A Co-rotational Virtual Element Method for 2D Elasticity and Plasticity

TL;DR

This paper introduces a novel co-rotational virtual element method for 2D elasticity and plasticity that handles large displacements and rotations within a small strain framework, expanding VEM applications to nonlinear problems.

Contribution

It presents the first co-rotational VEM formulation for nonlinear solid mechanics, enabling efficient analysis of large displacements, rotations, and plasticity in 2D problems.

Findings

Successfully solves nonlinear elasticity and plasticity problems.

Demonstrates robustness of the co-rotational VEM in benchmark tests.

Provides implementation details and discusses future research directions.

Abstract

The virtual element method (VEM) allows discretization of the problem domain with polygons in 2D. The polygons can have an arbitrary number of sides and can be concave or convex. These features, among others, are attractive for meshing complex geometries. VEM applied to linear elasticity problems is now well established. Nonlinear problems involving plasticity and hyperelasticity have also been explored by researchers using VEM. Clearly, techniques for extending the method to nonlinear problems are attractive. In this work a novel first order consistent virtual element method is applied within a static co-rotational framework. To the author's knowledge this has not appeared before in the literature with virtual elements. The formulation allows for large displacements and large rotations in a small strain setting. For some problems avoiding the complexity of finite strains, and alternative stress measures, is warranted. Furthermore, small strain plasticity is easily incorporated. The basic method, VEM specific implementation details for co-rotation, and representative benchmark problems are illustrated. Consequently, this research demonstrates that the co-rotational VEM formulation successfully solves certain classes of nonlinear solid mechanics problems. The work concludes with a discussion of results for the current formulation and future research directions.