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

A novel energy-fitted hexagonal quadrature scheme enables low-cost and high-fidelity peridynamic computations - Schaller, Emely; Javili, Ali; Steinmann, Paul (Computer Methods in Applied Mechanics and Engineering, 2025)
In this contribution, we propose a novel hexagonal quadrature scheme for one-neighbor interactions in continuum-kinematics-inspired peridynamics equivalent to bond-based peridynamics. The hexagonal quadrature scheme is fitted to correctly integrate the stored energy density within the nonlocal finite-sized neighborhood of a continuum point subject to affine expansion. Our proposed hexagonal quadrature scheme is grid-independent by relying on appropriate interpolation of pertinent quantities from collocation to quadrature points. In this contribution, we discuss linear and quadratic interpolations and compare our novel hexagonal quadrature scheme to common grid-dependent quadrature schemes. For this, we consider both, tetragonal and hexagonal discretizations of the domain. The accuracy of the presented quadrature schemes is first evaluated and compared by computing the stored energy density of various prescribed affine deformations within the nonlocal neighborhood. Furthermore, we perform three different boundary value problems, where we measure the effective Poisson's ratio resulting from each quadrature scheme and evaluate the deformation of a unit square under extension and beam bending. Key findings of our studies are: The Poisson's test is a good indicator for the convergence behavior of quadrature schemes with respect to the grid density. The accuracy of quadrature schemes depends, as expected, on their ability to appropriately capture the deformation within the nonlocal neighborhood. Our novel hexagonal quadrature scheme, rendering the correct effective Poisson's ratio of 1/3 for small deformations, together with quadratic interpolation consequently yields the most accurate results for the studies presented in this contribution, thereby effectively reducing the computational cost.
CRIS-Team Scopus Importer:2025-04-01
Keywords: Accuracy; Computational efficiency; Peridynamics; Quadrature scheme

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

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

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)

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)