In crystalline materials, plastic deformation was driven by the non-local long-range interaction of dislocations. This interaction was responsible for a series of features that obey scaling laws, such as the formation of fractal cellular structures, the intermittent plastic flow with scale-free avalanches following a power law and the Hall-Petch relation in which the yield stress depended on the sample size following a power law. A phase-field model of dislocations was described. The present theory was able to reproduce the jerky character of dislocation motion as well as size dependence in small-scale plasticity.

Scaling Laws in Plastic Deformation. M.Koslowski: Philosophical Magazine, 2007, 87[8-9], 1175-84