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

TL;DR

This paper demonstrates that the Virtual Element Method (VEM) offers superior accuracy and efficiency over traditional finite element methods in the computational homogenization of electro-magneto-mechanically coupled polycrystalline materials, including hybrid microstructures.

Contribution

It introduces a VEM-based homogenization approach for electro-magneto-mechanical problems and compares its performance with FEM across various microstructures and anisotropies.

Findings

VEM outperforms FEM for the same number of nodes in electro-mechanical problems.

VEM provides more accurate solutions for hybrid electro-magneto-mechanical microstructures.

VEM reduces degrees of freedom while maintaining high accuracy.

Abstract

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 are 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 a electro-magneto-mechanically coupled microstructure. Again, VEM provides a more accurate solution strategy.