A nonsingular solution of the edge dislocation in the gauge theory of dislocations

TL;DR

This paper presents a linear, nonsingular solution for the edge dislocation within the gauge theory of defects, ensuring well-defined fields everywhere, including the core, and relating it to classical and nonlocal theories.

Contribution

It introduces a modified stress function method to obtain a globally defined, nonsingular solution for edge dislocations in gauge theory, aligning with classical and strain gradient elasticity results.

Findings

Stress, strain, and displacement fields are nonsingular at the core.

The solution matches classical far-field behavior.

The relation to nonlocal elasticity theory is established.

Abstract

A (linear) nonsingular solution for the edge dislocation in the translational gauge theory of defects is presented. The stress function method is used and a modified stress function is obtained. All field quantities are globally defined and the solution agrees with the classical solution for the edge dislocation in the far field. The components of the stress, strain, distortion and displacement field are also defined in the dislocation core region and they have no singularity there. The dislocation density, moment and couple stress for an edge dislocation are calculated. The solution for the stress and strain field obtained here is in agreement with those obtained by Gutkin and Aifantis through an analysis of the edge dislocation in the strain gradient elasticity. Additionally, the relation between the gauge theory and Eringen's so-called nonlocal theory of dislocations is given.