Dislocations in the Field Theory of Elastoplasticity

TL;DR

This paper develops a linear elastoplasticity framework to model screw and edge dislocations in isotropic solids, eliminating classical singularities and providing detailed stress and strain field solutions.

Contribution

It introduces modified stress functions for dislocations within elastoplasticity, removing singularities present in classical elasticity models.

Findings

Stress and strain fields are non-singular near dislocation cores.

Explicit solutions for dislocation densities and moment stresses are provided.

Modified stress functions improve the physical realism of dislocation modeling.

Abstract

By means of linear theory of elastoplasticity, solutions are given for screw and edge dislocations situated in an isotropic solid. The force stresses, strain fields, displacements, distortions, dislocation densities and moment stresses are calculated. The force stresses, strain fields, displacements and distortions are devoid of singularities predicted by the classical elasticity. Using the so-called stress function method we found modified stress functions of screw and edge dislocations.