Strain due to a continuous, isotropic distribution of screw dislocations

Abstract

The density for a continuous distribution of dislocations, represented by the torsion tensor, is separated into its two irreducible parts. One part characterizes an isotropic, homogeneous distribution of screw dislocations; the other, a mixture of screw and edge. A second order non-linear differential equation for the metric is established using the condition of zero affine curvature. In principle this equation can be solved for the metric once the distribution of dislocations is determined. The Robertson-Walker metric which describes an isotropic, homogeneous space is realized for an isotropic, homogeneous distribution of screw dislocations. The strain due to this distribution is then easily found from the simple relation between strain and metric.