Stabilization-free virtual element method for 2D elastoplastic problems

In this paper, a novel first- and second-order stabilization-free virtual element method is proposed for two-dimensional elastoplastic problems. In contrast to traditional virtual element methods, the improved method does not require any stabilization, making the solution of nonlinear problems more reliable. The main idea is to modify the virtual element space to allow the computation of the higher-order $L_2$ projection operator, ensuring that the strain and stress represent the element energy accurately. Considering the flexibility of the stabilization-free virtual element method, the elastoplastic mechanical problems can be solved by radial return methods known from the traditional finite element framework. $J_2$ plasticity with hardening is considered for modeling the nonlinear response. Several numerical examples are provided to illustrate the capability and accuracy of the stabilization-free virtual element method.