A 3-dimensional multi-dislocation system in a polycrystal under an applied stress was treated as being a particular case of the phase-field micro-elasticity theory of multivariant stress-induced martensitic transformations in polycrystals. This approach reduced the evolution of a dislocation system to the solution of a non-linear integrodifferential Ginzburg-Landau equation. In this formalism, the elastic interaction between dislocations and elastic coupling between grains were taken into account by an exact analytical solution to the elasticity problem. Dislocation reactions, such as multiplication and annihilation, were taken into account automatically.

Phase Field Micro-Elasticity Theory of Dislocation Dynamics in a Polycrystal - Model and Three-Dimensional Simulations. Y.M.Jin, A.G.Khachaturyan: Philosophical Magazine Letters, 2001, 81[9], 607-16