On the nature of a Lorentzian force on a moving dislocation

Abstract

A dislocation loop that moves with a non-zero velocity in a continuous elastic solid subject to time-dependent loads is subject to a ‘Lorentzian’ force that is linearly proportional to the dislocation velocity and to the time derivative of the elastic displacements due to the time-dependent loads. It is also perpendicular to the motion so that it does not do work. Proofs of this statement are offered, as well as criticism of previous arguments which claimed that this force is non-existent. The possible relevance of this result to the understanding of the dynamic instability of cracks in thin brittle plates is discussed.