Dynamics for Systems of Screw Dislocations

TL;DR

This paper analytically validates a model for the evolution of screw dislocation systems under antiplane shear, proving key properties like existence, uniqueness, and complex slip behaviors.

Contribution

It provides the first rigorous mathematical validation of a dislocation evolution law with detailed solution properties under specific shear conditions.

Findings

Proved short time existence and uniqueness of solutions.

Established conditions for cross-slip and fine cross-slip behaviors.

Validated the maximal dissipation criterion for dislocation motion.

Abstract

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.