Aa continuum model was proposed for the evolution of the total dislocation densities in face-centred cubic crystals, within the framework of rate-independent plasticity. The basic physical features which were taken into account were the role of dislocations in hardening, the relationships between the slip velocity and dislocation mobility, the energetics of self- and mutual interactions between dislocations, non-local effects in the interaction between dislocations. A set of reaction–diffusion equations was obtained, with mobilities which depended upon the slip velocities. These were able to describe the formation of dislocation walls and cells.

Dislocation Patterns and Work-Hardening in Crystalline Plasticity. L.Bortoloni, P.Cermelli: Journal of Elasticity, 2004, 76[2], 113-38