Flexible boundary conditions and nonlinear geometric effects in atomic dislocation modeling

A technique is described for applying flexible boundaries to an atomic region in computer simulation of dislocations or other line defects. The method results in continuity of equilibrium, under the chosen interatomic potential, across the interface between the atomic region and the outer region described in terms of anisotropic elastic continuum solutions. The technique has high numerical efficiency. It is shown that when the crystal is initially dislocated according to the Volterra solution for displacements, the finite strains give rise to geometrical nonlinear effects, usually disregarded in linear elasticity, which contribute to a volume change of the crystal. Allowance for this effect, and for elastic nonlinearity in the crystal beyond the boundary region, allows the overall dilatation of a finite body due to the dislocation to be rigorously computed. For illustration of the geometric nonlinear effect, and for comparison with earlier modeling methods, examples of computations are given for the 100 edge dislocation in α iron.