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

Phase field Micro-Elasticity 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