It was noted that meso-scale simulations had been developed in order to understand the collective behaviour of dislocations, and their effects upon mechanical response. These simulations discretized the dislocations into segments which were then allowed to move in a 3-dimensional discrete network which was a sub-lattice of the original crystalline lattice network. The minimum distance between 2 points was defined by the annihilation distance of 2 edge dislocations. That is, by the minimum distance at which 2 edge dislocations could coexist without instantaneous collapse. Elastic theory was still applicable in the simulated volume because the minimum distance was large when compared to the dislocation-core radius within which non-linear expressions had to be taken into account in dislocation-dislocation interactions. This property permitted the use of the superposition principle when imposing boundary conditions on the simulation box. Details were given of the rigorous boundary conditions which had to be applied when the simulation box was a bulk crystal, a free-standing film or a finite crystal which was submitted to complex loadings.

Developing Rigorous Boundary Conditions to Simulations of Discrete Dislocation Dynamics. M.C.Fivel, G.R.Canova: Modelling and Simulation in Materials Science and Engineering, 1999, 7[5], 753-68