A continuum theory of edge dislocations

The relations obtained yield two outcomes: First, there is a state parameter of the system, dislocation polarization; averaged stresses affect only dislocation polarization and cannot change other characteristics of the system. Second, the structure of dislocation phase space is strikingly simple. Dislocation phase space is split in a family of subspaces corresponding to constant values of dislocation polarizations; in each equipolarization subspace there are many local minima of energy; for zero external stresses the system is stuck in a local minimum of energy; for non-zero slowly changing external stress, dislocation polarization evolves, while the system moves over local energy minima of equipolarization subspaces. Such a simple picture of dislocation dynamics is due to the presence of two time scales, slow evolution of dislocation polarization and fast motion of the system over local minima of energy. The existence of two time scales is justified for a neutral system of edge dislocations.