Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity

TL;DR

This paper derives exact, nonsingular stress and strain fields for dislocations and disclinations within first strain gradient elasticity, eliminating classical singularities and providing insights into defect core behavior.

Contribution

It introduces explicit analytical solutions for defect fields in gradient elasticity, removing singularities and linking to nonlocal elasticity theories.

Findings

Stress and strain fields are finite at defect cores.

Maximum stress values can indicate potential fracture points.

Solutions connect gradient elasticity with nonlocal elasticity theories.

Abstract

The aim of this paper is to study the elastic stress and strain fields of dislocations and disclinations in the framework of Mindlin's gradient elasticity. We consider simple but rigorous versions of Mindlin's first gradient elasticity with one material length (gradient coefficient). Using the stress function method, we find modified stress functions for all six types of Volterra defects (dislocations and disclinations) situated in an isotropic and infinitely extended medium. By means of these stress functions, we obtain exact analytical solutions for the stress and strain fields of dislocations and disclinations. An advantage of these solutions for the elastic strain and stress is that they have no singularities at the defect line. They are finite and have maxima or minima in the defect core region. The stresses and strains are either zero or have a finite maximum value at the defect line. The maximum value of stresses may serve as a measure of the critical stress level when fracture and failure may occur. Thus, both the stress and elastic strain singularities are removed in such a simple gradient theory. In addition, we give the relation to the nonlocal stresses in Eringen's nonlocal elasticity for the nonsingular stresses.