A low order 3D virtual element formulation for finite elasto-plastic deformations

This work addresses an efficient low order 3D virtual element method for elastic-plastic solids undergoing large deformations. Virtual elements were introduced in the last decade and applied to various problems in solid mechanics. The successful application of the method to non-linear problems such as finite strain elasticity and plasticity in 2D leads naturally to the question of its effectiveness and robustness in the third dimension. This work is concerned with the extensions of the virtual element method to problems of 3D finite strain plasticity. Low-order formulations for problems in three dimensions, with elements being arbitrary shaped polyhedra, are considered. The formulation is based on minimization of a pseudo energy expression, with a generalization of a stabilization techniques, introduced for two dimensional polygons, to the three-dimensional domain. The resulting discretization scheme is investigated using different numerical examples that demonstrate efficiency, accuracy and convergence properties. For comparison purposes, results of the standard finite element method are also demonstrated.