Kinematics of edge dislocations. I: Involutive distributions of local slip planes (Q1388184)

The geometry of continuous distributions of dislocations and secondary point defects created by these distributions is considered. Particularly, the dependence of a distribution of dislocations on the existence of secondary point defects is modeled by treating dislocations as those located in a time-dependent Riemannian material space describing, in a continuous limit, the influence of these point defects on metric properties of a crystal structure. The notions of local glide systems and involutive distributions of local slip planes are introduced in order to describe, in terms of differential geometry, some aspects of the kinematics of the motion of edge dislocations.