A phenomenological model was formulated for treating the evolution of interacting dislocations in an isotropic elastic medium. The line-defect microstructure was described in terms of a spatially coarse-grained order parameter; the dislocation density tensor. The tensor field satisfied a conservation law which resulted from conservation of the Burgers vector. The dislocation motion was entirely dissipative and was assumed to be locally driven by the minimization of plastic free energy. The resultant equations of motion were developed to linear order in the dislocation density tensor, and gave rise to various stationary solutions.

Modelling of Dislocation Structures in Materials. J.M.Rickman, J.Viñals: Philosophical Magazine A, 1997, 75[5], 1251-62