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

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 fields 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 solutions for the stress and strain fields obtained here are 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.