Dislocation evolution during plastic deformation: Equations vs. discrete   dislocation dynamics study
  Equations for dislocation evolution bridge the gap between dislocation properties and continuum descriptions of plastic behavior of crystalline materials. Computer simulations can help us verify these evolution equations and find their fitting parameters. In this paper, we employ discrete dislocation dynamics to establish a continuum-based model for the evolution of the dislocation structure in polycrystalline thin films. Expressions are developed for the density of activated dislocation sources, as well as dislocation nucleation and annihilation rates. We demonstrate how size effect naturally enters the evolution equation. Good agreement between the simulation and the model results is obtained. The current approach is based on a two-dimensional discrete dislocation dynamics model, but can be extended to three-dimensional models. 
Kamyar M. Davoudi and Joost J. Vlassak
cond-mat.mtrl-sci