bernstein-Bezier surface representation of a cubic simplex. Numerical examples are presented to demonstrate the accuracy and efficiency of the proposed method.<br
UnivIS-Import:2015-03-09:Pub.2009.tech.FT.FT-TM.smooth

Solution of Multi-Field Problems using Finite and Boundary Element Methods - Gaul, L.; Fischer, M.; Nackenhorst, U.; Willner, Kai (Proceedings of the FENET/NAFEMS Seminar: FEM in Structral Dynamics, 2001)
UnivIS-Import:2015-04-16:Pub.2001.tech.FT.FT-TM.soluti

Some properties of the dissipative model of strain-gradient plasticity - Carstensen, C.; Ebobisse, Francois; Mcbride, A. T.; Reddy, B. D.; Steinmann, Paul (Philosophical Magazine, 2017)
A theoretical and computational investigation is carried out of a dissipative model of rate-independent strain-gradient plasticity and its regularisation. It is shown that the flow relation, when expressed in terms of the Cauchy stress, is necessarily global. The most convenient approach to formulating the flow relation is through the use of a dissipation function. It is shown, however, that the task of obtaining the dual version, in the form of a normality relation, is a complex one. A numerical investigation of problems in two space dimensions casts further light on the response using the dissipative theory in situations of non-proportional loading. The elastic gap, a feature reported in recent investigations, is observed in situations in which passivation has been imposed. The computational study indicates that the gap may be regarded as an efficient path between a load-deformation response corresponding to micro-free boundary conditions, and that corresponding to micro-hard boundary conditions, in which plastic strains are set equal to zero on all or part of the boundary.
CRIS-Team Scopus Importer:2022-08-05
Keywords: dissipative model; elastic gap; flow relation; Strain gradient plasticity

Spatiotemporal modeling of first and second wave outbreak dynamics of COVID‐19 in Germany - Lippold, Dorothee; Kergaßner, Andreas; Burkhardt, Christian; Kergaßner, Matthias; Loos, Jonas; Nistler, Sarah; Steinmann, Paul; Budday, Dominik; Budday, Silvia (Biomechanics and Modeling in Mechanobiology, 2021)
The COVID-19 pandemic has kept the world in suspense for the past year. In most federal countries such as Germany, locally varying conditions demand for state- or county-level decisions to adapt to the disease dynamics. However, this requires a deep understanding of the mesoscale outbreak dynamics between microscale agent models and macroscale global models. Here, we use a reparameterized SIQRD network model that accounts for local political decisions to predict the spatiotemporal evolution of the pandemic in Germany at county resolution. Our optimized model reproduces state-wise cumulative infec- tions and deaths as reported by the Robert Koch Institute and predicts the development for individual counties at convincing accuracy during both waves in spring and fall of 2020. We demonstrate the dominating effect of local infection seeds and identify effective measures to attenuate the rapid spread. Our model has great potential to support decision makers on a state and community politics level to individually strategize their best way forward during the months to come.
Keywords: COVID-19 · SIQRD model · Mesoscale outbreak dynamics · Germany

Spinal Cord Neuronal Network Formation in a 3D Printed Reinforced Matrix—A Model System to Study Disease Mechanisms - Fischhaber, Natalie; Faber, Jessica; Bakirci, Ezgi; Dalton, Paul D.; Budday, Silvia; Villmann, Carmen; Schaefer, Natascha (Advanced Healthcare Materials, 2021)
3D cell cultures allow a better mimicry of the biological and mechanical environment of cells in vivo compared to 2D cultures. However, 3D cell cultures have been challenging for ultrasoft tissues such as the brain. The present study uses a microfiber reinforcement approach combining mouse primary spinal cord neurons in Matrigel with melt electrowritten (MEW) frames. Within these 3D constructs, neuronal network development is followed for 21 days in vitro. To evaluate neuronal development in 3D constructs, the maturation of inhibitory glycinergic synapses is analyzed using protein expression, the complex mechanical properties by assessing nonlinearity, conditioning, and stress relaxation, and calcium imaging as readouts. Following adaptation to the 3D matrix-frame, mature inhibitory synapse formation is faster than in 2D demonstrated by a steep increase in glycine receptor expression between days 3 and 10. The 3D expression pattern of marker proteins at the inhibitory synapse and the mechanical properties resemble the situation in native spinal cord tissue. Moreover, 3D spinal cord neuronal networks exhibit intensive neuronal activity after 14 days in culture. The spinal cord cell culture model using ultrasoft matrix reinforced by MEW fibers provides a promising tool to study and understand biomechanical mechanisms in health and diseas

Statistical Analysis of Fatigue Data for Austenitic Stainless Steels in Water Environments - Wilhelm, Paul; Steinmann, Paul; Rudolph, Jürgen (Compacts of the 46th AMNT, 2015)

Statistical interpretation of LDA measurements in naturally developing turbulent drag-reducing flow using invariant theory - Moataz, Mohammad; Reiter, Nina; Al-Mqbas, Mona; Metelkin, Alexander; Latifi, A.; Jovanović, J.; Delgado, Antonio (International Journal of Heat and Fluid Flow, 2022)
Turbulent drag reduction by an extremely diluted aqueous solution of polyacrylamide was studied in a fully developed plane channel flow under non-tripped flow conditions allowing the natural development of turbulence presumably from the initially laminar like a flow state. Using laser-Doppler anemometry, all components of the Reynolds stress tensor were measured. This permitted the determination of the turbulence anisotropy and independent invariants of the anisotropy tensor. Introducing a measure for the departure of the Reynolds stress tensor from the statistically axisymmetric state that ensures laminarity, fundamental insights relating the origin of turbulence and turbulent drag reduction were analyzed in light of the measured results and existing databases of direct numerical simulations. The chief mechanism relevant to the onset of turbulence and turbulent drag reduction deduced from analytic considerations involving only kinematic constraints was confirmed by the experimental data. Parametrization of the drag reduction effect in terms of the Deborah number based on turbulence quantities evaluated at the wall supports the deduction of the polymer-turbulence interaction in terms of the elastic properties of the polymer and the near-wall turbulence structure.
CRIS-Team Scopus Importer:2021-12-17
Keywords: Turbulence measurements; Turbulence modeling; Turbulence simulation; Turbulent drag reduction

Statistical Model of Water Environment Effects on the Fatigue Behavior of Austenitic Stainless Steels - Wilhelm, Paul; Steinmann, Paul; Rudolph, Jürgen (Manuscripts of the 40th MPA Seminar, 2014)

Statistical Models for Estimating Fatigue Lives of Austenitic Stainless Steels in Light Water Reactor Environments - Wilhelm, Paul; Steinmann, Paul; Rudolph, Jürgen (Compacts of the 23th SMiRT Conference, 2015)

Stochastic local FEM for computational homogenization of heterogeneous materials exhibiting large plastic deformations - Pivovarov, Dmytro; Mergheim, Julia; Willner, Kai; Steinmann, Paul (Computational Mechanics, 2021)
Computational homogenization is a powerful tool allowing to obtain homogenized properties of materials on the macroscale from simulations of the underlying microstructure. The response of the microstructure is, however, strongly affected by variations in the microstructure geometry. In particular, we consider heterogeneous materials with randomly distributed non-overlapping inclusions, which radii are also random. In this work we extend the earlier proposed non-deterministic computational homogenization framework to plastic materials, thereby increasing the model versatility and overall realism. We apply novel soft periodic boundary conditions and estimate their effect in case of non-periodic material microstructures. We study macroscopic plasticity signatures like the macroscopic von-Mises stress and make useful conclusions for further constitutive modeling. Simulations demonstrate the effect of the novel boundary conditions, which significantly differ from the standard periodic boundary conditions, and the large influence of parameter variations and hence the importance of the stochastic modeling.
CRIS-Team WoS Importer:2021-11-05

STOKES FLOW INDUCED DRAG AND TORQUE ON ASBESTOS-LIKE FIBRES CANNOT BE ESTIMATED BY A SIMPLISTIC ELLIPSOIDAL APPROXIMATION - Ravnik, Jure; Štrakl, Mitja; Wedel, Jana; Steinmann, Paul; Hriberšek, Matjaž (WIT Transactions on Engineering Sciences, 2022)
In this paper we present an algorithm based on the Boundary Element Method for solving the Stokes flow around an arbitrarily shaped particle in multiphase flows. The objective of the algorithm is to determine the exact drag force and torque experienced by the particle during its motion in a turbulent flow field. The developed method is used to compare the predicted force and torque values on a realistic 3D model of a mineral fibre and its simplifying ellipsoidal approximation. We found that the force and torque values calculated for the real particle geometry differ greatly from the values obtained with the simplifying ellipsoidal approximation. On average, a relative error of less than 10% is achieved for only 10%–30% of the particle orientations.
CRIS-Team Scopus Importer:2022-09-16
Keywords: asbestos; boundary element method; Lagrangian simulation; mineral; multiphase flows; muscovite

Structural optimization of shape and topology using an evolutionary-type advancing front algorithm - Riehl, Stefan; Steinmann, Paul (Conference Proceedings of the YIC GACM 2015, 2015)
UnivIS-Import:2015-10-26:Pub.2015.tech.FT.FT-TM.struct_2

Studies of a geometrical nonlinear friction damped system using NNMs - Jerschl, Martin; Süß, Dominik; Willner, Kai; Jerschl, Martin (34th IMAC, A Conference and Exposition on Structural Dynamics, 2016, 2016)
In the 1960s Rosenberg extended the definition of linear normal modes (LNM) for conservative systems to nonlinear systems: On a Nonlinear Normal Mode (NNM) every degree-of-freedom (DOF) vibrates in unison. Later Shaw and Pierre provided a definition for nonconservative systems and defined NNMs as invariant manifolds in phase space. If the system vibrates on such a manifold all other modes shall remain quiescent for all time. Nowadays there are many publications using the concept of NNMs to investigate systems with polynomial nonlinearities. But until now the upper mentioned definition is mostly used to investigate viscously damped systems. In this paper an oscillator containing a geometrically nonlinear (cubic) spring and a dry friction damper is considered. The system is driven into resonance and decay processes are evaluated. Wavelet analysis is used to identify which frequencies and harmonics remain during the decay process.
Keywords: Friction; Nonlinear coupling; Nonlinear dynamics; Nonlinear normal modes (NNMs); Optimal system design

Studying the mechanical behavior of a generic thermoplastic by means of a fast coarse-grained molecular dynamics model - Dötschel, Vincent; Pfaller, Sebastian; Ries, Maximilian (Polymers and Polymer Composites, 2023)
Polymers play an emerging role in modern engineering applications due to their comparatively low cost, low density, and versatile manufacturing. The addition of nano-sized fillers further enhances the polymer’s properties but also induces a strong dependence on the resulting microstructure, particularly the matrix-filler interphase. Since an experimental characterization of this nano-sized interphase is extremely difficult, molecular dynamics (MD) simulations are used to study the effects at such small scales. However, MD’s high computational costs usually limit the scope of a mechanical characterization. Therefore, this study presents the methodology and tools to generate and analyze samples of an efficient generic thermoplastic model. In this first contribution, we focus on the neat polymer and introduce a versatile and numerically stable self-avoiding random walker with adjustable linearity of chain growth. Moreover, we verify our equilibration procedure by preparing samples in liquid and solid state which behave physically sound. Finally, we perform uniaxial tensile tests with a maximum strain of 10 % to evaluate the mechanical properties. In the liquid case, the polymer chains are sufficiently mobile, such that the tensile stresses fluctuate only around zero, while the solid exhibits an almost linear elastic regime followed by a nonlinear part. This contribution forms the basis for a thorough mechanical characterization of polymer nanocomposites which we will address in future studies. The methodology and tools introduced are not limited to our generic polymer, but applicable to many coarse-grained models.
CRIS-Team Scopus Importer:2023-11-24
Keywords: coarse graining; material modeling; molecular dynamics; self-avoiding random walk; thermoplastics

Study on Electric Motor Vibration Suppression by Active Dynamic Vibration Absorber - Okada, Takeshi; Isobe, Makoto; Kosaka, Takashi; Steinmann, Paul; Matsumori, Hiroaki; Matsui, Nobuyuki (2023 IEEE International Electric Machines and Drives Conference, IEMDC 2023, 2023)
This paper presents a study on an active dynamic vibration absorber (DVA) to reduce the vibration and acoustic noise generated from electric motors for variable speed drives. As a DVA is just additional components, miniaturization and cost reduction are expected by reducing the number of parts and high reliability owing to lifetime prolongation thanks to its jointless structure. In addition, a variable stiffness function can be realized as an active DVA by equipping with an actuator. This study aims to realize the isolation and suppression of the multiple vibration resonances that inherently come from the electric motor being operated over a wide speed range. As a prototype hybrid excitation flux switching motor for automotive traction drive is dealt with as an example of target electric machines, an active DVA is designed sequentially along with the proposed design scheme using FEA and topology optimization. Finally, its usefulness for motor vibration suppression is demonstrated through FEA-based simulation and experiments using DVAs fabricated by 3D printing.
CRIS-Team Scopus Importer:2023-10-06
Keywords: dynamic vibration absorber; hybrid excitation flux switching motor; motor vibration suppression; variable speed drive; variable stiffness

Study on Fatigue Analysis for Operational Load Histories - Wilhelm, Paul; Steinmann, Paul; Rudolph, Jürgen (Manuscripts of the 39th MPA Seminar, 2013)

Surface Deformation due to Shear and Ploughing in a Halfspace - Beyer, Florian; Willner, Kai (Proceedings in Applied Mathematics and Mechanics, 2014)
Sheet and bulk metal forming are widely used manufacturing methods. The interaction between worktool and workpiece in such a process causes friction which has a remarkable impact on the expended energy of the process. Therefore the influence of friction is important. Friction can be split into shearing and ploughing [1]. Ploughing is the plastic deformation of a soft surface by a hard contact partner. Shear forces are only transferred in the real contact area where material contact occurs. The investigation of the contribution of both ploughing and shearing to the total friction resistance is done with the use of an elasto-plastic halfspace model. The multiscale character of surfaces demands a fine discretization, which results in numerical effort. While a finite element method takes into account both surface and bulk of the contact partners, the halfspace model only regards the contact surfaces and thereby consumes less computing capacity. In order to identify the friction resistance, two rough surfaces get into contact. After full application of the normal load, the surfaces are moved relatively to each other. New asperities of the contact surfaces get into contact and are plastically deformed. These deformations are used to estimate the ploughing effect in dependency on the relative displacement. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

