Virtual Element Methods for Engineering Applications

Discretization schemes that base on the virtual element method (VEM) have gained over the last decade interest in the engineering community. VEM was applied to different problems in elasticity, elasto-plasticity, fracture and damage mechanics using different theoretical formulations like phase field approaches. For predictive simulations of such problems as well linear as nonlinear weak formulations have to be considered. This contribution is concerned with extensions of the virtual element method to problems of nonlinear nature where VEM has advantages, like in micromechanics, fracture and contact mechanics. Low-order formulations for problems in two dimensions, with elements being arbitrary polygons, are considered.