A link was established between a phenomenological Cosserat model of crystal plasticity and results obtained from the statistical theory of dislocations. The existence of a back-stress, related to the divergence of the couple stress tensor, was derived. According to several dislocation-based models of single slip, the kinematic hardening modulus was inversely proportional to the dislocation density. Phenomenological extensions to multi-slip situations could be proposed, based upon these generalized continuum approaches.

Some Links between Cosserat, Strain Gradient Crystal Plasticity and the Statistical Theory of Dislocations. S.Forest: Philosophical Magazine, 2008, 88[30-32], 3549-63