If there was an equilibrium arrangement of a given collection of dislocations, each having a fixed size and shape, in an externally loaded or unloaded elastic body, the corresponding potential energy will be stationary with respect to infinitesimal perturbations of the dislocation positions. This led to the dislocation equilibrium conditions: the Peach–Koehler forces along the dislocation line of each dislocation due to externally applied stress and the interaction of the dislocation with other dislocations and its own image field was a set of self-equilibrated forces. The earlier proof of this result presented in the literature was based upon an incomplete expression for the elastic strain energy. This was modified here by using the elastic strain energy expression that accounted for all dislocation core energy.

Dislocation Equilibrium Conditions Revisited. V.A.Lubarda: International Journal of Solids and Structures, 2006, 43[11-12], 3444-58