Surface electrostatics - Theory and computations - Chatzigeorgiou, Georgios; Javili, Ali; Steinmann, Paul (Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2014)
The objective of this work is to study the electrostatic response of materials accounting for boundary surfaces with their own (electrostatic) constitutive behaviour. The electric response of materials with (electrostatic) energetic boundary surfaces (surfaces that possess material properties and constitutive structures different from those of the bulk) is formulated in a consistent manner using a variational framework. The forces and moments that appear due to bulk and surface electric fields are also expressed in a consistent manner. The theory is accompanied by numerical examples on porous materials using the finite-element method, where the influence of the surface electric permittivity on the electric displacement, the polarization stress and the Maxwell stress is examined.
UnivIS-Import:2015-04-14:Pub.2013.tech.FT.FT-TM.surfac_5

Surface Magnetoelasticity - Chatzigeorgiou, Georgios; Javili, Ali; Steinmann, Paul (Journal of the Mechanics and Physics of Solids, 2013)
UnivIS-Import:2015-04-14:Pub.2013.tech.FT.FT-TM.surfac

Surface magnetoelasticity theory - Chatzigeorgiou, Georgios; Javili, Ali; Steinmann, Paul (Archive of Applied Mechanics, 2015)
The boundary surface of a body behaves differently from its bulk. The elastic response of a boundary surface can be studied by the surface elasticity theory. Furthermore, it has been observed experimentally that the strength and direction of magnetization are markedly different between the boundary surface and the bulk. While the surface elasticity theory is well established today to study the mechanical behavior of nanomaterials, a theory to model boundary surface magnetic behavior is missing. The objective of this presentation was to study, from a phenomenological point of view, the magnetomechanical response of materials accounting for boundary surfaces contributions. To do so, the boundary surface of a body is endowed with its own mechanical and magnetic constitutive behavior in the spirit of the surface elasticity theory. The magnetomechanical response of materials is formulated in a thermodynamically consistent manner using both a variational framework and the governing equations of magnetomechanics, namely the Maxwell laws, the balance of linear and angular momentum, the balance of energy and the (in-)balance of entropy. Conceptually speaking, this contribution can be understood as an extension of the surface elasticity theory to the more general case of magnetoelasticity that, however, involves certain additional complexities due to the presence of a surface curl operator, which is not standard.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Magnetoelasticity; Magnetomechanics; Surface elasticity; Surface magnetism

Surface Models for Contact Laws - Willner, Kai (Computational Methods in Contact Mechanics V, 2001)
Contact laws for rough surfaces are used to obtain, e.g., contact stiffness or contact conductivity. Usually contact laws are derived on the basis of asperity deformation models in conjunction with a stochastic roughness model. As the stochastic parameters depend strongly on the measurement procedure, the obtained contact laws have to be used carefully. Fractal surface parameters can be obtained, which are independent of sampling interval or length, but the resulting contact laws are still dependent on these values.
UnivIS-Import:2015-04-16:Pub.2001.tech.FT.FT-TM.surfac

Surface plasticity: theory and computation - Esmaeili, Ali; Steinmann, Paul; Javili, Ali (Computational Mechanics, 2017)

Surface-Stiffened Halfspace Under the Action of a Horizontally Directed Mindlin Force - Willner, Kai; Selvadurai, A.P.S. (International Journal of Mechanical Sciences, 2006)
This paper presents an analytical solution to the problem of the interaction between a thin plate that is adhesively bonded to the surface of an isotropic elastic halfspace and a concentrated Mindlin-type force that acts parallel to the bonded surface. The model is an idealization of a surface-stiffened region that has potential applications ranging from mechanics of thin films, thermal barrier coatings, layering created by attrition and wear of surfaces and functionally graded materials. The solution also illustrates the influence of the flexural plate model in mitigating the development of unbounded displacements during the application of localized loading directly at the bonded plate. © 2006 Elsevier Ltd. All rights reserved.
UnivIS-Import:2015-03-09:Pub.2006.tech.FT.FT-TM.surfac_1
Keywords: Adhesively bonded plate; Cerruti's problem; Functionally graded solid; Internal loading of halfspace; Mechanics of thin films; Thermal barrier coatings

SURROGATE MODELING CONSIDERING MEASURING DATA AND THEIR MEASUREMENT UNCERTAINTY - Oberleiter, Thomas; Müller, Andreas; Hausotte, Tino; Willner, Kai (Uncecomp 2019 Proceedings, 2019)
Virtual approaches to manufacturing processes are a common tool in developing components today. Simulations are always containing uncertainties like simplifying assumptions in computer aided modelling, material deviations, fluctuating external loads or other known and unknown influences. To integrate such uncertainties in an early design stage, the input parameters should be defined as intervals, because insufficient data may be available at this stage to provide probability distributions. To consider such epistemic uncertainties, a large number of intervals can be merged into a fuzzy number. For each interval a membership value is assigned which depends on the interval limits and an expert estimation. However, this interval modelling leads to a very high number of expensive evaluations, which is not feasible for a high number of uncertain input parameters. To reduce the calculation time, surrogate models are used. Here, the full model is evaluated only at some grid points and the system response is approximated by mathematical approaches. Design and Analysis of Computer Experiments (DACE) offers a suitable surrogate model based on the Kriging method. The system model substituted in this way can be evaluated in an efficient way, but in addition to the uncertain simulation results, the approximation error dependent on the surrogate model has to be considered. Investigations of first prototypes lead to new knowledge that can be used to improve the surrogate model. Measurements, however, also include errors that are composed of systematic and random errors. The systematic measurement errors are specific errors for each measuring system and task, which are usually corrected during the measurement. However, an estimation of the random measurement error, which represents the precision of the measurement can be taken into account. Two methods are presented. Either an additional constant term is implemented in the standard Kriging or a superposition of two standard Kriging models, which are based on the simulation data and the measurement data, is used. As an application example a cold forging process of a steel gearwheel is employe
Keywords: Kriging; Measuring Data; Measuring Uncertainty; Surrogate Modeling

Symmetry Breaking in Wrinkling Patterns: Gyri Are Universally Thicker than Sulci - Holland, Maria; Goriely, Alain; Budday, Silvia; Kuhl, Ellen (Physical Review Letters, 2018)
Wrinkling instabilities appear in soft materials when a flat elastic layer on an elastic substrate is sufficiently stressed that it buckles with a wavy pattern to minimize the energy of the system. This instability is known to play an important role in engineering, but it also appears in many biological systems. In these systems, the stresses responsible for the wrinkling instability are often created through differential growth of the two layers. Beyond the instability, the upper and lower sides of the elastic layer are subject to different forces. This difference in forces leads to an interesting symmetry breaking whereby the thickness becomes larger at ridges than at valleys. Here we carry out an extensive analysis of this phenomenon by combining analytical, computational, and simple polymer experiments to show that symmetry breaking is a generic property of such systems. We apply our idea to the cortical folding of the brain for which it has been known for over a century that there is a thickness difference between gyri and sulci. An extensive analysis of hundreds of human brains reveals a systematic region-dependent thickness variation. Our results suggest that the evolving thickness patterns during brain development, similar to our polymer experiments, follow simple physics-based laws: Gyri are universally thicker than sulci.

Systematic study of homogenization and the utility of circular simplified representative volume element - Firooz, Soheil; Saeb, Saba; Chatzigeorgiou, George; Meraghni, Fodil; Steinmann, Paul; Javili, Ali (Mathematics and Mechanics of Solids, 2019)
Although both computational and analytical homogenization are well-established today, a thorough and systematic study to compare them is missing in the literature. This manuscript aims to provide an exhaustive comparison of numerical computations and analytical estimates, such as Voigt, Reuss, Hashin–Shtrikman, and composite cylinder assemblage. The numerical computations are associated with canonical boundary conditions imposed on either tetragonal, hexagonal, or circular representative volume elements using the finite-element method. The circular representative volume element is employed to capture an effective isotropic material response suitable for comparison with associated analytical estimates. The analytical results from composite cylinder assemblage are in excellent agreement with the numerical results obtained from a circular representative volume element. We observe that the circular representative volume element renders identical responses for both linear displacement and periodic boundary conditions. In addition, the behaviors of periodic and random microstructures with different inclusion distributions are examined under various boundary conditions. Strikingly, for some specific microstructures, the effective shear modulus does not lie within the Hashin–Shtrikman bounds. Finally, numerical simulations are carried out at finite deformations to compare different representative volume element types in the nonlinear regime. Unlike other canonical boundary conditions, the uniform traction boundary conditions result in nearly identical effective responses for all types of representative volume element, indicating that they are less sensitive with respect to the underlying microstructure. The numerical examples furnish adequate information to serve as benchmarks.
CRIS-Team Scopus Importer:2019-06-04
Keywords: circular representative volume element; composite cylinder assemblage; composites; Hashin–Shtrikman bounds; hexagonal representative volume element; Homogenization

Temperature-dependent vibration energy harvesting performance of polyimide/(Na,K)NbO3 piezoelectric composites - Yamamoto, Ryota; Hegendörfer, Andreas; Mergheim, Julia; Kakimoto, Ken-Ichi (Japanese Journal of Applied Physics, 2022)
A composite structure of piezoelectric particles and soft polymer composite material is one of the candidates that converts environmental vibration energy into electrical energy. Presently, expanding the usage of applications is needed in terms of the working environment at harsh temperatures. Polyimide is flexible and temperature-stable polymer. In this research, we report a synthesis of polyimide/(Na,K)NbO3 (PI/NKN) flexible composites. We constructed a setup, where vibration and heat are simultaneously applied to the PI/NKN composites. The frequency and temperature dependence of the output voltage were investigated at room temperature up to 200 °C. Relative permittivity, piezoelectric constant, and output voltage of the PI/NKN showed temperature stability. Flexibility and glass transition temperature of a polymer matrix are important factors. PI/NKN composites are potential energy harvesting materials with flexibility and excellent high-temperature stability.
Created from Fastlane, Scopus look-up
Keywords: piezoelectric; polymer/ceramic composite; thermal stability; vibration energy harvesting

Temperature distribution and entropy generation during Darcy–Forchheimer–Brinkman electrokinetic flow in a microfluidic tube subject to a prescribed heat flux - Misra, J. C.; Mallick, B.; Steinmann, Paul (Meccanica, 2020)
Electrokinetically modulated flow through a hydrophobic microtube embedded in a Darcy–Forchheimer porous medium is investigated in this paper. The steric effect has been taken into account in the electrical double layer (EDL) region. Heat transfer is analysed in the case of Darcy–Forchheimer–Brinkman flow subject to Joule heating. The flow is supposed to take place under the combined influence of electroosmosis and imposed pressure gradient. The governing nonlinear partial differential equations for electric potential, fluid flow and heat transfer are solved numerically by developing an iterative finite difference method that has second order accuracy. The thermal efficiency is discussed under the purview of the second law of thermodynamics. Influences/impact of different physical parameters on velocity, temperature and entropy are investigated and demonstrated graphically. The paper shows that with an increase in the steric effect, the electrokinetic velocity diminishes and that thermal irreversibility is very high in the electrical double layer region, but it reduces drastically in the neighbourhood of the central region of the microtube. Results of the study are likely to be of profuse interest in the design and development of microfluidic devices that deal with critical types of fluid transport mechanism in non-Darcian porous media.
CRIS-Team Scopus Importer:2020-04-17
Keywords: Entropy generation; Finite difference method; Non-Darcy porous medium; Steric effect; Uniform heat flux

Testing, modelling, and parameter identification for adhesively bonded joints under the influence of temperature - Schmelzle, Lars; Striewe, Marius; Mergheim, Julia; Meschut, Gerson; Possart, Gunnar; Teutenberg, Dominik; Hein, David; Steinmann, Paul (Journal of Adhesion Science and Technology, 2022)
Epoxy resin adhesives are widely used in lightweight and structural applications and their mechanical properties are strongly temperature-dependent. In this study, shear and butt joint specimens are tested under quasi-static loading within a temperature interval from −40 to 80 °C to determine the influence of temperature on the mechanical properties of adhesively bonded joints. In addition to the experimental studies, the highly nonlinear inelastic Toughened Adhesive Polymer (TAPO) material model is extended by defining the model parameters as functions of temperature. The experimental results are then used to parameterize the extended model such that it can be used in Finite Element simulations. The main results are: For both load cases the yield stresses as well as the maximum stresses reach their maxima at the lowest temperature and decrease continuously with increasing temperature. The critical strain at maximum stress and also the failure strain increase with rising temperature. The energy absorption is generally higher under shear load than under tensile load. Due to interactions between parameters of the TAPO model which can lead to ambiguous solutions, the identification of temperature functions for the parameters is a challenge. The isolation of interacting parameters as well as the introduction of dependencies are used to effectively limit such interactions. The measures taken lead to a multistep procedure of alternating parameter identification and fitting of temperature functions. Simulations with the calibrated extended TAPO model show very good agreement with the experimental data for all temperatures.<br

The Capriccio Method: An Arlequin‐Based Approach to Couple Molecular Dynamics and Finite Element Simulations of Polymers - Pfaller, Sebastian; Steinmann, Paul (GDR Polynano 3661 - Scientific Workshop on multiscale modeling, experimental characterization and simulations of nanocomposites, 2015)

The Capriccio method: a scale bridging approach for polymers extended towards inelasticity - Zhao, Wuyang; Pfaller, Sebastian (Proceedings in Applied Mathematics and Mechanics, 2021)
In this contribution we present an extension of the multiscale Capriccio method towards inelasticity. This enables coupled simulations of a particle domain embedded into a continuum with particular focus on polymer systems. Starting from the method's initial implementation of pure elasticity, we substitute the nonlinear elastic continuum constitutive law by a recently developed viscoelastic‐viscoplastic one which is able to capture the mechanical behaviour of the particle system in a much larger strain range. Furthermore, we discuss numerical aspects like the choice of time steps and iteration numbers.<br

