A node-based uniform strain virtual element method for elastoplastic solids

TL;DR

This paper extends the node-based uniform strain virtual element method (NVEM) to small strain elastoplastic solids, enabling accurate, locking-free simulations with all variables tracked at nodes, improving computational efficiency and precision.

Contribution

The paper introduces a novel extension of NVEM for elastoplastic solids, allowing all field variables to be tracked solely at nodes, enhancing accuracy and computational efficiency.

Findings

NVEM is locking-free in elastoplastic simulations.

The method achieves linearly precise results.

Validated through various benchmark problems.

Abstract

A recently proposed node-based uniform strain virtual element method (NVEM) is here extended to small strain elastoplastic solids. In the proposed method, the strain is averaged at the nodes from the strain of surrounding linearly precise virtual elements using a generalization to virtual elements of the node-based uniform strain approach for finite elements. The averaged strain is then used to sample the weak form at the nodes of the mesh leading to a method in which all the field variables, including state and history-dependent variables, are related to the nodes and thus they are tracked only at these locations during the nonlinear computations. Through various elastoplastic benchmark problems, we demonstrate that the NVEM is locking-free while enabling linearly precise virtual elements to solve elastoplastic solids with accuracy.