VIRTUAL ELEMENT METHOD FOR COMPUTATIONAL HOMOGENIZATIONS OF UNIDIRECTIONAL FIBER-REINFORCED COMPOSITE MATERIALS

Abstract

The Virtual Element Method (VEM) is a generalization of the Finite Element Method (FEM) for the treatment of general polygonal/polyhedral mesh elements. Despite its recent introduction, VEM has been applied to several problems in structural mechanics. Due to such capability of dealing with mesh elements of general shape and of naturally addressing the presence of hanging nodes, the VEM ensures a noticeable simplification in the data preparation stage of the analysis, allowing implementing a mesh generation process over complex multi-domain geometries in a fully automated way. Moreover, for the lowest order VEM used in this contribution,no numerical integration is required to compute the system stiffness matrix, thus considerably reducing the computational cost of the analysis with respect to standard FEM. In this contribution, we present an application of the lowest order VEM to the material homogenisation of unidirectional (UD) fibre-reinforced materials. The representation of a material microstructure generally constitutes a remarkable effort in terms of input preparation, especially when there is not evident microstructural symmetry. For such a reason, computational icromechanics may represent a challenging benchmark for showing the potential of VEM, which forms the aim of the present work.