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 concluded 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 only. This was a normalized energy which had a close similarity to the celebrated Peach-Kohler force. The cases of anti-plane shear and linear isotropic elasticity were treated.

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