Arbitrary order 2D virtual elements for polygonal meshes: Part II, inelastic problem

TL;DR

This paper extends the Virtual Element Method (VEM) for 2D continuum problems to nonlinear materials, demonstrating its accuracy, ease of implementation, and versatility across various nonlinear constitutive laws through numerical examples.

Contribution

It introduces a nonlinear VEM formulation for 2D problems, capable of handling diverse nonlinear constitutive laws with straightforward implementation.

Findings

VEM maintains accuracy with nonlinear materials

The method is easily integrated into standard FEM frameworks

Numerical examples confirm versatility across different nonlinear laws

Abstract

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.