The computational framework for continuum-kinematics-inspired peridynamics - Javili, A.; Firooz, S.; McBride, A. T.; Steinmann, Paul (Computational Mechanics, 2020)
Peridynamics (PD) is a non-local continuum formulation. The original version of PD was restricted to bond-based interactions. Bond-based PD is geometrically exact and its kinematics are similar to classical continuum mechanics (CCM). However, it cannot capture the Poisson effect correctly. This shortcoming was addressed via state-based PD, but the kinematics are not accurately preserved. Continuum-kinematics-inspired peridynamics (CPD) provides a geometrically exact framework whose underlying kinematics coincide with that of CCM and captures the Poisson effect correctly. In CPD, one distinguishes between one-, two- and three-neighbour interactions. One-neighbour interactions are equivalent to the bond-based interactions of the original PD formalism. However, two- and three-neighbour interactions are fundamentally different from state-based interactions as the basic elements of continuum kinematics are preserved precisely. The objective of this contribution is to elaborate on computational aspects of CPD and present detailed derivations that are essential for its implementation. Key features of the resulting computational CPD are elucidated via a series of numerical examples. These include three-dimensional problems at large deformations. The proposed strategy is robust and the quadratic rate of convergence associated with the Newton–Raphson scheme is observed.
CRIS-Team Scopus Importer:2020-08-07
Keywords: Computational implementation; Continuum kinematics; Peridynamics

The deal.II code gallery: Quasi-Static Finite-Strain Compressible Elasticity - Pelteret, Jean-Paul; McBride, Andrew (2016)
Classical quasi-static finite-strain elasticity solving the Cook membrane problem composed of a compressible Neo-Hookean material.
Keywords: Finite elements; Finite strain nonlinear elasticity

The deal.II code gallery: Quasi-static Finite-Strain Quasi-incompressible Visco-elasticity - Pelteret, Jean-Paul (2017)
Quasi-static finite-strain quasi-incompressible rate-dependent elasticity computing the displacement history of a thin viscoelastic strip with a hole.
Keywords: Finite elements; Finite strain nonlinear visco-elasticity; Quasi-incompressibility; Mixed methods

The deal.II Library, Version 9.1 - Arndt, Daniel; Bangerth, Wolfgang; Clevenger, Thomas C.; Davydov, Denis; Fehling, Marc; Garcia-Sanchez, Daniel; Harper, Graham; Heister, Timo; Heltai, Luca; Kronbichler, Martin; Maguire Kynch, Ross; Maier, Matthias; et al. (Journal of Numerical Mathematics, 2019)
This paper provides an overview of the new features of the finite element library deal.II, version 9.1.
CRIS-Team Scopus Importer:2019-07-19

The Effect of Heat Treatments at Different Plastic States on the Isotropic Hardening Behavior of Austenitic Stainless Steel - Wilhelm, Paul; Steinmann, Paul; Rudolph, Jürgen (Compacts of the 47th AMNT, 2016)

The Gaul resonator: Experiments for the isolated investigation of a bolted lap joint - Süß, Dominik; Janeba, Anton; Willner, Kai (Springer International Publishing, 2017)
CRIS-Team Scopus Importer:2022-08-05

The Hybrid Capriccio Method: A 1D Study for Further Advancement - Ries, Maximilian; Steinmann, Paul; Pfaller, Sebastian (Multiscale and Multiphysics Systems, 2021, 2021)
Polymers and, in particular, polymer composites are known for the enormous adjustability of their mechanical, chemical, and thermal behavior. Multiscale methods are increasingly employed to unravel the polymer microstructure's impact on the material properties. These methods combine the accuracy of particle-based techniques with the efficiency of continuum mechanical approaches. Amorphous polymers pose a special challenge since their microstructure does not continue periodically, and therefore special attention needs to be paid to the particle domain boundary. In this study, we introduce a coupling via an interface between the continuum and the particle domain. Padding atoms as particle representations of the continuum, which serve as interaction partners for the atoms in the particle region, allow for the transfer of displacements and forces between the domains. We present a straightforward 1D example with simple interactions, evaluate the scheme's performance, discuss the resulting energy contributions, and identify an optimal set of coupling parameters. Eventually, this forms the basis for future 3D implementations. <br
Keywords: Particle-continuum coupling; Domain decomposition; Multiscale-modeling

The influence of the orthotropic tissue in an electromechanical heart model - Holz, David; Martonová, Denisa; Schaller, Emely; Duong, Minh Tuan; Alkassar, Muhannad; Leyendecker, Sigrid (conference, 27th Congress of the European Society of Biomechanics, 2022)

The mechanical importance of myelination in the central nervous system - Weickenmeier, Johannes; de Rooij, Rijk; Budday, Silvia; Ovaert, Timothy; Kuhl, Ellen (Journal of the Mechanical Behavior of Biomedical Materials, 2017)
Neurons in the central nervous system are surrounded and cross-linked by myelin, a fatty white substance that wraps around axons to create an electrically insulating layer. The electrical function of myelin is widely recognized; yet, its mechanical importance remains underestimated. Here we combined nanoindentation testing and histological staining to correlate brain stiffness to the degree of myelination in immature, pre-natal brains and mature, post-natal brains. We found that both gray and white matter tissue stiffened significantly (p ≪ 0.001) upon maturation: the gray matter stiffness doubled from 0.31 ± 0.20 kPa pre-natally to 0.68 ± 0.20 kPa post-natally; the white matter stiffness tripled from 0.45 ± 0.18 kPa pre-natally to 1.33±0.64kPa post-natally. At the same time, the white matter myelin content increased significantly (p ≪ 0.001) from 58 ± 2% to 74 ± 9%. White matter stiffness and myelin content were correlated with a Pearson correlation coefficient of ρ=0.92 (p ≪ 0.001). Our study suggests that myelin is not only important to ensure smooth electrical signal propagation in neurons, but also to protect neurons against physical forces and provide a strong microstructural network that stiffens the white matter tissue as a whole. Our results suggest that brain tissue stiffness could serve as a biomarker for multiple sclerosis and other forms of demyelinating disorders. Understanding how tissue maturation translates into changes in mechanical properties and knowing the precise brain stiffness at different stages of life has important medical implications in development, aging, and neurodegeneration.
Keywords: Brain; Stiffness; Indentation; White matter; Myelin; Myelination

The modal behaviour of a violin corpus - Akar, Özge; Willner, Kai (Journal of New Music Research, 2024)
Violins incorporate numerous interfaces and anisotropic behaviour due to natural materials. Hence, the modelling of these instruments is extremely complex. The present work investigates the structural dynamics of a specific violin corpus (violin resonant body) with the aim of using numerical modelling to accurately understand the modal behaviour of the violin using a novel stepwise approach. In the first step, an inverse material parameter identification via experimental and numerical modal analysis of the raw woods is performed to obtain the material parameters of the individual woods. In the second step, an experimental modal analysis of the violin substructures is performed using 2D scanning laser Doppler vibrometry and building finite element models based on accurate 3D scans of the parts manufactured by a luthier. The experimentally obtained modal parameters of the individual parts are compared with the numerical results. In the third step, the whole violin corpus, i.e. the resonant body of the instrument, is assessed. The good agreement between the numerical and the experimental results demonstrates that the application of standard techniques of modal analysis on a very complex mechanical system, the violin body, is possible. Our methodology offers a novel approach to analysing individual components of bowed string instruments, facilitating a comprehensive vibrational analysis with implications for broader musical research, including luthier optimisation tools, digital reconstruction of historical violins, and advancements in instrument design for improved playability and tonal quality.
CRIS-Team Scopus Importer:2024-03-15
Keywords: Digital twin; Finite elements; Laser-Doppler vibrometry; Modal analysis; Violin

The modelling of carrier-wall collision with drug particle detachment for dry powder inhaler applications - Cui, Yan; Sommerfeld, Martin (Powder Technology, 2019)
The paper proposes a novel particle-wall collision model for calculating temporal changes of particle velocities and forces acting on the particle during the collision between an elastic particle and a plane solid wall. The purpose is to determine the maximum inertia force acting on the particle in connection with an accurate prediction of the transition between the sliding and non-sliding periods. This method is successfully applied to the calculation of drug detachment probability via particle-wall collisions within dry powder inhalers, in which fine drug particles are usually blended with larger carrier particles as one particle cluster for better dispersion. The present novel model is firstly verified in the micro-scale simulation of a single collision between the particle cluster and the wall. The simulation results reveal that the inertia force acting on drug particles is much larger than the fluid dynamic force and dominates the drug detachment. The detachment can occur through lift-off, sliding or rolling. Nearly half of the drug particles on the carrier surface can be detached by lift-off, and most of the remaining drug particles follow up with a sliding or rolling detachment. Based on these studies, a Lagrangian particle tracking algorithm is developed and is used to predict drug detachment probability within an inhaler device through one inhalation. By tracking 1024 particle clusters moving through the inhaler (i.e. the macro-scale simulation), the influence of different flow rates (i.e. 100 l/min and 70 l/min), friction coefficients between the carrier and the wall (i.e. 0.1 and 0.2), and carrier sizes (i.e. 100 μm and 500 μm) on drug detachment are investigated. The improved understanding of particle-wall collision detachment study will be the basis for optimising inhaler design.<br
Keywords: Dry powder inhaler; Inertia force; Collision detachment model; Drug detachment probability; Particle-wall collision

The origin of compression influences geometric instabilities in bilayers - Andres, Sebastian; Steinmann, Paul; Budday, Silvia (Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 2018)
Geometric instabilities in bilayered structures control the surface morphology in a wide range of biological and technical systems. Depending on the application, different mechanisms induce compressive stresses in the bilayer. However, the impact of the chosen origin of compression on the critical conditions, post-buckling evolution and higher-order pattern selection remains insufficiently understood. Here, we conduct a numerical study on a finite element setup and systematically vary well-known factors contributing to pattern selection under the four main origins of compression: film growth, substrate shrinkage and whole-domain compression with and without pre-stretch. We find that the origin of compression determines the substrate stretch state at the primary instability point and thus significantly affects the critical buckling conditions. Similarly, it leads to different post-buckling evolutions and secondary instability patterns when the load further increases. Our results emphasize that future phase diagrams of geometric instabilities should incorporate not only the film thickness but also the origin of compression. Thoroughly understanding the influence of the origin of compression on geometric instabilities is crucial to solve real-life problems such as the engineering of smart surfaces or the diagnosis of neuronal disorders, which typically involve temporally or spatially combined origins of compressio
Keywords: Thin films; Bilayered systems; Instabilities; Post-wrinkling; Bifurcations; Soft matter

Thermal modelling of selective beam melting processes using heterogeneous time step sizes - Soldner, Dominic; Mergheim, Julia (Computers & Mathematics with Applications, 2019)
In the context of powder bed-based additive manufacturing, complex part geometries are realised in a layer-by-layer fashion and by the fusion of powdered material in locally defined regions by means of e.g. a laser or electron beam. Simulating these manufacturing processes from a macroscopic point of view may lead to computationally expensive models, due to different scales in space and time, highly non-linear material behaviour and methods to account for the layer-wise build, i.e. dynamic growth of the computational domain. Aiming towards a reduction of the computational cost multiple numerical methods are therefore combined.
CRIS-Team WoS Importer:2019-10-15

Thermal modelling of selective beam melting processes using heterogeneous time step sizes - Soldner, Dominic; Steinmann, Paul; Mergheim, Julia (Simulation for Additive Manufacturing 2017, Sinam 2017, 2017)
CRIS-Team Scopus Importer:2022-08-05
Keywords: Multi-scale methods; Process simulation; Thermal modelling

Thermodynamically Consistent Model to Predict the Magneto-Rheological Behavior of Magneto-Sensitive Elastomers - Saxena, Prashant; Walter, Bastian; Kaschta, Joachim; Fey, Tobias; Steinmann, Paul; Schubert, Dirk W. (9th Annual European Rheology Conference, 2014)

Thermodynamic formulation of a unified multi-mechanism continuum viscoplastic damage model with application to high-Cr steels - Cai, Xiaodan; Steinmann, Paul; Yao, Xiaohu; Wang, Jiong (International Journal of Plasticity, 2019)
In this paper, a unified multi-mechanism continuum viscoplastic damage model is proposed to simulate the thermomechanical behavior of high-Cr steels at elevated temperatures. To represent the effects of material degradation under external loads, a total damage tensor is incorporated, which is composed of the low-cycle fatigue damage, the creep damage and the ductile damage. Within the small strain framework, the model is established through a thermodynamically consistent approach. First, some kinematic assumptions are proposed and the concept of effective stress is adopted. Then, based on a state potential with proper constitutive form, the constitutive equations can be derived from the second law of thermodynamics. By further considering the postulate of maximum dissipation, a Lagrangian functional is constructed through a regularization scheme. The stationary points of the Lagrangian functional yield the evolution equations of the dissipative variables. For the isotropic damage case, the damage tensor can be represented by a scalar damage variable and the constitutive evolution equations in the model can be simplified. To be prepared for practical applications, numerical integration algorithms are proposed to solve the constitutive evolution equations, and the material parameters in the model are identified based on the experimental data. To demonstrate the efficiency of the current model, it is applied to simulate the thermomechanical response of high-Cr steels under different loading conditions. The simulation results can fit the experimental data at a quantitative level and the damage mechanisms under the different loading conditions can be revealed. Besides that, the model is further modified to take into account the microcracks closure effect of the ductile damage. The current model would be helpful for the safety design and lifetime evaluation of high-Cr steel components in practical applications.
CRIS-Team WoS Importer:2019-03-20

Thermo-elastic deformations of the workpiece when dry turning aluminum alloys - A finite element model to predict thermal effects in the workpiece - Schindler, Stefan; Zimmermann, Marco; Aurich, Jan C.; Steinmann, Paul (CIRP Journal of Manufacturing Science and Technology, 2014)
The workpiece is subjected to severe thermal loads when turning. These loads deforming the workpiece lead to a deviation between the actual and the nominal depth of cut. The accuracy of machining is thereby decreased. This paper presents a finite element technique to determine such thermal loads and deformations with regard to the cutting condition used and the actual tool position. The turning process can therefore be virtually optimized prior to actual turning in order to decrease thermally induced deformation of the workpiece. © 2014 CIRP.
UnivIS-Import:2015-03-09:Pub.2014.tech.FT.FT-TM.thermo
Keywords: Cutting condition; Finite element simulation; Machining accuracy; Thermo-elastic deformation

