A virtual element method for transversely isotropic hyperelasticity

This work considers the application of a low-order displacement-based virtual element method (VEM) to plane problems of transversely isotropic hyperelasticity, with a novel approach to the computation of stabilization parameters. The method is applied to a range of numerical examples and a variety of transversely isotropic material models are considered. For each of the material models the performance of the virtual element method is investigated under varying degrees of compressibility and extensibility, including near-incompressibility and near-inextensibility, both separately and in combination. Through the range of examples the convergence behaviour of the method is demonstrated with robust, accurate and locking-free behaviour exhibited for all considered choices of material model and material parameter.