The virtual element method for the numerical homogenization of electro-mechanical responses

The virtual element method (VEM) has been attracting interest for applications in micromechanical homogenization. This work aims to introduce and analyze multiphysical formulations in a VEM-based numerical homogenization scheme. Addressing electromechanical polycrystalline materials, the performance of a VEM-based approach with respect to FEM-based approaches is investigated. Results show the outperformance of VEM with respect to FEM models (with the same number of degrees of freedom) on the obtained value of homogenized quantities. The coarse mesh permitted by the VEM rationale, where each grain might represent one element, allows to maintain a low computational cost with a high accuracy.