A discontinuous Galerkin formulation for classical and gradient plasticity – Part 1: Formulation and analysis

A discontinuous Galerkin formulation is developed and analyzed for the cases of classical and gradient plasticity. The model of gradient plasticity is based on the von Mises yield function, in which dependence is on the isotropic hardening parameter and its Laplacian. The problem takes the form of a variational inequality of the second kind. The discontinuous Galerkin formulation is shown to be consistent and convergent. Error estimates are obtained for the cases of semi- and fully discrete formulations; these mimic the error estimates obtained for classical plasticity with the conventional Galerkin formulation.