A node-based uniform strain virtual element method for compressible and nearly incompressible elasticity

TL;DR

This paper introduces the node-based uniform strain virtual element method (NVEM), a displacement-based approach that accurately models compressible and nearly incompressible elasticity without volumetric locking, suitable for nonlinear simulations.

Contribution

The paper develops NVEM, a novel virtual element method that averages strain at nodes, avoiding additional degrees of freedom and volumetric locking, with proven optimal convergence.

Findings

NVEM is accurate for elasticity problems.

NVEM is free from volumetric locking.

NVEM shows optimal convergence in benchmarks.

Abstract

We propose a combined nodal integration and virtual element method for compressible and nearly incompressible elasticity, wherein the strain is averaged at the nodes from the strain of surrounding virtual elements. For the strain averaging procedure, a nodal averaging operator is constructed using a generalization to virtual elements of the node-based uniform strain approach for finite elements. We refer to the proposed technique as the node-based uniform strain virtual element method (NVEM). No additional degrees of freedom are introduced in this approach, thus resulting in a displacement-based formulation. A salient feature of the NVEM is that the stresses and strains become nodal variables just like displacements, which can be exploited in nonlinear simulations. Through several benchmark problems in compressible and nearly incompressible elasticity as well as in elastodynamics, we demonstrate that the NVEM is accurate, optimally convergent and devoid of volumetric locking.