A Virtual Element Method for transversely isotropic elasticity

TL;DR

This paper develops a low-order Virtual Element Method for transversely isotropic elasticity problems, demonstrating robustness and locking-free performance in both homogeneous and non-homogeneous cases with various geometries.

Contribution

It introduces a novel VEM approach tailored for transversely isotropic elasticity, including non-homogeneous fibre directions, with extensive numerical validation.

Findings

VEM is robust and locking-free for various geometries.

Method effectively handles near-incompressibility and near-inextensibility.

Performance confirmed for both homogeneous and non-homogeneous fibre directions.

Abstract

This work studies the approximation of plane problems concerning transversely isotropic elasticity, using a low-order Virtual Element Method (VEM), with a focus on near-incompressibility and near-inextensibility. Additionally, both homogeneous problems, in which the plane of isotropy is fixed; and non-homogeneous problems, in which the fibre direction defining the isotropy plane varies with position, are explored. In the latter case various options are considered for approximating the non-homogeneous fibre directions at element level. Through a range of numerical examples the VEM approximations are shown to be robust and locking-free for several element geometries and for fibre directions that correspond to mild and strong non-homogeneity.