A discontinuous Galerkin method for continuum dislocation dynamics in a fully-coupled elastoplasticity model

Classical continuum plasticity model fail to describe the size effects observed on micro-scale. For this reason, plasticity models which incorporate the dislocation microstructure are of great interest. The numerical simulation of dislocation motion on small scales is, however, unfeasible for engineering applications owing to the high computational expense. In a bottom-up approach, continuum dislocation theories aim to represent the underlying physical effects while keeping the numerical effort within reasonable limits. Despite the advances in the understanding of dislocation motion and interaction in a continuum framework, the numerical simulation of such models still entails high numerical costs. This work provides a numerical approximation method for elastoplasticity based on the continuum dislocation dynamics theory allowing for three-dimensional computations with multiple slip systems. Proceeding from a validation of the presented method in several numerical tests, it is applied to a tensile test of a tricrystalline geometry. The results are compared to discrete dislocation dynamics data.