English

A virtual element method for isotropic hyperelasticity

Numerical Analysis 2020-06-24 v2 Numerical Analysis Analysis of PDEs

Abstract

This work considers the application of the virtual element method to plane hyperelasticity problems with a novel approach to the selection of stabilization parameters. The method is applied to a range of numerical examples and well known strain energy functions, including neo-Hookean, Mooney-Rivlin and Ogden material models. For each of the strain energy functions the performance of the method under varying degrees of compressibility, including near-incompressibility, is investigated. Through these examples the convergence behaviour of the virtual element method is demonstrated. Furthermore, the method is found to be robust and locking free for a variety of element geometries, including elements with a high degree of concavity.

Keywords

Cite

@article{arxiv.1910.09459,
  title  = {A virtual element method for isotropic hyperelasticity},
  author = {Daniel van Huyssteen and Batmanathan Dayanand Reddy},
  journal= {arXiv preprint arXiv:1910.09459},
  year   = {2020}
}
R2 v1 2026-06-23T11:50:05.448Z