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

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.

26 pages, 5 figures

References in corpus (2)

• An elastoplastic theory of dislocations as a physical field theory with torsion
• Screw dislocations in the field theory of elastoplasticity

Cited by in corpus (18)

• Geometric Theory of Defects
• On Dislocations in a Special Class of Generalized Elasticity
• Exact vacuum solution of a (1+2)-dimensional Poincare gauge theory: BTZ solution with torsion
• Non-singular dislocation continuum theories: Strain gradient elasticity versus Peierls-Nabarro model
• The gauge theory of dislocations: static solutions of screw and edge dislocations
• Variational approach in dislocation theory
• Torsion in quantum field theory through time-loops on Dirac materials
• Torsion at different scales: from materials to the Universe
• Wedge disclination in the field theory of elastoplasticity
• 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
• Twist disclination in the field theory of elastoplasticity
• Impact of lattice rotation on dislocation motion
• Group Theoretical Analysis of Light-Cone Dominated Hadronic Processes and Twist Decomposition of Nonlocal Operators in Quantum Chromodynamics
• Non-singular screw dislocations as the Coulomb gas with smoothed out coupling and the renormalization of the shear modulus
• On gradient enriched elasticity theories: A reply to "Comment on 'On non-singular crack fields in Helmholtz type enriched elasticity theories' " and important theoretical aspects
• A Modified Screw Dislocation With Non-Singular Core of Finite Radius From Einstein-Like Gauge Equation (Non-Linear Approach)
• Time-loops to spot torsion on bidimensional Dirac materials with dislocations
• Displacement Field and Elastic Energy of a Circular Twist Disclination for Large Deformations - an Example how to Treat Nonlinear Boundary Value Problems with Computer Algebra Systems