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A translational gauge approach of the Einstein type is proposed for obtainingthe stresses that are due to non-singular screw dislocation. The stressdistribution of second order around the screw dislocation is classically knownfor the hollow circular cylinder with traction-free external and internalboundaries. The inner boundary surrounds the dislocation's core, which is notcaptured by the conventional solution. The present gauge approach enables us tocontinue the classically known quadratic stresses inside the core. The gaugeequation is chosen in the Hilbert--Einstein form, and it plays the role ofnon-conventional incompatibility law. The stress function method is used, andit leads to the modified stress potential given by two constituents: theconventional one, say, the `background' and a short-ranged gauge contribution.The latter just causes additional stresses, which are localized. The asymptoticproperties of the resulting stresses are studied. Since the gauge contributionsare short-ranged, the background stress field dominates sufficiently far fromthe core. The outer cylinder's boundary is traction-free. At sufficientlymoderate distances, the second order stresses acquire regular continuationwithin the core region, and the cut-off at the core does not occur. Expressionsfor the asymptotically far stresses provide self-consistently new length scalesdependent on the elastic parameters. These lengths could characterize anexteriority of the dislocation core region.

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