The geometry of continuous distributions of dislocations, and the secondary point defects which were created by these distributions, were considered. In particular, the dependence of a distribution of dislocations upon the existence of secondary point defects was modelled by treating dislocations being located in a time-dependent Riemannian material space which described, in the continuum limit, the influence of these point defects upon the metric properties of a crystal structure. The concepts of local glide systems and of involuted distributions of local slip planes were introduced in order to describe, in terms of differential geometry, some aspects of the kinematics of the motion of edge dislocations. The analysis led, among other things, to the definition of a class of distributions of dislocations having an involuted distribution of local slip planes. It was concluded that such that a formula, of mesoscale nature, was valid for the description of the effect of edge dislocations upon the mean curvature of glide surfaces.

Kinematics of Edge Dislocations - I. Involute Distributions of Local Slip Planes. A.Trzesowski: International Journal of Theoretical Physics, 1997, 36[12], 2877-93