Inserted: 4 dec 2018
Last Updated: 4 dec 2018
Journal: Journal of Nonlinear Science
In this paper we provide an existence result for the energetic evolution of a set of dislocation lines in a three-dimensional single crystal. The variational problem consists of a polyconvex stored-elastic energy plus a dislocation energy and some higher-order terms. The dislocations are modeled by means of integral one-currents. Moreover, we discuss a novel dissipation structure for such currents, namely the flat distance, that will serve to drive the evolution of the dislocation clusters.