A 3-dimensional multi-dislocation system, in an elastically anisotropic crystal under an applied stress, was considered to be a particular case of the phase-field micro-elasticity theory of multivariant stress-induced martensitic transformations. This approach reduced the evolution of the dislocation system to the solution of the non-linear integrodifferential Ginzburg-Landau equation. The elastic interaction between dislocations was incorporated via an exact analytical solution to the elasticity problem. Dislocation reactions, such as multiplication and annihilation, were automatically taken into account. The dislocations were able to choose the optimum evolution path.

Application of Phase Field Micro-Elasticity Theory of Phase Transformations to Dislocation Dynamics: Model and Three-Dimensional Simulations in a Single Crystal. Y.U.Wang, Y.M.Jin, A.M.Cuitiño, A.G.Khachaturyan: Philosophical Magazine Letters, 2001, 81[6], 385-93