High-order virtual element method for the homogenization of long fiber nonlinear composites

A high-order virtual element method (VEM) for homogenization of long fiber reinforced composites is presented. In particular, periodic composites are considered studying square or rectangular unit cell arrays and circular inclusions. A suitable displacement representation form is adopted reducing the three-dimensional problem to an equivalent two-dimensional one. Material nonlinearity is taken into account for the matrix which can be plastic or visco-plastic. The formulation is proposed for linear and high-order virtual elements. Numerical applications are performed to assess the accuracy of the VEM formulation in comparison with the classical finite element approach. In particular, convergence investigations on the overall elastic moduli and on the Mises equivalent stress are performed. Elasto-plastic and visco-plastic analyses are carried out exploiting the local mesh refinement features typical of VEM showing efficiency of polygonal discretizations.