A Particle Virtual Element Method for Elastoplastic Solids

Abstract

A particle method for elastoplastic solids that is formulated from the virtual element method (VEM) is presented. The proposed scheme is termed the particle virtual element method (PVEM). In the PVEM, the strain tensor is obtained directly at the nodes from the strain of the surrounding virtual elements using a nodal operator that is constructed for this purpose. In this scheme, the first-order virtual element approximation is used without introducing additional degrees of freedom, resulting in a displacement-based formulation. The stabilization of the method is inherited from the virtual element framework. A distinctive feature of the PVEM is that state- and history-dependent variables are stored and tracked directly at the nodes, thereby facilitating the handling of these variables within the nonlinear solver and in the post-processing stage. Through some standard benchmark tests in elastoplasticity, it is demonstrated that the PVEM enables first-order virtual elements to solve elastoplastic solids problems with precision and robustness.