A translational gauge approach of Einstein-type was proposed in order to obtain the stresses due to non-singular screw dislocations. The stress distribution of second order around the screw dislocation had long been known for a hollow circular cylinder with traction-free external and internal boundaries. The inner boundary, surrounding the dislocation core, was not treatable via the conventional solution. The present gauge approach permitted continuation of the known quadratic stresses to within the core. The chosen gauge equation was of Hilbert–Einstein form, and played the role of a non-conventional incompatibility law. The stress function method was used, and led to a modified stress potential given by 2 constituents: a conventional (background) one and a short-range gauge contribution. The latter simply caused additional stresses which were localized. The asymptotic properties of the resultant stresses were studied. Because the gauge contributions were short-range, the background stress-field dominated sufficiently far from the core. The outer cylinder-boundary was traction-free. At sufficiently moderate distances, the second-order stresses acquired a regular continuation within the core region and the cut-off at the core did not occur. Expressions for the asymptotically far stresses provided self-consistent new length-scales which depended upon the elastic parameters.

The Einsteinian T(3)-Gauge Approach and the Stress Tensor of the Screw Dislocation in the Second Order - Avoiding the Cut-Off at the Core. C.Malyshev: Journal of Physics A, 2007, 40[34], 10657-84