Thermomechanical coupling in glassy polymers: An effective temperature theory - Xiao, Rui; Tian, Chuanshuai; Xu, Yangguang; Steinmann, Paul (International Journal of Plasticity, 2022)
Glassy polymers exhibit a strong thermomechanical coupling when subjected to mechanical loading. A homogeneous strain distribution can be achieved in uniaxial compression conditions. However, a clear temperature increase is observed when the loading rate is relatively high, which further results in a decrease in stress due to thermal softening. In tensile tests, necking instability can easily occur. A temperature change is accompanied by the nucleation and propagation of necked regions. In this work, we apply the effective temperature theory, which can capture the nonequilibrium structure evolution of amorphous polymers, to investigate the thermomechanical behavior of glassy polymers. We demonstrate that a finite element model based on the effective temperature theory can well capture the stress response and the temper-ature increase of polycarbonate (PC) compressed at different loading rates. We further combine experiments and simulations to investigate the effects of the loading rate and aging treatment on the necking behavior in amorphous glassy polymer poly(ethylene terephthalate)-glycol (PETG) in uniaxial tension loading tests. Through employing digital image correlation and infrared thermometry, the strain distribution and the temperature field can be fully characterized during the formation and propagation of necked regions. The model captures all important features of localization behavior observed in experiments, including the force-displacement relationship, and the strain and temperature distribution with necking propagation. However, it underestimates the maximum strain and temperature when the displacement is large. Both experimental and simulative results indicate that increasing loading rate and aging time can induce an increase of the intrinsic strain softening due to a more active structural state caused by mechanical rejuvenation. This further leads to more pronounced localized behavior and a ductile-brittle transition. Our work proves that the effective temperature model is a powerful theoretical framework to predict the complex thermomechanical response of glassy polymers.
CRIS-Team WoS Importer:2022-07-29

Thermomechanical finite element simulations of selective electron beam melting processes: Performance considerations - Riedlbauer, Daniel-Rouven; Steinmann, Paul; Mergheim, Julia (Computational Mechanics, 2014)
The present contribution is concerned with the macroscopic modelling of the selective electron beam melting process by using the finite element method. The modelling and simulation of the selective electron beam melting process involves various challenges: complex material behaviour, phase changes, thermomechanical coupling, high temperature gradients, different time and length scales etc. The present contribution focuses on performance considerations of solution approaches for thermomechanically coupled problems, i.e. the monolithic and the adiabatic split approach. The material model is restricted to nonlinear thermoelasticity with temperature-dependent material parameters. As a numerical example a straight scanning path is simulated, the predicted temperatures and stresses are analysed and the performance of the two algorithms is compared. The adiabatic split approach turned out to be much more efficient for linear thermomechanical problems, i.e. the solution time is three times less than with the monolithic approach. For nonlinear problems, stability issues necessitated the use of the Euler backward integration scheme, and therefore, the adiabatic split approach required small time steps for reasonable accuracy. Thus, for nonlinear problems and in combination with the Euler backward integration scheme, the monolithic solver turned out to be more efficient. © 2014 Springer-Verlag Berlin Heidelberg.
UnivIS-Import:2015-03-09:Pub.2014.tech.FT.FT-TM.thermo_9
Keywords: Adaptivity; Adiabatic split approach; performance; Process simulation; Selective electron beam melting; Thermoelasticity

Thermomechanical Simulation of the Electron Beam Melting Process for TiAl6V4 - Riedlbauer, Daniel-Rouven; Mergheim, Julia; Steinmann, Paul (Proceedings in Applied Mathematics and Mechanics, 2014)
In the present contribution a nonlinear thermomechanical finite element model with temperature dependent material parameters is used to simulate the electron beam melting process for TiAl6V4. The beam is modeled as a moving heat source and the isentropic split solution scheme is applied. The temperature and stress distribution during the process were simulated and showed sound results from a qualitative point of view. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)
UnivIS-Import:2015-04-16:Pub.2014.tech.FT.FT-TM.thermo_6

Thermomechanical simulation of the selective laser melting process for PA12 including volumetric shrinkage - Riedlbauer, Daniel-Rouven; Steinmann, Paul; Mergheim, Julia (PROCEEDINGS OF PPS-30, 2015)
The present contribution is concerned with the finite element simulation of the thermomechanical material behavior in the selective laser melting process for PA12. In the process shrinkage of the powder material is observed when becoming melt, as the porous character of the powder vanishes due to the phase transition. A nonlinear thermomechanical finite element model is developed, which captures the shrinkage of the material and includes temperature dependent material parameters. The model is used to simulate the shrinkage of the material in the process, where an adaptive mesh refinement is applied for increasing the accuracy of the simulation. The results are qualitatively compared with experimental data and show a good agreemen
UnivIS-Import:2015-07-08:Pub.2015.tech.FT.FT-TM.thermo

Thermo-mechanical simulations of powder bed fusion processes: accuracy and efficiency - Burkhardt, Christian; Steinmann, Paul; Mergheim, Julia (Advanced Modeling and Simulation in Engineering Sciences, 2022)
In this contribution, the accuracy and efficiency of various modeling assumptions and numerical settings in thermo-mechanical simulations of powder bed fusion (PBF) processes are analyzed. Thermo-mechanical simulations are used to develop a better understanding of the process and to determine residual stresses and distortions based on the temperature history. In these numerically very complex simulations, modeling assumptions are often made that reduce computational effort but lead to inaccuracies. These assumptions include the omission of the surrounding powder or the use of geometrically linearized material models. The numerical setting, in particular the temporal and spatial discretizations, can further lead to discretization errors. Here, a highly parallelized and adaptive finite element method based on the open source C++ library deal.II is validated and utilized, to investigate some of these modeling assumptions and to identify the required temporal and spatial discretizations for the simulation of PBF of Ti-6Al-4V. The insights initially gained on a simple wall-like geometry are transferred to a larger open rectangular profile where the results of a detailed simulation are compared with those of a more efficient one. The results for the efficient approach show a maximum deviation of ≈8%" role="presentation">≈8% in the displacements and ≈3.5%" role="presentation">≈3.5% in the residual stresses while significantly reducing the computational tim

Thermomechanics of solids with general imperfect coherent interfaces - Käßmair, Stefan; Javili, Ali; Steinmann, Paul (Archive of Applied Mechanics, 2014)
The objective of this contribution is to develop a thermodynamically consistent theory for general imperfect coherent interfaces in view of their thermomechanical behavior and to establish a unified computational framework to model all classes of such interfaces using the finite element method. Conventionally, imperfect interfaces with respect to their thermal behavior are often restricted to being either highly conducting (HC) or lowly conducting (LC) also known as Kapitza. The interface model here is general imperfect in the sense that it allows for a jump of the temperature as well as for a jump of the normal heat flux across the interface. Clearly, in extreme cases, the current model simplifies to HC and LC interfaces. A new characteristic of the general imperfect interface is that the interface temperature is an independent degree of freedom and, in general, is not a function of only temperatures across the interface. The interface temperature, however, must be computed using a new interface material parameter, i.e., the sensitivity. It is shown that according to the second law, the interface temperature may not necessarily be the average of (or even between) the temperatures across the interface. In particular, even if the temperature jump at the interface vanishes, the interface temperature may be different from the temperatures across the interface. This finding allows for a better, and somewhat novel, understanding of HC interfaces. That is, a HC interface implies, but is not implied by, the vanishing temperature jump across the interface. The problem is formulated such that all types of interfaces are derived from a general imperfect interface model, and therefore, we establish a unified finite element framework to model all classes of interfaces for general transient problems. Full details of the novel numerical scheme are provided. Key features of the problem are then elucidated via a series of three-dimensional numerical examples. Finally, we recall since the influence of interfaces on the overall response of a body increases as the scale of the problem decreases, this contribution has certain applications to nano-composites and also thermal interface materials.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Finite element method; General imperfect interface; Generalized Young-Laplace; Highly conducting; Kapitza; Lowly conducting; Nano-materials; Thermal interface materials

Thermomechanics of Solids with Lower-Dimensional Energetics: On the Importance of Surface, Interface and Curve Structures at the Nanoscale. A Unifying Review - Javili, Ali; McBride, Andrew; Steinmann, Paul (Applied Mechanics Reviews, 2012)
Surfaces and interfaces can significantly influence the overall response of a solid body. Their behavior is well described by continuum theories that endow the surface and interface with their own energetic structures. Such theories are becoming increasingly important when modeling the response of structures at the nanoscale. The objectives of this review are as follows. The first is to summarize the key contributions in the literature. The second is to unify a select subset of these contributions using a systematic and thermodynamically consistent procedure to derive the governing equations. Contributions from the bulk and the lower-dimensional surface, interface, and curve are accounted for. The governing equations describe the fully nonlinear response (geometric and material). Expressions for the energy and entropy flux vectors, and the admissible constraints on the temperature field, all subject to the restriction of non-negative dissipation, are explored. A particular emphasis is placed on the structure of these relations at the interface. A weak formulation of the governing equations is then presented that serves as the basis for their approximation using the finite element method. Various forms for a Helmholtz energy that describes the fully coupled thermomechanical response of the system are given. They include the contribution from surface tension. The vast majority of the literature on surface elasticity is framed in the infinitesimal deformation setting. The finite deformation stress measures are, thus, linearized and the structure of the resulting stresses discussed. The final objective is to elucidate the theory using a series of numerical example problems.
UnivIS-Import:2015-03-09:Pub.2012.tech.FT.FT-TM.thermo_8

The Role of Mechanics during Brain Development - Budday, Silvia (Friedrich-Alexander-Universität Erlangen-Nürnberg, 2018)
The characteristically folded surface morphology is a classical hallmark of the mammalian brain. During development, the initially smooth surface evolves into an elaborately convoluted pattern, which closely correlates with brain function. The surface pattern serves as a clinical indicator for physiological and pathological conditions. Despite its importance, however, the regulators of brain folding in evolution and development remain poorly understood. Recent evidence suggests that physical forces play an important role in pattern selection. This work combines analytical, computational, and experimental analyses to explore the role of mechanics during brain development. After thouroughly characterizing the time-independent and time-dependent, region-specific mechanical response of brain tissue under multiple loading conditions, a mechanical model of brain growth is established using the nonlinear field theories of continuum mechanics, supplemented by the theory of finite growth. The model consists of a morphogenetically growing outer cortex and a stretch-induced growing inner core, and thus combines the two popular but competing hypotheses that cortical folding is either driven by axonal tension or differential growth. Analytical analyses quantify the critical conditions at the onset of folding, and computational analyses additionally predict the highly nonlinear post-buckling behavior. They allow us to carefully investigate both growth-induced primary and secondary instabilities and to provide new evidence towards the emergence of advanced, higher order wrinkling modes. The analytical and computational predictions are experimentally validated using a model system comprised of an elastomeric bilayer. Taken together, the current work emphasizes that the key regulators of pattern selection in the developing brain include cortical thickness, brain geometry, stiffness, and growth. The presented results suggest that an interplay of the inwards folding of mechanically weak spots and growth-induced instabilities shape the developing brain with primary folds that are consistent between individuals and highly variable secondary and tertiary folds. The mechanical model explains why larger mammalian brains tend to be more convoluted than smaller brains. Numerical predictions agree well with the classical pathologies of lissencephaly and polymicrogyria. Thus, the model is capable of bridging the scales from cellular events on the microscopic level towards form and function on the organ level. Combining physics and biology holds promise to further advance our understanding of human brain development and to enable early diagnostics of cortical malformations with the ultimate goal to improve treatment of neurodevelopmental disorders such as epilepsy, autism spectrum disorder, and schizophreni
Keywords: brain mechanics; growth; cortical folding; neurodevelopment; instabilities; thin films; period- doubling; period-tripling; human brain tissue; nanoindentation; biomechanical testing; constitutive modeling; Ogden model; finite viscoelasticity; parameter identification

The role of mechanics during brain development - Budday, Silvia; Steinmann, Paul; Kuhl, Ellen (Journal of the Mechanics and Physics of Solids, 2014)
Convolutions are a classical hallmark of most mammalian brains. Brain surface morphology is often associated with intelligence and closely correlated with neurological dysfunction. Yet, we know surprisingly little about the underlying mechanisms of cortical folding. Here we identify the role of the key anatomic players during the folding process: cortical thickness, stiffness, and growth. To establish estimates for the critical time, pressure, and the wavelength at the onset of folding, we derive an analytical model using the Föppl-von Kármán theory. Analytical modeling provides a quick first insight into the critical conditions at the onset of folding, yet it fails to predict the evolution of complex instability patterns in the post-critical regime. To predict realistic surface morphologies, we establish a computational model using the continuum theory of finite growth. Computational modeling not only confirms our analytical estimates, but is also capable of predicting the formation of complex surface morphologies with asymmetric patterns and secondary folds. Taken together, our analytical and computational models explain why larger mammalian brains tend to be more convoluted than smaller brains. Both models provide mechanistic interpretations of the classical malformations of lissencephaly and polymicrogyria. Understanding the process of cortical folding in the mammalian brain has direct implications on the diagnostics of neurological disorders including severe retardation, epilepsy, schizophrenia, and autism.
UnivIS-Import:2015-03-09:Pub.2014.tech.FT.FT-TM.therol
Keywords: Brain development; Cortical folding; Growth; Instabilities; Thin films

The deal.II Library, Version 8.4 - Bangerth, Wolfgang; Davydov, Denis; Heister, Timo; Heltai, Luca; Kanschat, Guido; Kronbichler, Martin; Maier, Matthias; Turcksin, Bruno; Wells, David (Journal of Numerical Mathematics, 2016)

The deal.II Library, Version 8.5 - Arndt, Daniel; Bangerth, Wolfgang; Davydov, Denis; Heister, Timo; Heltai, Luca; Kronbichler, Martin; Maier, Matthias; Pelteret, Jean-Paul; Turcksin, Bruno; Wells, David (Journal of Numerical Mathematics, 2017)

