  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.
