The Dislocation Stress Functions From the Double Curl T(3)-Gauge Equation: Linearity and a Look Beyond

TL;DR

This paper explores a T(3)-gauge model for defects, deriving stress functions for dislocations, revealing constraints on solutions, and proposing a non-linear extension with a new gauge Lagrangian in Hilbert-Einstein form.

Contribution

It introduces a novel translational gauge equation that reproduces standard dislocation stress fields and extends the model non-linearly with a Hilbert-Einstein type Lagrangian.

Findings

The gauge equation constrains stress functions, affecting dislocation stress components.

The double curl gauge equation reproduces standard edge and screw dislocation stresses.

A non-linear extension improves defect solutions beyond linear approximation.

Abstract

T(3)-gauge model of defects based on the gauge Lagrangian quadratic in the gauge field strength is considered. The equilibrium equation of the medium is fulfilled by the double curl Kroner's ansatz for stresses. The problem of replication of the static edge dislocation along third axis is analysed under a special, though conventional, choice of this ansatz. The translational gauge equation is shown to constraint the functions parametrizing the ansatz (the stress functions) so that the resulting stress component $\sigma_{3 3}$ is not that of the edge defect. Another translational gauge equation with the double curl differential operator is shown to reproduce both the stress functions, as well as the stress tensors, of the standard edge and screw dislocations. Non-linear extension of the newly proposed translational gauge equation is given to correct the linear defect solutions in next orders. New gauge Lagrangian is suggested in the Hilbert-Einstein form.