Time-dependent hyper-viscoelastic parameter identification of human articular cartilage and substitute materials - Weizel, A.; Distler, Thomas; Detsch, Rainer; Boccaccini, Aldo R.; Seitz, H.; Budday, Silvia (Journal of the Mechanical Behavior of Biomedical Materials, 2023)
Numerical simulations are a valuable tool to understand which processes during mechanical stimulations of hydrogels for cartilage replacement influence the behavior of chondrocytes and contribute to the success or failure of these materials as implants. Such simulations critically rely on the correct prediction of the material response through appropriate material models and corresponding parameters. In this study, we identify hyper-viscoelastic material parameters for numerical simulations in COMSOL Multiphysics® v. 5.6 for human articular cartilage and two replacement materials, the commercially available ChondroFillerliquid and oxidized alginate gelatin (ADA-GEL) hydrogels. We incorporate the realistic experimental boundary conditions into an inverse parameter identification scheme based on data from multiple loading modes simultaneously, including cyclic compression-tension and stress relaxation experiments. We provide individual parameter sets for the unconditioned and conditioned responses and discuss how viscoelastic effects are related to the materials’ microstructure. ADA-GEL and ChondroFillerliquid exhibit faster stress relaxation than cartilage with lower relaxation time constants, while cartilage has the largest viscoelastic stress contribution. The elastic response predominates in ADA-GEL and ChondroFillerliquid, while the viscoelastic response predominates in cartilage. These results will help to simulate mechanical stimulations, support the development of suitable materials with distinct mechanical properties in the future and provide parameters and insight into the time-dependent material behavior of human articular cartilage.
CRIS-Team Scopus Importer:2023-01-06
Keywords: Finite viscoelasticity; Human articular cartilage; Hydrogels; Parameter identification; Tissue engineering

Time–temperature correlations of amorphous thermoplastics at large strains based on molecular dynamics simulations - Zhao, Wuyang; Xiao, Rui; Steinmann, Paul; Pfaller, Sebastian (Mechanics of Materials, 2024)
In this paper, we investigate the time–temperature correlation of amorphous thermoplastics at large strains based on coarse-grained molecular dynamics simulations. This correlation behavior is characterized by the strain hardening modulus in uniaxial tension simulations at different strain rates across the glass transition region. The temperature regime is divided into a melt zone, a glassy zone, and a transition zone between them, according to the storage modulus calculated from dynamic mechanical analysis (DMA) at small strains. In the melt zone, the existence of time–temperature superposition (TTS) at large strains is verified by constructing a master curve of the hardening modulus. The obtained shift factors are then compared to those from DMA at small strains, showing that the TTS behavior is transferable between small and large strains. In the glassy zone, the effects of time and temperature are not superposable at large strains but still can be correlated. To demonstrate this correlation behavior, we introduce a level set of the hardening modulus with a variable pair of strain rate and temperature. Pairs lying in the same level result in coincident stress–strain curves at large strains. The transferability of the correlation behavior between large and small strains is validated by comparing these stress–strain curves at small strains in the pre-yield region. In the transition zone, the correlation behavior is studied with both aforementioned methods, showing that TTS is applicable to large strains but not transferable to small strains. Finally, we propose a phenomenological constitutive model for uniaxial tension to demonstrate the time–temperature correlation at large strains, considering different constant strain rates and temperatures.<br
Keywords: Time–temperature superposition; Amorphous polymers; Molecular dynamics simulations; Large strain; Constitutive modeling

Tissue-Scale Biomechanical Testing of Brain Tissue for the Calibration of Nonlinear Material Models - Faber, Jessica; Hinrichsen, Jan; Greiner, Alexander; Reiter, Nina; Budday, Silvia (Current Protocols, 2022)
Brain tissue is one of the most complex and softest tissues in the human body. Due to its ultrasoft and biphasic nature, it is difficult to control the deformation state during biomechanical testing and to quantify the highly nonlinear, time-dependent tissue response. In numerous experimental studies that have investigated the mechanical properties of brain tissue over the last decades, stiffness values have varied significantly. One reason for the observed discrepancies is the lack of standardized testing protocols and corresponding data analyses. The tissue properties have been tested on different length and time scales depending on the testing technique, and the corresponding data have been analyzed based on simplifying assumptions. In this review, we highlight the advantage of using nonlinear continuum mechanics based modeling and finite element simulations to carefully design experimental setups and protocols as well as to comprehensively analyze the corresponding experimental data. We review testing techniques and protocols that have been used to calibrate material model parameters and discuss artifacts that might falsify the measured properties. The aim of this work is to provide standardized procedures to reliably quantify the mechanical properties of brain tissue and to more accurately calibrate appropriate constitutive models for computational simulations of brain development, injury and disease. Computational models can not only be used to predictively understand brain tissue behavior, but can also serve as valuable tools to assist diagnosis and treatment of diseases or to plan neurosurgical procedures. © 2022 The Authors. Current Protocols published by Wiley Periodicals LLC.
CRIS-Team Scopus Importer:2022-04-15
Keywords: brain tissue; constitutive modeling; indentation; large strains; multi-modal mechanical testing; parameter identification

Topology Optimization in Additive Manufacturing Considering the Grain Structure of Inconel 718 using Numerical Homogenization - Hübner, Daniel; Gotterbarm, Martin; Kergaßner, Andreas; Köpf, Johannes; Pobel, Christoph; Markl, Matthias; Mergheim, Julia; Steinmann, Paul; Körner, Carolin; Stingl, Michael (Proceedings of 7th International Conference on Additive Technologies, 2018)
This paper introduces a new manufacturing aware design approach which exploits the possibilities of additive manufacturing processes to generate arbitrary geometries and simultaneously adjust the grain structure of the materials by choosing particular scan strategies. A combined experimental-simulative approach is developed which experimentally analyses the producible grain structures in the selective electron beam process, computes macroscopic material properties for these grain structures and employs these material properties in an optimization procedure in which the topology of a part and the orientation of the grains are optimized. In one example, the stiffness of a designed part can be increased by 30% when the grain orientation is taken into account.
Keywords: selective electron beam melting; optimization; grain structure

Towards a computational model of magneto-sensitive polymers - Pelteret, Jean-Paul; Saxena, Prashant; Walter, Bastian; Davydov, Denis; Steinmann, Paul (85th Annual Meeting of the International Association of Applied Mathematics and Mechanics, 2014)

Towards a computational model of thermal- and magneto-sensitive polymers - Pelteret, Jean-Paul; Davydov, Denis; Javili, Ali; Walter, Bastian; Steinmann, Paul (5th International Conference on Computational Methods for Coupled Problems in Science and Engineering, 2013)

Towards advanced piezoelectric metamaterial design via combined topology and shape optimization - Stankiewicz, Gabriel; Dev, Chaitanya; Weichelt, Michelle; Fey, Tobias; Steinmann, Paul (Structural and Multidisciplinary Optimization, 2024)
Metamaterials open up a spectrum of artificially engineered properties otherwise unreachable in conventional bulk materials. For electromechanical energy conversion systems, lightweight materials with high hydrostatic piezoelectric coupling coefficients and negative Poisson’s ratio can be obtained. Thus, in this contribution, we explore the possibilities of piezoelectric metamaterials design by employing structural optimization. More specifically, we apply a sequential framework of topology and shape optimization to design piezoelectric metamaterials with negative Poisson’s ratio for electromechanical energy conversion under uniform pressure. Topology optimization is employed to generate the initial layout, whereas shape optimization fine tunes the design and improves durability and manufacturability of the structures with the help of a curvature constraint. An embedding domain discretization (EDD) method with adaptive domain and shape refinement is utilized for an efficient and accurate computation of the state problem in the shape optimization stage. Multiple case studies are conducted to determine the importance of desired stiffness characteristics, symmetry conditions and objective formulations on the design of piezoelectric metamaterials. Results show that the obtained designs are highly dependent on the desired stiffness characteristics. Moreover, the addition of the EDD-based shape optimization step introduces significant changes to the designs, confirming the usability of the sequential framework.
CRIS-Team Scopus Importer:2024-03-01
Keywords: Cellular materials; Manufacturing constraints; Microstructure design; Piezoelectric metamaterials; Shape optimization; Topology optimization

Towards an efficient two-scale approach to model technical textiles - Fillep, Sebastian; Mergheim, Julia; Steinmann, Paul (Computational Mechanics, 2017)
The paper proposes and investigates an efficient two-scale approach to describe the material behavior of technical textiles. On the macroscopic scale the considered textile materials are modeled as homogeneous by means of shell elements. The heterogeneous microstructure, which consists e.g. of woven fibers, is explicitly resolved in representative volume elements (RVE). A shell-specific homogenization scheme is applied to connect the macro and the micro scale. The simultaneous solution of the macroscopic and the nonlinear microscopic simulations, e.g. by means of the FE2-method, is very expensive. Therefore, a different approach is applied here: the macro constitutive response is computed in advance and tabulated for a certain RVE and for different loading scenarios. These homogenized stress and tangent values are then used in a macroscopic simulation without the need to explicitly resort to the microscopic simulations. The efficiency of the approach is analyzed by means of numerical examples.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Computational homogenization; Shell kinematics; Tabulated macro constitutive model; Tangent calculation; Technical textiles

Towards an holistic account on residual stresses in full-forward extruded rods: Experiment, modeling and simulation of forming and operation phases - Floros, Dimosthenis; Jobst, Andreas; Kergaßner, Andreas; Merklein, Marion; Steinmann, Paul (Archive of Applied Mechanics, 2021)
An holistic view is attempted towards prediction of the effect of residual stresses induced by full-forward extrusion on fatigue life of workpieces during operation. To study the effect of constitutive model on the accuracy of forming simulations, a combined nonlinear isotropic/kinematic hardening model as well as the isotropic hardening part of the same model are calibrated based on five compression-tension-compression uniaxial stress experiments. A full-forward extrusion finite element model is developed adapting both the aforementioned hardening plasticity models and the predicted residual stress states at the surface of the workpiece are compared against that of a corresponding forming experiment. Results show residual stress predictions of remarkable accuracy by the FE-models with the isotropic hardening model. The effect of residual stresses on fatigue life of the workpiece is qualitatively studied by uncoupled multiscale simulations featuring gradient crystal plasticity at the microscale. While the effective (homogenized) macroscale response indicates elastic response during a macroscopically cyclic loading, plasticity accompanying reduction of residual stresses is still present at the microscale within, e.g. grain boundaries.
CRIS-Team Scopus Importer:2021-03-19
Keywords: Cold forming; FE-simulations; Kinematic hardening; Multiscale modeling; Residual stress

Towards a thermo-magneto-mechanical coupling framework for magneto-rheological elastomers - Mehnert, Markus; Mokarram, Hossain; Steinmann, Paul (International Journal of Solids and Structures, 2017)
Magnetorheological elastomers (MREs) are a relatively new class of smart materials that can undergo large deformations resulting from external magnetic excitation. These are promising candidates in producing sensors and actuators. Due to their inherent chemical compositions, most polymeric materials are highly susceptible to temperature. While performing experiments on MREs that are exposed to magneto-mechanically coupled loads, maintaining a constant temperature profile is a non-trivial task for various reasons, e.g., i) experiments need to be performed in a temperature chamber that can maintain a prescribed temperature throughout a test, and ii) additional temperature gradients can be generated internally. In this paper, a thermo-magneto-mechanically coupled constitutive model is devised that is based on the total energy approach frequently used in MREs modelling and computation. Relevant constitutive equations are derived exploiting basic laws of thermodynamics that result in a thermodynamically consistent formulation. We demonstrate the performance of the proposed thermo-magneto-mechanically coupled framework with the help of a widely-used non-homogeneous boundary value problem, the extension and inflation of an axisymmetric cylindrical tube under thermo-magneto-mechanically coupled loads that is solved analytically. The results capture various thermo-magneto-mechanical couplings with the formulation proposed for MRE.
Keywords: Magneto-elasticity; magneto-thermo-mechanical coupled problem; nonlinear elasticity; thermo-mechanical couplings

Towards a unified shear-induced lift model for prolate spheroidal particles moving in arbitrary non-uniform flow - Cui, Yan; Ravnik, Jure; Hriberšek, Matjaž; Steinmann, Paul (Computers & Fluids, 2020)
The paper proposes a unified shear-induced lift force model which divides the lift force into four lift components arising from the spin tensor, the volumetric and the deviatoric parts of the rate of deformation tensor, and the inertia effect of the Stokes drag. This unified model is successfully simplified into a shear-induced lift model for prolate spheroidal particles moving in arbitrary flow conditions via analogy arguments. The simplified shear-induced lift model for prolate spheroidal particles is verified by comparing it with several established lift force models via simulation of a prolate spheroidal particle moving in the Poiseuille and lid-driven cavity flows. The computational results demonstrate that the present lift force model for prolate spheroidal particles is applicable in flow cases with streamwise and non-streamwise flow shear. The implementation of the simplified lift model leads to computational results with reasonably small difference to the results of the full lift model of Cui et al. [Int. J. Multiph. Flow, 111, 232–240 (2019)], with a significantly decreased computational cost, rendering it as suitable for the implementation in large scale Lagrangian particle tracking.
CRIS-Team Scopus Importer:2019-11-05
Keywords: Lagrangian particle tracking; Prolate spheroidal particle; Saffman-type lift; Unified shear-induced lift

Towards elasto-plastic continuum-kinematics-inspired peridynamics - Javili, A.; McBride, A. T.; Mergheim, Julia; Steinmann, P. (Computer Methods in Applied Mechanics and Engineering, 2021)
The main objective of this contribution is to develop a dissipation-consistent elasto-plastic peridynamic (PD) formulation that is also geometrically exact. We distinguish between one-neighbour, two-neighbour and three-neighbour interactions. One-neighbour interactions are equivalent to the bond-based interactions of the original PD formalism. However, two- and three-neighbour interactions are fundamentally different to state-based interactions, as the basic elements of continuum kinematics are preserved exactly. We investigate the consequences of the angular momentum balance and provide a set of appropriate arguments for the interaction potentials accordingly. Furthermore, we elaborate on restrictions on the interaction energies and derive dissipation-consistent constitutive laws through a Coleman–Noll-like procedure. Although the framework is suitable for finite deformations, an additive decomposition of the kinematic quantities into elastic and plastic parts is rigorously proven to be a correct choice. Crucially, in our proposed scheme, the elasto-plastic framework resembles standard one-dimensional plasticity, for all interactions. Finally, we demonstrate the capability of our proposed framework via a series of numerical examples.
CRIS-Team Scopus Importer:2021-04-16
Keywords: Continuum kinematics; Elasto-plasticity; Peridynamics

