TY - JOUR

T1 - Electro-magneto-mechanically response of polycrystalline materials: Computational homogenization via the Virtual Element Method

AU - Böhm, Christoph

AU - Hudobivnik, Blaž

AU - Marino, Michele

AU - Wriggers, Peter

N1 - Funding Information: CB and PW gratefully acknowledge the German Research Foundation (DFG, Deutsche Forschungsgemeinschaft) for financial support to this work with the Collaborative Research Center 1153 (CRC 1153) “Process chain for the production of hybrid high-performance components through tailored forming” with the subproject C4 “Modeling and Simulation of the Joining Zone”, project number 252662854. MM acknowledges the Italian Ministry of Education, University and Research (MIUR) for funding in the framework of the Rita Levi Montalcini Program (Programma per Giovani ricercatori – anno 2017 “Rita Levi Montalcini”). BH and PW gratefully acknowledge financial support to this work by the German Research Foundation (DFG) with the cluster of excellence PhoenixD (EXC 2122).

PY - 2021/7

Y1 - 2021/7

N2 - This work presents a study on the computational homogenization of electro-magneto-mechanically coupled problems through the Virtual Element Method (VEM). VE-approaches have great potential for the homogenization of the physical properties of heterogeneous polycrystalline microstructures with anisotropic grains. The flexibility in element shapes can be exploited for creating VE-mesh with a significant lower number of degrees of freedom if compared to finite element (FE) meshes, while maintaining a high accuracy. Evidence that VE-approaches outperform FEM is available in the literature, but only addressing purely-mechanic problems (i.e. elastic properties) and transversely anisotropic materials. The aim of this work is twofold. On one hand, the study compares VE-and FE-based numerical homogenization schemes for electro-mechanically coupled problems for different crystal lattice structures and degrees of elastic anisotropy. Within all considered materials, the VE-approach outperforms the FE-approach for the same number of nodes. On the other hand, a hybrid microstructure made up by both electro-mechanical and magneto-mechanical grains is investigated resulting in an electro-magneto-mechanically coupled microstructure. Again, VEM provides a more accurate solution strategy.

AB - This work presents a study on the computational homogenization of electro-magneto-mechanically coupled problems through the Virtual Element Method (VEM). VE-approaches have great potential for the homogenization of the physical properties of heterogeneous polycrystalline microstructures with anisotropic grains. The flexibility in element shapes can be exploited for creating VE-mesh with a significant lower number of degrees of freedom if compared to finite element (FE) meshes, while maintaining a high accuracy. Evidence that VE-approaches outperform FEM is available in the literature, but only addressing purely-mechanic problems (i.e. elastic properties) and transversely anisotropic materials. The aim of this work is twofold. On one hand, the study compares VE-and FE-based numerical homogenization schemes for electro-mechanically coupled problems for different crystal lattice structures and degrees of elastic anisotropy. Within all considered materials, the VE-approach outperforms the FE-approach for the same number of nodes. On the other hand, a hybrid microstructure made up by both electro-mechanical and magneto-mechanical grains is investigated resulting in an electro-magneto-mechanically coupled microstructure. Again, VEM provides a more accurate solution strategy.

KW - Computational homogenization

KW - Electro-magneto-mechanics

KW - Microstructure

KW - Virtual Element Method (VEM)

UR - http://www.scopus.com/inward/record.url?scp=85103279626&partnerID=8YFLogxK

U2 - 10.1016/j.cma.2021.113775

DO - 10.1016/j.cma.2021.113775

M3 - Article

VL - 380

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

SN - 0045-7825

M1 - 113775

ER -