The Frenkel-Kontorova model for an edge dislocation was analyzed. Solutions of the continuum limit of such a model (the sine-Gordon equation) were obtained in a form which was convenient for the investigation of the dynamics of a large number of interacting dislocations. On the basis of these solutions, various non-stationary processes (dislocation generation, diffusion of dislocations, crack/dislocation interaction) were considered. Simple relationships were found between the rate of plastic deformation, the density and velocity of dislocations, and the interaction force between dislocations. The nucleation of dislocations at a moving crack tip was analyzed.

N.I.Gershenzon: Physical Review B, 1994, 50[18], 13308-14