Towards inverse form finding methods for a deep drawing steel DC04 - Germain, Sandrine; Steinmann, Paul (15th ESAFORM Conference Proceeding, 2012)
A challenge in the design of functional parts in metal forming processes is the determination of the initial, undeformed shape such that under a given load a part will obtain the desired deformed shape. An inverse mechanical or a shape optimization formulation might be used to solve this problem, which is inverse to the standard kinematic analysis in which the undeformed shape is known and the deformed shape unknown. The objective of the inverse mechanical formulation aims in the inverse deformation map that determines the (undeformed) material configuration, where the spatial (deformed) configuration and the mechanical loads are given. The shape optimization formulation predicts the initial shape in the sense of an inverse problem via successive iterations of the direct problem. In this paper, both methods are presented using a formulation in the logarithmic strain space. An update of the reference configuration of the sheet of metal during the optimization process is proposed in order to avoid mesh distortions. A first example showed the results obtained with both methods in isotropic hyperelasticity. A second example illustrated a simplified deep drawing computed with the shape optimization formulation in isotropic elastoplasticity. From the undeformed shapes obtained with both methods the deformed shapes are acquired with the direct mechanical formulation. Compared to the target deformed shape a minor difference in node coordinates is found. The computation time is lower with the inverse mechanical formulation in hyperelasticity. The update of the reference configuration in the shape optimization formulation allowed to avoid mesh distortions but increased the computational costs. © (2012) Trans Tech Publications.
UnivIS-Import:2015-04-16:Pub.2012.tech.FT.FT-TM.toward
Keywords: Inverse form finding; Large strain; Metal forming; Shape optimization

Towards microstructure-informed material models for human brain tissue - Budday, Silvia; Sarem, Melika; Starck, Laurent; Sommer, Gerhard; Pfefferle, Jule; Phunchago, Nichapa; Kuhl, Ellen; Paulsen, Friedrich; Steinmann, Paul; Shastri, V. Prasad; Holzapfel, Gerhard A. (Acta Biomaterialia, 2020)
Emerging evidence suggests that the mechanical behavior of the brain plays a critical role in development, disease, and aging. Recent studies have begun to characterize the mechanical behavior of gray and white matter tissue and to identify sets of material models that best reproduce the stress-strain behavior of different brain regions. Yet, these models are mainly phenomenological in nature, their parameters often lack clear physical interpretation, and they fail to correlate the mechanical behavior to the underlying microstructural composition. Here we make a first attempt towards identifying general relations between microstructure and mechanics with the ultimate goal to develop microstructurally motivated constitutive equations for human brain tissue. Using histological staining, we analyze the microstructure of brain specimens from different anatomical regions, the cortex, basal ganglia, corona radiata, and corpus callosum, and identify the regional stiffness and viscosity under multiple loading conditions, simple shear, compression, and tension. Strikingly, our study reveals a negative correlation between cell count and stiffness, a positive cor- relation between myelin content and stiffness, and a negative correlation between proteoglycan content and stiffness. Additionally, our analysis shows a positive correlation between lipid and proteoglycan content and viscosity. We demonstrate how understanding the microstructural origin of the macroscopic behavior of the brain can help us design microstructure-informed material models for human brain tissue that inherently capture regional heterogeneities. This study represents an important step towards using brain tissue stiffness and viscosity as early diagnostic markers for clinical conditions including chronic traumatic encephalopathy, Alzheimer’s and Parkinson’s disease, or multiple sclerosis.
Keywords: material modeling; biomechanical testing; hyperelasticity; Ogden model; human brain tissue; microstructure

Towards Modeling the Curing Processes of Thermosets - Mokarram, Hossain; Possart, Gunnar; Steinmann, Paul (Proceedings of 79th GAMM Annual Conference, 2008)
UnivIS-Import:2015-04-16:Pub.2008.tech.FT.FT-TM.toward_7

Towards modelling the curing process in particle-filled electro-active polymers - Mokarram, Hossain; Steinmann, Paul (PAMM, 2015)
A large actuation voltage is required to produce a desired mechanical deformation in dielectric elastomers. To reduce the amount of the actuation voltage, several mechanisms can be applied and the inclusion of high dielectric permittivity fillers in the matrix material in the uncured stage is one of them. Moreover, to obtain a maximum advantage from the high dielectric permittivity fillers, an electric field is applied during the curing process which helps the particles to align in a preferred direction. The stiffness gaining during curing is modelled by an appropriate constitutive relation where the temporal evolution of the material parameters is considered. In this paper we present a phenomenologically-inspired large strain framework for simulating the curing process of polymers that can work under the use of an electro-mechanically coupled load.
UnivIS-Import:2015-10-26:Pub.2015.tech.FT.FT-TM.toward_1

Towards optimization of crack resistance of composite materials by adjustment of fiber shapes - Prechtel, Marina; Leugering, Günter; Stingl, Michael; Steinmann, Paul (Engineering Fracture Mechanics, 2011)
We investigate the evolution and propagation of cracks in 2-d elastic domains, which are subjected to quasi-static loading scenarios. In addition to the classical variational formulation, where the standard potential energy is minimized over the cracked domain under physical conditions characterizing the behavior of the material close to the crack (e.g. non-penetration conditions), we include a 'cohesive traction term' in the energy expression. In this way we obtain a mathematically concise set of partial differential equations with non-linear boundary conditions at the crack interfaces. We perform a finite element discretization using a combination of standard continuous finite elements and so-called cohesive elements. During the simulation process cohesive elements are adaptively inserted at positions where a certain stress bound is exceeded. In our numerical studies we consider domains consisting of a matrix material with fiber inclusions. Beyond pure crack path simulation, our ultimate goal is to determine an optimal shape of the fibers resulting in a crack path that releases for a given load scenario as much energy as possible without destroying the specimen completely. We develop a corresponding optimization model and propose a solution algorithm for the same. The article is concluded by numerical results. © 2011 Elsevier Ltd.
UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.toward
Keywords: Cohesive zone modeling; Crack growth; Fiber reinforced material; Shape optimization

Towards the Algorithmic Treatment of 3D Strong Discontinuities - Mergheim, Julia; Kuhl, Ellen; Steinmann, Paul (Communications in Numerical Methods in Engineering, 2007)
A geometrically non-linear finite element framework for the modelling of propagating discontinuities in three-dimensional continua is presented. By doubling the degrees of freedom in the discontinuous elements, the algorithm allows for arbitrary discontinuities which are not restricted to inter-element boundaries. The deformation field is interpolated independently on both sides of the discontinuity. In contrast to the X-FEM, the suggested approach thus relies exclusively on displacement degrees of freedom. On the discontinuity surface, the jump in the deformation is related to the cohesive tractions to account for smooth crack opening. Computational difficulties characteristic of three-dimensional crack propagation are addressed. The performance of the method is elaborated by means of a homogeneous three-dimensional tension problem and by means of the classical peel test. Copyright © 2006 John Wiley & Sons, Ltd.
UnivIS-Import:2015-03-09:Pub.2007.tech.FT.FT-TM.toward
Keywords: Cohesive surfaces; Discontinuous elements; Nitsche's method; Propagating discontinuities

Towards the optimisation and adaptation of dry powder inhalers - Cui, Yan; Schmalfuß, Silvio; Zellnitz, Sarah; Sommerfeld, Martin; Urbanetz, Nora (International Journal of Pharmaceutics, 2014)
Pulmonary drug delivery by dry powder inhalers is becoming more and more popular. Such an inhalation device must insure that during the inhalation process the drug powder is detached from the carrier due to fluid flow stresses. The goal of the project is the development of a drug powder detachment model to be used in numerical computations (CFD, computational fluid dynamics) of fluid flow and carrier particle motion through the inhaler and the resulting efficiency of drug delivery. This programme will be the basis for the optimisation of inhaler geometry and dry powder inhaler formulation. For this purpose a multi-scale approach is adopted. First the flow field through the inhaler is numerically calculated with OpenFOAM® and the flow stresses experienced by the carrier particles are recorded. This information is used for micro-scale simulations using the Lattice–Boltzmann method where only one carrier particle covered with drug powder is placed in cubic flow domain and exposed to the relevant flow situations, e.g. plug and shear flow with different Reynolds numbers. Therefrom the fluid forces on the drug particles are obtained. In order to allow the determination of the drug particle detachment possibility by lift-off, sliding or rolling, also measurements by AFM (atomic force microscope) were conducted for different carrier particle surface structures. The contact properties, such as van der Waals force, friction coefficient and adhesion surface energy were used to determine, from a force or moment balance (fluid forces versus contact forces), the detachment probability by the three mechanisms as a function of carrier particle Reynolds number. These results will be used for deriving the drug powder detachment model.<br
Keywords: Surface modification; Carrier glass beads; Dry powder inhaler; Computational fluid dynamics; Prediction of drug detachment; Fluid stresses on carrier

Towards the treatment of boundary conditions for global crack path tracking in three-dimensional brittle fracture - Jäger, Paul; Steinmann, Paul; Kuhl, Ellen (Computational Mechanics, 2009)
The aim of the present paper is a systematic elaboration of a three dimensional finite element analysis tool for discontinuous fracture in brittle solids. Brittle or quasi-brittle fracture usually occurs when a material reaches the limit of its strength and no plastic deformation has been observed prior to failure. In the present approach, this kind of failure is characterized by three sets of governing equations: (i) the elastic bulk problem and (ii) the cohesive interface problem regarding the solid deformation field and (iii) the crack tracking problem concerning the crack kinematics. This manuscript describes a unique modular tool set for the coupled set of nonlinear equations. We focus in particular on the boundary conditions for the crack tracking problem of this analysis tool. We critically discuss important implementation details: (i) the choice of crack onset boundary conditions for the additional global field, (ii) the numerical integration, (iii) the modeling of geometrically exact crack tips for cohesive fracture, and (iv) the post-processing procedure for the discontinuity visualization. The potential of the method to simulate brittle fracture is demonstrated by qualitative and quantitative comparisons with experiments from the literature as well as by common benchmark problems. © 2009 Springer-Verlag.
UnivIS-Import:2015-03-09:Pub.2009.tech.FT.FT-TM.toward_2
Keywords: Brittle fracture; Cohesive crack concept; Concrete modeling; Discontinuous failure; Interface; Visualization

Transmural fibre orientations based on Laplace-Dirichlet-Rule-Based-Methods and their influence on human heart simulations - Holz, David; Martonová, Denisa; Schaller, Emely; Duong, Minh Tuan; Alkassar, Muhannad; Weyand, Michael; Leyendecker, Sigrid (Journal of Biomechanics, 2023)

Two reduction methods for stochastic FEM based homogenization using global basis functions - Pivovarov, Dmytro; Steinmann, Paul; Willner, Kai (Computer Methods in Applied Mechanics and Engineering, 2018)
The computationally most expensive part of stochastic FEM based homogenization is the inversion of the stochastic stiffness matrix. Previously we studied different combinations of global and local basis functions in the stochastic domain while keeping the common FEM discretization in the physical domain. Simulation results showed that a local basis (SL-FEM) results in a sparse but bigger stiffness matrix compared to a global basis (SG-FEM). In this work we introduce a SFEM modification involving global basis functions in both the physical and the stochastic domain. We introduce two different strategies for the implementation of the global basis. The first is the application of a trigonometric basis within a global Galerkin framework. The second is the use of vibration modes of some simple deterministic auxiliary model as global basis functions. The second approach in particularly results in a basis reduction technique. However this approach differs markedly from stochastic spectral decomposition which uses the matrix of the original stochastic problem. We address two very important questions, namely the treatment of the Gibbs phenomenon in the case of physical-stochastic trigonometric basis functions and the evaluation of the eigenvectors for the stochastic problem which are suitable for further basis reduction. Convergence studies and detailed comparison with Monte-Carlo results are presented for both methods.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Computational homogenization; eXtended FEM; Global basis; Random geometry; Reduced order modeling; Stochastic FEM

Two-scale computational homogenization of electro-elasticity at finite strains - Keip, Marc-Andre; Steinmann, Paul; Schroeder, Joerg (Computer Methods in Applied Mechanics and Engineering, 2014)
This contribution addresses a two-scale computational homogenization framework for the simulation of electro-active solids at finite strains. A generalized form of the Hill-Mandel condition is employed for the derivation of energetically consistent transition conditions between the scales. The continuum mechanical formulation is implemented into a two-scale finite element environment, in which we attach a microscopic representative volume element at each integration point of the macroscopic domain. In order to allow for an efficient solution of the macroscopic boundary value problem an algorithmically consistent tangent of the macroscopic problem is derived. The method will be applied to the analysis of dielectric polymer-ceramic composites, where we determine the effective actuation of composites with different microstructures. Furthermore, we show the applicability of the proposed method to the computation of two-scale electro-mechanically coupled boundary value problems in consideration of large deformations.
CRIS-Team Scopus Importer:2022-08-05
Keywords: Computational homogenization; Dielectric composites; Electro-active polymers; Electro-mechanical coupling; FE; Finite deformations

Two-scale elastic parameter identification from noisy macroscopic data - Schmidt, Ulrike; Steinmann, Paul; Mergheim, Julia (Archive of Applied Mechanics, 2015)
A two-scale parameter identification procedure to identify microscopic elastic parameters from macroscopic data is introduced and thoroughly analyzed. The macroscopic material behavior of microscopically linear elastic heterogeneous materials is described by means of numerical homogenization. The microscopic material parameters are assumed to be unknown and are identified from noisy macroscopic displacement data. Various examples of microscopically heterogeneous materials—with regularly distributed pores, particles, or layers—are considered, and their parameters are identified from different macroscopic experiments by means of a gradient-based optimization procedure. The reliability of the identified parameters is analyzed by their standard deviations and correlation matrices. It was found that the two-scale parameter identification works well for cellular materials, but has to be designed carefully for layered materials. If the homogenized macroscopic material behavior can be described by less material parameters than the microscopic material behavior, as, e.g., for regularly distributed particles, the identification of all microscopic parameters from macroscopic experiments is not possible.

