A fast convergent rate preserving discontinuous Galerkin framework for rate-independent plasticity problems

In this paper a finite element framework based on the incomplete interior penalty Galerkin formulation, a non-symmetric discontinuous Galerkin method, is consistently formulated for modeling plasticity problems with small deformation. Because of its pure displacement-based framework, this proposed discontinuous Galerkin method is possibly able to completely preserve numerical integration algorithms efficiently developed in the traditional continuous Galerkin framework. Besides stresses on element interior quadrature points, stresses on element surface quadrature points are also required to return on yielding surfaces in this discontinuous Galerkin framework, which is able to provide more accurate material yielding profiles than the continuous Galerkin framework. The performance of the proposed discontinuous Galerkin framework has been evaluated in detail for J2 and pressure-dependent plasticities using perfect plasticity, plasticity with hardening, and associative and non-associative material models. Quadratic convergent rates compatible to the tradition continuous Galerkin method for modeling plasticity problems have been achieved within a large penalty range in a nodal-based discontinuous Galerkin implementation.