VEM Approach for Homogenization of Fibre-Reinforced Composites with Curvilinear Inclusions

Abstract

We propose a curvilinear virtual element method (VEM) for the asymptotic homogenization of fibre-reinforced composites with straight long fibres having general curvilinear cross sections. This technique is able to exactly represent the microstructural curvilinear geometry still granting all the standard features of VEM methods for elliptical boundary value problems. Themethod is here applied to doubly periodic fibre arrangements. Accuracy and computational efficiency of the proposed homogenization procedure is confirmed by numerical examples by comparison with semi-analytical solutions.