2014/10/23 by Timothy Blass, Irene Fonseca, Blass, Timothy +5
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS
paper · pdf · doi:10.48550/arxiv.1410.6306
35 pages, 5 figures
arxiv created 2014/10/23 · arxiv updated 2014/10/24
The goal of 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. 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.