Calculus of Variations and Geometric Measure Theory

T. Blass - I. Fonseca - G. Leoni - M. Morandotti

Dynamics for Systems of Screw Dislocations

created by morandott on 23 Oct 2014
modified on 07 Feb 2017


Published Paper

Inserted: 23 oct 2014
Last Updated: 7 feb 2017

Journal: SIAM Journal on Applied Mathematics
Volume: 75
Pages: 393-419
Year: 2015
Doi: 10.1137/140980065

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