A variational approach was presented to calculate the stress field generated by a system of dislocations. It was shown that in the simplest case, when the material containing the dislocations obeys Hooke's law, the variational framework gave the same field equations as Kröner's theory. However, the proposed variational method permitted the study of many other problems, such as dislocation core regularization, the role of elastic anharmonicity and the dislocation-solute atom interaction. The present aim was to demonstrate that these problems could be handled in a systematic manner.

Variational Approach in Dislocation Theory. I.Groma, G.Györgyi, P.D.Ispánovity: Philosophical Magazine, 2010, 90[27-28], 3679-95