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 problem of the evolution of a dislocation system to the solution of a non-linear integrodifferential Ginzburg-Landau equation. In this formalism, elastic interactions between dislocations were taken into account via an exact analytical solution of the elasticity problem. Dislocation reactions, such as multiplication and annihilation, were automatically taken into account, and the dislocations were free to choose the optimum evolution path.

Application of Phase Field Microelasticity 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