A reaction-diffusion equation was used to take account of both mobile and immobile dislocation behavior, and a stress-strain curve was calculated which reproduced the 3 stages that were observed experimentally. An homogeneous distribution of dislocations in its initial stages was destabilized, and heterogeneous pattern formation took place. Serrations which were seen in the early stages of deformation were explained in terms of a microscopic inhomogeneous multiplication of dislocations which led to self-organization.

Reaction-Diffusion Equation for Dislocation Multiplication Process. T.Shoji, S.Miura, T.Mohri: Materials Transactions, 2000, 41[5], 585-8