A multipolar expansion was presented for the interaction energy between dislocations in 3 dimensions; based upon a straightforward expansion of familiar energy expressions. An evaluation of the required line integrals was conveniently achieved by numerical integration over parametric representations of the dislocation loops. It was shown that the multipole expansion converged very quickly.

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