Variational approach in dislocation theory

A variational approach is presented to calculate the stress field generated by a system of dislocations. It is shown that in the simplest case, when the material containing the dislocations obeys Hooke's law the variational framework gives the same field equations as Kr\"oner's theory. However, the variational method proposed allows to study many other problems like dislocation core regularisation, role of elastic anharmonicity and dislocation--solute atom interaction. The aim of the paper is to demonstrate that these problems can be handled on a systematic manner.