Dynamics for Systems of Screw Dislocations

<p>The goal of this paper is the analytical validation of a model of Cermelli and Gurtin [<em>Arch. Ration. Mech. Anal.</em>, 148 (1999), pp. 3--52] for an evolution law for systems of screw dislocations under the assumption of antiplane shear. The motion of the dislocations is restricted to a discrete set of glide directions, which are properties of the material. The evolution law is given by a “maximal dissipation criterion,” leading to a system of differential inclusions. Short time existence, uniqueness, cross-slip, and fine cross-slip of solutions are proved.<br><br></p>