Inserted: 23 oct 2014
Last Updated: 7 feb 2017
Journal: SIAM Journal on Applied Mathematics
CNA Preprint 14-CNA-025
The goal of this this paper is the analytical validation of a model of Cermelli and Gurtin for an evolution law for systems of screw dislocations under the assumption of antiplane shear. First, an expression for the so-called renormalized energy of the system is derived via a variational approach, and then it is used to derive an expression for the Peach-Köhler force, which drives the motion of the system. 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.
Keywords: Variational methods, differential inclusions, dislocation dynamics, renormalized energy