Arbitrary order 2D virtual elements for polygonal meshes: Part II, inelastic problem
For researchers in computational mechanics, this work provides a VEM formulation for inelastic problems on polygonal meshes, but it is an incremental extension of the authors' prior linear elastic VEM.
This paper extends a previously developed Virtual Element Method (VEM) for 2D continuum problems from linear elasticity to material nonlinearity, implementing three different nonlinear constitutive laws (viscoplastic, Mises plasticity, and shape memory alloy) and demonstrating through numerical examples that the method retains accuracy and ease of implementation comparable to standard nonlinear FEM.
The present paper is the second part of a twofold work, whose first part is reported in [3], concerning a newly developed Virtual Element Method (VEM) for 2D continuum problems. The first part of the work proposed a study for linear elastic problem. The aim of this part is to explore the features of the VEM formulation when material nonlinearity is considered, showing that the accuracy and easiness of implementation discovered in the analysis inherent to the first part of the work are still retained. Three different nonlinear constitutive laws are considered in the VEM formulation. In particular, the generalized viscoplastic model, the classical Mises plasticity with isotropic/kinematic hardening and a shape memory alloy (SMA) constitutive law are implemented. The versatility with respect to all the considered nonlinear material constitutive laws is demonstrated through several numerical examples, also remarking that the proposed 2D VEM formulation can be straightforwardly implemented as in a standard nonlinear structural finite element method (FEM) framework.