On the Theory of Dislocations

TLDR: In this article, it was shown that dislocations of a more general type than encountered in classical theory can be obtained for states of plane and anti-plane strain in a hollow right circular cylinder when the surface of discontinuity is a single stationary plane barrier.

Abstract: If, in a multiply‐connected elastic solid, discontinuities are permitted across a stationary barrier in either the strain or its first derivatives or both, dislocations of a more general type than encountered in classical theory are possible. A number of these more general dislocations have been obtained for states of plane and anti‐plane strain in a hollow right circular cylinder when the surface of discontinuity is a single stationary plane barrier. Some of the dislocations found possess the characteristic that although the strain is continuous across the barrier the displacement discontinuity is not one which would be possible in a rigid body. Examination of the conditions for the uniqueness of solution of the boundary value problems of elasticity reveals that when dislocations of the more general type are admitted appropriate data must be given at each point on the specified barrier in addition to the usual information.