A continuum model for two-dimensional dislocation distributions

Abstract

Abstract Continuum models are formulated for two-dimensional arrays of screw and edge dislocations under the assumption that the dislocations are infinitely long and parallel. The models are formulated in terms of the number density of the dislocations and the boundary of the array, both of which are unknown. Some exact steady and unsteady solutions are presented in which the applied stress is spatially linear and the boundary is an ellipse inside which the number density of dislocations is constant.