Extended modelling of dislocation transport-formulation and finite element implementation

In the past decade, several higher-order crystal plasticity models have been developed to properly capture size effects, dislocation pile-up and patterning. Here we consider a formulation which accounts for the presence and behavior of both positive and negative dislocations in terms of densities. We derive an implicit finite element implementation for the continuum crystal plasticity model including dislocation transport, using a generalised continuum expression for the short-range dislocation interactions, by discretizing the two governing non-linear transport equations in time and space. The resulting non-linear algebraic equations are solved by an incremental-iterative solution scheme. We compare the resulting numerical solutions with discrete dislocation simulations. This analysis shows the capabilities of the implicit FEM framework to solve continuum dislocation transport in crystal plasticity with the added energetic dislocation interactions