A low order virtual element formulation for finite elasto-plastic deformations

The virtual element method has been developed over the last decade and applied to problems in elasticity and other areas. The successful application of the method to linear problems leads naturally to the question of its effectiveness in the nonlinear regime. This work is concerned with extensions of the virtual element method to problems of finite strain plasticity. Low-order formulations for problems in two dimensions, with elements being arbitrary polygons, are considered. The formulation is based on minimization of an incremental energy expression, with a novel construction of the stabilization energy for elasto-plasticity. The resulting discretization scheme is investigated using different numerical examples that demonstrate efficiency, accuracy and convergence properties.