Virtual Elements for computational anisotropic crystal plasticity

authored by: Christoph Böhm, Lukas Munk, Blaž Hudobivnik, Fadi Aldakheel, Jože Korelc, Peter Wriggers
Abstract: In this contribution, the Virtual Element Method (VEM) with a linear ansatz is applied to a computational crystal plasticity framework in a micro-structural environment. Furthermore, a simple anisotropic energetic contribution, based on invariant-formulations of tensorial deformation measures and structural tensors, is presented for the cubic elastic anisotropy of the underlying crystal structure. The anisotropic elastic formulation recovers the elasticity tensor structure of a cubic material in the limit of small deformations. The authors propose a new stabilization degradation formulation which is purely based on the dissipative response of the problem. Representative examples illustrate the robustness and performance of VEM with regard to locking phenomena in the crystal plasticity framework, when bench-marked against the solutions of classical finite element approaches. Further examples investigate the performance and current limitations of VEM within a crystal plasticity framework, when being applied to heterogeneous microstructures for both, structured element topology as well as flexible element topology.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Technische Universität Dresden
Swansea University
University of Ljubljana
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 405
ISSN: 0045-7825
Publication date: 15.02.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, Physics and Astronomy(all), Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.cma.2022.115835 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{8a4b45cbed764a718f412f9b5f7ba632,
title = "Virtual Elements for computational anisotropic crystal plasticity",
abstract = "In this contribution, the Virtual Element Method (VEM) with a linear ansatz is applied to a computational crystal plasticity framework in a micro-structural environment. Furthermore, a simple anisotropic energetic contribution, based on invariant-formulations of tensorial deformation measures and structural tensors, is presented for the cubic elastic anisotropy of the underlying crystal structure. The anisotropic elastic formulation recovers the elasticity tensor structure of a cubic material in the limit of small deformations. The authors propose a new stabilization degradation formulation which is purely based on the dissipative response of the problem. Representative examples illustrate the robustness and performance of VEM with regard to locking phenomena in the crystal plasticity framework, when bench-marked against the solutions of classical finite element approaches. Further examples investigate the performance and current limitations of VEM within a crystal plasticity framework, when being applied to heterogeneous microstructures for both, structured element topology as well as flexible element topology.",
keywords = "AceGen, Crystal plasticity, Crystalline microstructure, Cubic anisotropy, Finite deformation, Virtual element method (VEM)",
author = "Christoph B{\"o}hm and Lukas Munk and Bla{\v z} Hudobivnik and Fadi Aldakheel and Jo{\v z}e Korelc and Peter Wriggers",
note = "Funding Information: CB, FA and PW gratefully acknowledge the German Research Foundation (DFG, Deutsche Forschungsgemeinschaft) for financial support to this work with the Collaborative Research Centre 1153 (CRC 1153) “Process chain for the production of hybrid high-performance components through tailored forming” with the subproject C4 “Modelling and Simulation of the Joining Zone”, project number 252662854 . LM and PW thank for financial support of this study by the German research foundation (DFG, Deutsche Forschungsgemeinschaft) under contract WR19/57-1 . BH and PW gratefully acknowledge financial support to this work by the German Research Foundation (DFG) with the cluster of excellence PhoenixD (EXC 2122, Project ID 390833453 ). This work was supported by the compute cluster, which is funded by the Leibniz Universit{\"a}t Hannover, Germany , the Lower Saxony Ministry of Science and Culture (MWK), Germany and the German Research Association (DFG) . ",
year = "2023",
month = feb,
day = "15",
doi = "10.1016/j.cma.2022.115835",
language = "English",
volume = "405",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}