Phase-field theory, and a model, were developed for describing multi-dislocation dynamics in an elastically anisotropic crystal under an applied stress. The proposed 3-dimensional model was a particular case of a published phase-field micro-elasticity model for stress-induced martensitic transformations. A spontaneous self-organization of dislocations in the evolving ensemble, involving multiplication/annihilation and movement of dislocations controlled by their elastic interaction, could described by the Ginzburg–Landau kinetic equation.

Phase Field Microelasticity Theory and Modelling of Multiple Dislocation Dynamics. Y.U.Wang, Y.M.Jin, A.M.Cuitiño, A.G.Khachaturyan: Applied Physics Letters, 2001, 78[16], 2324-6