It was pointed out that a dislocation loop which moved with non-zero velocity, in a continuous elastic solid that was subject to time-dependent loads, experienced a so-called Lorentzian force. That is, a force that was linearly proportional to the dislocation velocity and to the time derivative of the elastic displacements due to time-dependent loads. It was also perpendicular to the motion, and so it did not do any work. Proofs of this were provided, as well as criticisms of previous arguments which had claimed that this force did not exist.

On the Nature of a Lorentzian Force on a Moving Dislocation F.Lund: Philosophical Magazine B, 1998, 78[2], 177-89