Variationally consistent self-stabilized Virtual Elements for 2D locking-free elastoplasticity

A variationally consistent numerical approach based on the Virtual Element Method (VEM) is presented for the analysis of 2D elastoplasticity problems. The mixed Hu-Washizu functional of elasticity is extended to incorporate the energy contributions specific to the finite-step elastoplastic problem. It is demonstrated how the governing equations of the discretized elastoplastic problem - including the loading-unloading conditions - emerge naturally as the stationarity conditions of the VEM-discretized functional. Spurious hourglass modes are prevented by formulating a self-stabilized version of Virtual Elements (VEs) that exploits the possibility offered by the mixed approach to define strain and displacement approximations of the same order. The insensitivity of VEs to element distortion and the possibility to use polygonal elements with any shape and number of edges is tested with the analysis of several benchmarks from the literature. It is shown how accurate solutions can be obtained also in the case of non-convex quadrilateral or pentagonal elements. Additionally, the role of internal moment degrees of freedom in preventing elastoplastic locking at the plastic failure limit is elucidated.