Analysis and comparison of two finite element algorithms for dislocation density based crystal plasticity

The purpose of the current work is the formulation and comparison of two finite element algorithms for a dislocation density based crystal plasticity model. We study multiscale inelastic materials whose behavior is influenced by the evolution of inelastic microstructure and the corresponding material or internal lengthscales. The work is an extension of the first investigation in Klusemann et al. [1] which was limited to a one-dimensional bar. In the γ -algorithm, the displacement u and glide system slips γ_α are global unknowns and determined via weak field relations. The non-dimensional densities of geometrically necessary dislocations ρ̄_α are local quantities and solved for via a strong field relation. In the Q -algorithm, both the displacement uand dislocation densities ρ̄_α are modeled as global, and the glide system slips γ_α as local. As it turns out, both algorithms generally predict the same microstructural behavior on a single crystal level. However, for a polycrystal the two solution strategies predict different material behaviors due to the formulation-dependent representation of the boundary conditions. The introduction of a boundary layer in the model leads to good agreement between both algorithms for single and polycrystal simulations.