Two-scale off-and online approaches to geometrically exact elastoplastic rods - Herrnböck, Ludwig; Kumar, Ajeet; Steinmann, Paul (Computational Mechanics, 2022)
This work compares two different computational approaches to geometrically exact elastoplastic rods. The first approach applies an elastoplastic constitutive model in terms of stress resultants, i.e. forces and moments. It requires knowledge of the rod’s elasticity and yield-criterion in terms of stress resultants. Furthermore a resultant-type hardening expression must be formulated. These are obtained by integrating elastoplastic stress and hardening measures from three-dimensional continuum mechanics over the rod’s deformed cross-section, which is performed in an offline stage. The second approach applies an FE2 approach as established in computational homogenization. Therein, the macro-scale describing the geometrically exact rod is coupled to the micro-scale, i.e., the cross-section of the rod. A novelty of the presented work is the determination of a hardening tensor for use in the stress resultant approach. The mechanical response of both approaches is first compared on the material point level, a single cross-section of a uniformly strained rod. Later, also the mechanical response and the deformation of finitely and non-uniformly strained rods are investigated.
CRIS-Team Scopus Importer:2022-07-15
Keywords: Determination of hardening tensor; FE; Geometrically exact elastoplastic rods; Multiscale homogenization

Two-Scale Parameter Identification for heterogeneous elastoplastic materials - Schmidt, Ulrike; Mergheim, Julia; Steinmann, Paul (Proceeding of 11h International Conference on Computational Plasticity, Fundamentals and Applications, 2011)
The aim of this paper is to describe a method for identifying micro material parameters using only macroscopic experimental data. The FE 2 method is used to model the behavior of the complex materials with heterogeneous micro-structure. The resulting least squares problem, with the difference of the simulated and the measured macroscopic data in the objective function, is minimized using gradient-based optimization algorithms with respect to the microscopic material parameters. The gradient information is derived analytically within the discretized scheme.
UnivIS-Import:2015-04-16:Pub.2011.tech.FT.FT-TM.twosca_1
Keywords: Computational plasticity; Homogenization; Inverse problem; Multi-scale; Parameter identification

Uncertainty modeling using fuzzy arithmetic based on sparse grids: Applications to dynamic systems - Willner, Kai; Wohlmuth, B. I.; Klimke, A. (International Journal of Uncertainty Fuzziness and Knowledge-Based Systems, 2004)
Fuzzy arithmetic provides a powerful tool to introduce uncertainty into mathematical models. With Zadeh's extension principle, one can obtain a fuzzy-valued extension of any real-valued objective function. An efficient and accurate approach to compute expensive multivariate functions of fuzzy numbers is given by fuzzy arithmetic based on sparse grids. In this paper, we illustrate the general applicability of this new method by computing two dynamic systems subjected to uncertain parameters as well as uncertain initial conditions. The first model consists of a system of delay differential equations simulating the periodic outbreak of a disease. In the second model, we consider a multibody mechanism described by an algebraic differential equation system. © World Scientific Publishing Company.
UnivIS-Import:2015-03-09:Pub.2004.tech.FT.FT-TM.uncert_9
Keywords: Computing fuzzy functions; Differential equations; Extension principle; Fuzzy numbers; Multibody mechanism; Uncertainty modeling

Unconstrained and Cauchy-Born-constrained atomistic systems: deformational and configurational mechanics - Steinmann, Paul; Ricker, Sarah; Aifantis, Elias (Archive of Applied Mechanics, 2011)
In this contribution, the deformational and configurational mechanics of (elastic) discrete atomistic systems in relation to their continuum counterparts are considered for the quasi-static case. Thereby, we firstly investigate the basic unconstrained case in the sense of lattice statics as a reference. Based on these results, we consider two Cauchy-Born-type constraints that (locally) describe the change of the position of atoms (between the material and the spatial configuration) in terms of either a linear or a quadratic map, respectively. Insertion of these kinematic constraints into the variation of the total potential energy of the unconstrained case renders eventually Cauchy-Born-type definitions for atomistic stresses and hyperstresses, for both deformational and configurational cases. In the continuum limit, these are the relevant continuum stresses and hyperstresses contributing to the local force balances of first- (classical) and second-order (non-classical) gradient continua (here first- and second-order gradient refers to the highest gradient of the deformation map characterizing the kinematics). It is emphasized that the atomistic and the Cauchy-Born-type configurational quantities represent novel and unexpected contributions. Among other things, they may be useful in assessing the singular or non-singular character of deformation fields at crack tips and comparing numerical estimates resulting from atomistic simulations with analytical predictions resulting from solutions of related boundary value problems for gradient continua. © 2010 Springer-Verlag.
UnivIS-Import:2015-03-09:Pub.2011.tech.FT.FT-TM.deform
Keywords: Cauchy-Born constraint; Configurational mechanics; Gradient continua; Homogenization

Unconventional Discretisations of the Temperature Equation in Earth Mantle Dynamics - Baloglu, Maximilian Volkan; Nadjafabadi Farahani, Mohammad Hassan; Rettinger, Christoph; Vogel, Constantin (2014)
Due to the high Péclet-number occurring in Earth mantle dynamics, the energy equation can be approximated by a pure advection equation for the temperature. However, conventional approaches like the Finite Element Method introduce undesired diffusion. Therefore, the task of our BGCE Honours Project is to develop and evaluate unconventional discretisations of the temperature equation that tackle the problem of artificial diffusion. We come up with two different methods: One is based on the Bresenham algorithm stemming from computer graphics. It uses offset values to determine the advection direction of the temperature. The other method features a Lagrangian description of the problem. We achieve this by deploying particles that incorporate temperature values and are advected only by the underlying velocity field. Simulations in one- and two-dimensional domains reveal inherent shortcomings of the Bresenham Method which cannot be overcome by several attempts. On the other hand, the Lagrangian Method yields promising results that can be further improved by additional treatments. We extend the Lagrangian Method to work on triangle and tetrahedron grids to offer an interface to the implementation of the Earth mantle dynamics solver of the Terra-Neo project. Additional advantages of the proposed method are the parallelisation capability, a straight-forward extension for advecting other physical quantities and the possible inclusion of physical diffusion in an operator-splitting approach.

Uniaxial deformation of polystyrene–silica nanocomposites studied by hybrid molecular dynamics–finite element simulations - Liu, Shengyuan; Pfaller, Sebastian; Rahimi, Mohammad; Possart, Gunnar; Steinmann, Paul; Böhm, Michael C.; Müller-Plathe, Florian (Computational Materials Science, 2016)
This contribution investigates, based on molecular dynamics (MD), the mechanical deformation behavior of polystyrene-silica nanocomposites and focuses on the influence of  micromechanical properties as e.g. filler particle size and filler mass fraction. With regard to simulations of macroscopic problems with system sizes not capable by pure MD approaches, our investigations are complemented by hybrid molecular dynamics – finite element (MD-FE) simulations. Our computational approach shows show that an increasing total interfacial area between the nanoparticles and the polymer matrix stiffens the nanocomposite. As expected, small nanoparticles have more significant impact on the macroscopic mechanical properties of nanocomposites than large ones. We show that, for the same mass fraction of nanoparticles, the Young’s modulus increases by about 4–5% when the nanoparticle diameter is decreased from 5 to 2 nm. Furthermore, we find that: (i) the end-to-end distances of free polymer chains in the vicinity of nanoparticles are larger than in the bulk; (ii) the addition of nanoparticles slows down the global dynamics of free polymer chains; and (iii) the interphase thickness of nanocomposites is about 1–1.5 nm. Beyond that, we study structural properties at the microscale under uniaxial tension and find that the presence of nanoparticles hinders the orientation of free polymer chains under deformation. This hindrance is more pronounced for small nanoparticles and high mass fractions. Polymer structural descriptors as the chain end-to-end vector and a molecular anisotropy parameter largely change in line with the geometrical transformation of the whole sample.
Keywords: Polymer nanocomposites; Deformation; Hybrid particle-continuum approach; Molecular dynamics; Finite element

Unified magnetomechanical homogenization framework with application to magnetorheological elastomers - Chatzigeorgiou, Georgios; Javili, Ali; Steinmann, Paul (Mathematics and Mechanics of Solids, 2012)
The aim of this work is to present a general homogenization framework with application to magnetorheological elastomers under large deformation processes. The macroscale and microscale magnetomechanical responses of the composite in the material and spatial description are presented and the conditions for a well-established homogenization problem in Lagrangian description are identified. The connection between the macroscopic magnetomechanical field variables and the volume averaging of the corresponding microscopic variables in the Eulerian description is examined for several types of boundary conditions. It is shown that the use of kinematic and magnetic field potentials instead of kinetic field and magnetic induction potentials provides a more appropriate homogenization process.
UnivIS-Import:2015-04-14:Pub.2012.tech.FT.FT-TM.unifie

Unraveling the Local Relation Between Tissue Composition and Human Brain Mechanics Through Machine Learning - Linka, Kevin; Reiter, Nina; Würges, Jasmin; Schicht, Martin; Cyron, Christian J.; Paulsen, Friedrich; Budday, Silvia; Bräuer, Lars (Frontiers in Bioengineering and Biotechnology, 2021)
The regional mechanical properties of brain tissue are not only key in the context of brain injury and its vulnerability towards mechanical loads, but also affect the behavior and functionality of brain cells. Due to the extremely soft nature of brain tissue, its mechanical characterization is challenging. The response to loading depends on length and time scales and is characterized by nonlinearity, compression-tension asymmetry, conditioning, and stress relaxation. In addition, the regional heterogeneity–both in mechanics and microstructure–complicates the comprehensive understanding of local tissue properties and its relation to the underlying microstructure. Here, we combine large-strain biomechanical tests with enzyme-linked immunosorbent assays (ELISA) and develop an extended type of constitutive artificial neural networks (CANNs) that can account for viscoelastic effects. We show that our viscoelastic constitutive artificial neural network is able to describe the tissue response in different brain regions and quantify the relevance of different cellular and extracellular components for time-independent (nonlinearity, compression-tension-asymmetry) and time-dependent (hysteresis, conditioning, stress relaxation) tissue mechanics, respectively. Our results suggest that the content of the extracellular matrix protein fibronectin is highly relevant for both the quasi-elastic behavior and viscoelastic effects of brain tissue. While the quasi-elastic response seems to be largely controlled by extracellular matrix proteins from the basement membrane, cellular components have a higher relevance for the viscoelastic response. Our findings advance our understanding of microstructure - mechanics relations in human brain tissue and are valuable to further advance predictive material models for finite element simulations or to design biomaterials for tissue engineering and 3D printing applications.
Keywords: human brain; viscoelasticity; constitutive modeling; microstructure; mechanical properties; artificial neural network; extracellular matrix

Untersuchungen zum Bremsenquitschen am Balken-Scheibe Modell - Allgaier, R.; Gaul, L.; Willner, Kai; Keiper, W. (Konstruktion, 2005)
UnivIS-Import:2015-03-09:Pub.2005.tech.FT.FT-TM.unters

Unveiling Consumer Behavior in District Heating Network: A Contrastive Learning Approach to Clustering - Basak, Pooja; Ramachandran, Adithya; Maier, Andreas; Bayer, Siming (SESAAU2024 – Smart Energy Systems Conference, 2024)

Using dropout based active learning and surrogate models in the inverse viscoelastic parameter identification of human brain tissue - Hinrichsen, Jan; Ferlay, Carl; Reiter, Nina; Budday, Silvia (Frontiers in Physiology, 2024)
Inverse mechanical parameter identification enables the characterization of ultrasoft materials, for which it is difficult to achieve homogeneous deformation states. However, this usually involves high computational costs that are mainly determined by the complexity of the forward model. While simulation methods like finite element models can capture nearly arbitrary geometries and implement involved constitutive equations, they are also computationally expensive. Machine learning models, such as neural networks, can help mitigate this problem when they are used as surrogate models replacing the complex high fidelity models. Thereby, they serve as a reduced order model after an initial training phase, where they learn the relation of in- and outputs of the high fidelity model. The generation of the required training data is computationally expensive due to the necessary simulation runs. Here, active learning techniques enable the selection of the “most rewarding” training points in terms of estimated gained accuracy for the trained model. In this work, we present a recurrent neural network that can well approximate the output of a viscoelastic finite element simulation while significantly speeding up the evaluation times. Additionally, we use Monte-Carlo dropout based active learning to identify highly informative training data. Finally, we showcase the potential of the developed pipeline by identifying viscoelastic material parameters for human brain tissue.
CRIS-Team Scopus Importer:2024-02-16
Keywords: active learning; human brain tissue; neural network; parameter identification; surrogate model

Using the ESPI-Technique to Determine Material Properties of Plates - Gaul, L.; Willner, Kai; Hurlebaus, S. (Proceedings of the 4th International ESPI User Meeting, 1997)
UnivIS-Import:2015-04-16:Pub.1997.tech.FT.FT-TM.usingt

Variational issues in the homogenization of discrete systems - Ricker, Sarah; Mergheim, Julia; Menzel, Andreas; Steinmann, Paul (Proceedings of ECCOMAS, 2007)
UnivIS-Import:2015-04-16:Pub.2007.tech.FT.FT-TM.variat

Variationally consistent computational homogenization of chemomechanical problems with stabilized weakly periodic boundary conditions - Käßmair, Stefan; Runesson, Kenneth; Steinmann, Paul; Jänicke, Ralf; Larsson, Fredrik (International Journal for Numerical Methods in Engineering, 2021)
A variationally consistent model-based computational homogenization approach for transient chemomechanically coupled problems is developed based on the classical assumption of first-order prolongation of the displacement, chemical potential, and (ion) concentration fields within a representative volume element (RVE). The presence of the chemical potential and the concentration as primary global fields represents a mixed formulation, which has definite advantages. Nonstandard diffusion, governed by a Cahn–Hilliard type of gradient model, is considered under the restriction of miscibility. Weakly periodic boundary conditions on the pertinent fields provide the general variational setting for the uniquely solvable RVE-problem(s). These boundary conditions are introduced with a novel approach in order to control the stability of the boundary discretization, thereby circumventing the need to satisfy the LBB-condition: the penalty stabilized Lagrange multiplier formulation, which enforces stability at the cost of an additional Lagrange multiplier for each weakly periodic field (three fields for the current problem). In particular, a neat result is that the classical Neumann boundary condition is obtained when the penalty becomes very large. In the numerical examples, we investigate the following characteristics: the mesh convergence for different boundary approximations, the sensitivity for the choice of penalty parameter, and the influence of RVE-size on the macroscopic response.
CRIS-Team Scopus Importer:2021-08-20
Keywords: chemomechanical coupling; computational homogenization; Dirichlet and Neumann RVE-conditions; failsafe; variationally consistent; weak periodicity

