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

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

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

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

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.

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