Virtual Element Formulation for Finite Plasticity

The application of virtual elements covers a wide range in solid mechanics. Besides pure elastic behaviour, material models can be introduced that include path dependency and thus history variables. The treatment of such constitutive models needs a special approach with respect to algorithms and the formulation of the virtual element method. The details will be discussed in the following for the case of three-dimensional von Mises plasticity at finite strains. This chapter follows the approach provided in Wriggers and Hudobivnik (2017) and Hudobivnik et al. (2018). Application of virtual element discretizations for rolling processes involving plastic behaviour can be found in Böhm et al. (2020). Extensions to applications involving anisotropic crystal-plasticity are discussed in Böhm et al. (2023).