The classical approach to the dislocation problem in linear equilibrium elasticity was considered, and a formulation was provided in terms of variational principles. It was pointed out that, even if the energy functional was not finite in the presence of a dislocation, it was still possible to define a function of the defect position alone: the normalized energy. This had a close relationship to the familiar Peach-Kohler force. The case of anti-plane shear and linear isotropic elasticity was treated, because of the possibility of an explicit representation of the fields involved.

A Singular Variational Problem in Dislocation Theory. E.Buzano, P.Cermelli: Zeitschrift für Angewandte und Mathematische Physik, 2000, 51[6], 968-83