Variational approach in dislocation theory

TL;DR

This paper introduces a variational method for calculating dislocation stress fields, aligning with classical theory in simple cases and enabling systematic study of complex dislocation phenomena.

Contribution

It presents a new variational framework that extends dislocation theory to include core regularization, anharmonic effects, and solute interactions.

Findings

Matches Kr"oner's theory for Hooke's law materials

Enables systematic study of dislocation core regularization

Allows analysis of elastic anharmonicity and solute interactions

Abstract

A variational approach is presented to calculate the stress field generated by a system of dislocations. It is shown that in the simplest case, when the material containing the dislocations obeys Hooke's law the variational framework gives the same field equations as Kr\"oner's theory. However, the variational method proposed allows to study many other problems like dislocation core regularisation, role of elastic anharmonicity and dislocation--solute atom interaction. The aim of the paper is to demonstrate that these problems can be handled on a systematic manner.