On the Non-Uniqueness of Solution for Screw Dislocations in Multiply Connected Regions

It is well-known that the solution for a straight dislocation in an infinite medium does not depend on the cut along which the displacement discontinuity is imposed. This is also true for a semi-infinite medium, or any simply-connected region. The stress and strain fields, energy and dislocation forces are the same regardless of the cut. Only displacements differ in the region between the two cuts by a rigidbody translation. For multiply connected regions, the solution depends on the cut used to create a dislocation, and if the connectivity of the region is n, there are that many possible solutions. This is demonstrated here by considering a screw dislocation in a hollow cylinder and near a cavity in an infinite medium. The consideration for a screw dislocation is simpler than for an edge dislocation, since it only requires appropriately located image dislocations to achieve the traction-free boundary conditions.