Deformation band patterns and dislocation structures in finite strain crystal viscoplasticity

Deformation band patterning in single crystals is investigated using a finite strain crystal viscoplasticity model based on the evolution of dislocation densities. In the presence of strong latent hardening and weak rate dependence, the deformation organizes into laminate microstructures consisting of single-slip regions separated by dislocation walls. The influence of material and numerical parameters on the nucleation and morphology of these patterns is analyzed in 2D single crystals under plane strain compression. Pattern formation is also observed in 3D single-crystal cylinders subjected to tension, where the characteristic size of deformation microstructures is found to depend on mesh size and boundary conditions in the absence of an intrinsic material length scale. To address this limitation, strain gradient plasticity is introduced, providing a length scale that governs the size of the patterns. Finally, we demonstrate that deformation patterns and dislocation structures also emerge in 2D and 3D polycrystals, highlighting the generality of the phenomenon. • A finite strain crystal viscoplasticity model based on dislocation density evolution is presented and extended to incorporate strain gradient effects. • Deformation patterns naturally emerge under conditions of strong latent hardening and minimal rate dependence. • Lamination patterns lead to the formation of dislocation structures, including sub-grain boundaries. • Strain gradient plasticity introduces a material length scale that governs the characteristic size of deformation microstructures. • In both 2D and 3D polycrystals, deformation patterns and dislocation structures develop when the spatial resolution is sufficiently fine.