A Modified Screw Dislocation With Non-Singular Core of Finite Radius From Einstein-Like Gauge Equation (Non-Linear Approach)

A continual model of non-singular screw dislocation lying along a straight infinitely long circular cylinder is investigated in the framework of translational gauge approach with the Hilbert--Einstein gauge Lagrangian. The stress--strain constitutive law implies the elastic energy of isotropic continuum which includes the terms of second and third orders in the strain components. The Einstein-type gauge equation with the elastic stress tensor as a driving source is investigated perturbatively, and second order contribution to the stress potential of the modified screw dislocation is obtained. A stress-free boundary condition is imposed at the cylinder's external surface. A cut-off of the classical approach which excludes from consideration a tubular vicinity of the defect's axis is avoided, and the total stress obtained for the screw dislocation is valid in the whole body. An expression for the radius of the dislocation's core in terms of the second and third order elastic constants is obtained.