Variationally consistent quadratic finite element contact formulations for finite deformation contact problems on rough surfaces - Sitzmann, Saskia; Willner, Kai; Wohlmuth, B. I. (Finite Elements in Analysis and Design, 2016)
Although different discrete formulations for contact problems have been widely studied during the last decade, the numerical simulation of complex industrial applications is still challenging. While suitable Lagrange multiplier based formulations are well-known for their consistency and stability in the case of classical model problems of Coulomb type, rough surface contact laws and additional multi-point constraints are much less understood. In this paper, we focus on a quadratic finite element approach for quasi-static calculations and extend ideas from our previous work on constitutive contact laws combined with suitable solutions for multi-point constraints like cyclic symmetry on the contact boundary. The popular dual mortar method is used to enforce the contact constraints in a variationally consistent way without increasing the algebraic system size. To avoid possible consistency errors of the dual mortar approach in case of large curvatures or gradients in the contact zone, an alternative quadratic Petrov-Galerkin mortar formulation is presented. Numerical examples demonstrate the robustness of the derived numerical algorithm. Special focus is set to industrial motivated applications involving large deformations and plastic effects as well as rough surfaces on the micro-scale.
Keywords: Contact with regularization; Dual mortar methods; Industrial applications; Perturbed Lagrangian formulation; Petrov-Galerkin; Quadratic elements

Variational Setting - Steinmann, Paul (Spatial and Material Forces in Nonlinear Continuum Mechanics, 2022)
This chapter expands on the variational setting in terms of extended Hamilton and Dirichlet principles for conservative elasto-dynamic and elasto-static cases, respectively, and carefully analyzes the resulting spatial and material Euler-Lagrange equations.
CRIS-Team Scopus Importer:2022-04-15

Versagen von Silikonbrustimplantaten - Neuartige Kartierung und Aufdeckung von Produkt-Clustern - Daenicke, Jonas; Walter, Bastian; Horch, Raymund E.; Kaschta, Joachim; Schubert, Dirk W. (Plastische Chirurgie, 2013)
UnivIS-Import:2015-03-09:Pub.2013.tech.FT.FT-TM.versag

Versatile data-adaptive hyperelastic energy functions for soft materials - Wiesheier, Simon; Moreno Mateos, Miguel Angel; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2024)
Download full issue Search ScienceDirect Search ScienceDirect Outline Abstract Keywords 1. Introduction 2. Hyperelasticity based on a approximation of the strain energy function 3. Inverse identification of the parameters of the approximated strain energy function 4. Experimental insights: threefold application and validation of the model 5. Conclusion and outlook CRediT authorship contribution statement Declaration of competing interest Acknowledgment Appendix A. Normalized error plots of forces and vertical displacement fields Appendix B. Sensitivity matrix Data availability References Show full outline Figures (10) Fig. 1. Graphical comparison of linear basis functions (above, k=2) and cubic basis… Fig. 2. Sampled invariants Ī1 at the quadrature points (c) across all load steps of a… Fig. 3. Deformed samples featuring holes of different dimensions for three elastomers Fig. 4. Identification of the strain energy function W̄(I,Ī1) for the material… Fig. 5. Identification of the strain energy function W̄(I,Ī1) for the material DOWSIL Fig. 6. Identification of the strain energy function W̄(I,Ī1)+W̄(I,Ī2) for the… Show 4 more figures Elsevier Computer Methods in Applied Mechanics and Engineering Volume 430, 1 October 2024, 117208 Computer Methods in Applied Mechanics and Engineering Versatile data-adaptive hyperelastic energy functions for soft materials Author links open overlay panelSimon Wiesheier a, Miguel Angel Moreno-Mateos a, Paul Steinmann a b a Institute of Applied Mechanics, Friedrich-Alexander-Universität Erlangen–Nürnberg, Egerlandstr. 5, 91058, Erlangen, Germany b Glasgow Computational Engineering Centre, School of Engineering, University of Glasgow, G12 8QQ, United Kingdom Received 21 May 2024, Revised 25 June 2024, Accepted 30 June 2024, Available online 11 July 2024, Version of Record 11 July 2024. What do these dates mean? crossmark-logo Show less Add to Mendeley Share Cite https://doi.org/10.1016/j.cma.2024.117208 Get rights and content Under a Creative Commons license open access Abstract Applications of soft materials are customarily linked to complex deformation scenarios and material nonlinearities. In the bioengineering field, soft materials typically mimic the low stiffness of biological matter subjected to extreme deformations. Computational frameworks surge as a versatile tool to assist the design of functional applications. The constitutive model lies at the core of such frameworks. In this regard, the customary extreme non-linear behavior of elastomers poses an additional challenge to thoroughly capture the material behavior. Here, data-driven methodologies hold considerable promise for enhancing constitutive modeling when contrasted with phenomenological approaches. In this investigation, we introduce a versatile data-adaptive method tailored to the modeling of hyperelastic soft materials at finite strains. Specifically, our method substitutes an a priori chosen model for the strain energy function by a flexible interpolant defined on a discretized invariant space. Within this framework, the interpolation values assume the role of material parameters and are determined through finite element model updating to conform to measured experimental data — comprising full-field displacements coming from Digital-Image-Correlation and global reaction forces. We validate the method on uniaxial experimental tests of soft elastomers, encompassing , , and . Overall, we aim to establish a new route for the construction of hyperelastic energy functions, untethered from any predefined existing models or assumptions regarding the shape of the energ
Keywords: Data-driven; Parameter identification; Soft materials; Finite-element-method; Finite strains; Experimental mechanics

Vibration energy harvesting and internal electric potential of (Na,K)NbO3/polyimide piezoelectric composites - Yamamoto, Ryota; Hegendörfer, Andreas; Mergheim, Julia; Kakimoto, Ken-Ichi (Japanese Journal of Applied Physics, 2021)
A composite structure of piezoelectric particles and soft polymer composite materials is a promising component of vibration energy harvesters. However, the energy harvesting behavior which originates from ceramic particles inside the polymer has not been clarified. In this study, (Na,K)NbO3/polyimide composites sheets with NKN fraction of 0-40 vol% were fabricated and open-circuit voltage was measured. The open-circuit voltage was increased nonlinearly from 0.72 to 2.21 V with increasing of the particle fraction (10%-30%) The experimental results were confirmed using a microstructure based finite element method and electric potential and electromechanical coupling coefficients were higher value in the content of 30% NKN particles. Analysis indicates that the internal electric potential inside the matrix under strain could be an important factor for macroscopic piezoelectric constant and electrical output.
CRIS-Team WoS Importer:2021-09-10

Vibration Reduction by Energy Transfer Using Shape Adaption - Nowak, Alexander; Willner, Kai; Hasse, Alexander (Springer Science and Business Media Deutschland GmbH, 2024)
Within the Priority Programme Calm, Smooth and Smart, a new approach for deliberately introduced damping through variation of stiffness was presented. The proposed approach is a novel way of combining the concepts of damping and absorption inherently in a structure. By dynamically adapting the stiffness of a slender, beam-like structure through the use of shape adaption in the cross-section, energy is transferred from critical low-frequency modes into a specifically designed, higher frequency absorber mode, which can then be damped in an optimal way. Experimental studies were first conducted to examine the suitability of shape adaption for the proposed approach. Various investigations were carried out regarding application of the presented concept with different time laws for free and forced oscillations. In addition, thorough analytical and numerical studies were conducted to understand the internal energy transfers and provide the basis for decoupling of active and semi-active effects related to the reduction of vibrations. Another focus was on the synthesis of a structural layout that enables a defined stiffness change to be induced and an absorber mode (defined in shape and eigenfrequency) to be integrated into the structure.
CRIS-Team Scopus Importer:2023-10-06

Vibrations in the High Frequency Range - Willner, Kai; Strzyzakowski, Z. (Zeitschrift für angewandte Mathematik und Mechanik, 1992)
UnivIS-Import:2015-04-16:Pub.1992.tech.FT.FT-TM.vibrat

Virtual Work - Steinmann, Paul (Spatial and Material Forces in Nonlinear Continuum Mechanics, 2022)
This chapter capitalizes on the referential setting when introducing the notions of spatial and material virtual displacements and discussing the accompanying spatial and material virtual work principles.
CRIS-Team Scopus Importer:2022-04-15

Viscoelastic parameter identification of human brain tissue - Budday, Silvia; Sommer, Gerhard; Holzapfel, Gerhard A.; Steinmann, Paul; Kuhl, Ellen (Journal of the Mechanical Behavior of Biomedical Materials, 2017)
Understanding the constitutive behavior of the human brain is critical to interpret the physical environment during neurodevelopment, neurosurgery, and neurodegeneration. A wide variety of constitutive models has been proposed to characterize the brain at different temporal and spatial scales. Yet, their model parameters are typically calibrated with a single loading mode and fail to predict the behavior under arbitrary loading condi- tions. Here we used a finite viscoelastic Ogden model with six material parameters–an elastic stiffness, two viscoelastic stiffnesses, a nonlinearity parameter, and two viscous time constants–to model the characteristic nonlinearity, conditioning, hysteresis and tension-compression asymmetry of the human brain. We calibrated the model under shear, shear relaxation, compression, compression relaxation, and tension for four different regions of the human brain, the cortex, basal ganglia, corona radiata, and corpus callosum. Strikingly, un- conditioned gray matter with 0.36 kPa and white matter with 0.35 kPa were equally stiff, whereas conditioned gray matter with 0.52 kPa was three times stiffer than white matter with 0.18 kPa. While both unconditioned viscous time constants were larger in gray than in white matter, both conditioned constants were smaller. These rheological differences suggest a different porosity between both tissues and explain–at least in part–the ongoing controversy between reported stiffness differences in gray and white matter. Our unconditioned and conditioned parameter sets are readily available for finite element simulations with commercial software packages that feature Ogden type models at finite deformations. As such, our results have direct implications on improving the accuracy of human brain simulations in health and disease.
Keywords: Human brain; Rheological testing; Finite viscoelasticity; Ogden model; Parameter identification

Vorstellung eines Simulationsbenchmarks für die Blechmassivumformung - Schmaltz, Stefan; Landkammer, Philipp; Beyer, Florian; Kumor, Dustin; Rademacher, Andreas; Blum, Heribert; Steinmann, Paul; Willner, Kai (Tagungsband zum 2. Erlanger Workshop Blechmassivumformung 2013, 2013)
In diesem Artikel wird ein Simulationsbenchmark vorgestellt, der einen repräsentativen Prozess der Blechmassivumformung beschreibt und sich eignet, Phänomene der Materialmodellierung, der Formoptimierung, der Modelladaptivität und des Einflusses von Reibmodellen aufzuzeigen. Als Demonstrator-Prozess dient die Herstellung eines Mitnehmerrings. Hierzu werden in eine Ronde acht Stempel eingedrückt. Für die Simulation eines solchen Umformprozesses ist es hinsichtlich der Materialmodellierung von Bedeutung, dass anisotrope Materialeigenschaften berücksichtigt werden. Auch der Einfluss des Reibmodells ist entscheidend. Die stark variierenden auftretenden Spannungen während des Umformprozesses führen dazu, dass die Reibschubspannungen in einigen Kontaktbereichen durch herkömmliche Modelle, wie Reibzahl- oder Reibfaktormodell, nicht korrekt wiedergegeben werden. Daher wird ein komplexeres konstitutives Reibgesetz vorgeschlagen, welches die Defizite des Reibzahl- und des Reibfaktormodells kompensiert. Die modelladaptive Rechnung zeigt, dass bei adaptiver Verwendung der verschiedenen Reibmodelle es nicht unbedingt erforderlich ist, auf das konstitutive Reibgesetz zurückzugreifen. Bereits das weniger komplexe Reibfaktormodell reicht aus, um ein bestimmtes Fehlermaß zu erreichen. Dadurch kann hinsichtlich des numerischen Aufwands in den Algorithmen Rechenzeit eingespart werden. Ferner ist es mittels der Formoptimierung möglich, eine undeformierte Rondengeometrie so zu berechnen, dass durch den nachfolgenden Referenz-Umformprozess eine gewünschte deformierte Bauteilform entsteht.
UnivIS-Import:2015-04-16:Pub.2013.tech.FT.FT-TM.vorste
Keywords: Blechmassivumformung; Materialmodellierung; Reibeinfluss; Formoptimierung; Modelladaptivität

Wall slip of magnetorheological elastomers in parallel-plate rotational rheometry - Walter, Bastian; Pelteret, Jean-Paul; Kaschta, Joachim; Schubert, Dirk W.; Steinmann, Paul (7. TA Anwendertreffen Rheologie - Erlangen, 2015)

Wrinkling instabilities in soft bi-layered systems - Budday, Silvia; Andres, Sebastian; Walter, Bastian; Steinmann, Paul; Kuhl, Ellen (Philosophical Transactions of the Royal Society A-Mathematical Physical and Engineering Sciences, 2017)
Wrinkling phenomena control the surface morphology of many technical and biological systems. While primary wrinkling has been extensively studied, experimentally, analytically and computationally, higher-order instabilities remain insufficiently understood, especially in systems with stiffness contrasts well below 100. Here, we use the model system of an elastomeric bilayer to experimentally characterize primary and secondary wrinkling at moderate stiffness contrasts. We systematically vary the film thickness and substrate prestretch to explore which parameters modulate the emergence of secondary instabilities, including period-doubling, period-tripling and wrinkle-to-fold transitions. Our experiments suggest that period-doubling is the favourable secondary instability mode and that period-tripling can emerge under disturbed boundary conditions. High substrate prestretch can suppress period-doubling and primary wrinkles immediately transform into folds. We combine analytical models with computational simulations to predict the onset of primary wrinkling, the post-buckling behaviour, secondary bifurcations and the wrinkle-to-fold transition. Understanding the mechanisms of pattern selection and identifying the critical control parameters of wrinkling will allow us to fabricate smart surfaces with tunable properties and to control undesired surface patterns like in the asthmatic airway.
Keywords: thin film; instability; bifurcation; period-doubling; period-tripling