  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.
