Reaction-diffusion equation for dislocation multiplication process

The evolution of dislocation densities based on reaction-diffusion (R-D) type partial differential equation that yields a stress-strain curve and provides microscopic insight of multiplication process is described. The details of stability analysis and self-organized dislocation patterns are also discussed. Based on R-D equations formulated for mobile and immobile dislocations, a stress-strain curve is calculated. The existence of three distinctive stages in the stress-strain curve are reproduced in the calculations.