Developing rigorous boundary conditions to simulations of discrete dislocation dynamics

Mesoscale simulations have recently been developed in order to better under stand the collective behaviour of dislocations and their effects on the mec hanical response. Those simulations deal with dislocations discretized into segments which are allowed to move in a three-dimensional (3D) discrete ne twork. This network is a sublattice of the original crystalline lattice net work. The minimum distance between two points is defined by the annihilatio n distance for two edge dislocations, i.e. the minimum distance for which t wo edge dislocations can coexist without instantaneous collapse. The elasti c theory can still be applied in the simulated volume, since the minimum di stance is large compared to the dislocation core radius within which nonlin ear expressions should be taken into account in the dislocation-dislocation interaction. This property allows us to use the superposition principle to enforce boundary conditions on the simulation box. This paper details the rigorous boundary conditions applied when the simulation box is supposed to be either a bulk crystal, a free standing film or a finite crystal submitt ed to a complex loading.