On Dislocations in a Special Class of Generalized Elasticity

TL;DR

This paper compares various static theories of generalized elasticity, deriving nonsingular solutions for dislocations that improve upon classical models by eliminating singularities in elastic fields.

Contribution

It introduces and compares special classes of gradient and nonlocal elasticity theories, providing nonsingular solutions for dislocation fields in these frameworks.

Findings

Nonsingular elastic fields for screw and edge dislocations

Equilibrium equations for different elasticity theories

Relationship between gradient and nonlocal theories

Abstract

In this paper we consider and compare special classes of static theories of gradient elasticity, nonlocal elasticity, gradient micropolar elasticity and nonlocal micropolar elasticity with only one gradient coefficient. Equilibrium equations are discussed. The relationship between the gradient theory and the nonlocal theory is discussed for elasticity as well as for micropolar elasticity. Nonsingular solutions for the elastic fields of screw and edge dislocations are given. Both the elastic deformation (distortion, strain, bend-twist) and the force and couple stress tensors do not possess any singularity unlike `classical' theories.