A Taylor–Hood type virtual element formulations for large incompressible strains

Considerable progress has been made during the last decade with respect to the development of discretization techniques that are based on the virtual element method. Here we construct a new scheme for large strain problems that include incompressible material behavior. The idea is to use a formulations analogous to the classical Taylor–Hood element, Taylor and Hood (1972) which is based on a mixed principle where different interpolation functions are used for the deformation and pressure field. In this paper, a quadratic serendipity ansatz for the displacements is combined with a linear pressure field which leads to new virtual element formulations that are discussed and compared in this paper.