Some links between Cosserat, strain gradient crystal plasticity and the statistical theory of dislocations

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