The interaction between dislocations was long-range and anisotropic, leading to severe computational challenges for large-scale simulations. A multipolar expansion was presented here for the interaction energy between dislocations in 3 dimensions, based upon a straightforward expansion of some familiar energy expressions. An evaluation of the required line integrals was conveniently performed by numerical integration over parametric representations of the dislocation loops. It was shown that the multipole expansion converges very quickly, leading to potential savings in computational time for evaluating dislocation interactions.

Multipole Expansion of Dislocation Interactions - Application to Discrete Dislocations. R.LeSar, J.M.Rickman: Physical Review B, 2002, 65[14], 144110 (6pp)