The Einstein-like field theory and the dislocations with finite-sized core

TL;DR

This paper develops an Einstein-like field theory using Riemann-Cartan geometry to model dislocations with finite-sized cores in elastic solids, leading to smoothed stress fields and modified elastic constant renormalization.

Contribution

It introduces a novel Einstein-like Lagrangian framework for finite-core dislocations, incorporating torsion and curvature to improve upon traditional singular models.

Findings

Stress tensor is smoothed within the dislocation core.

Renormalization of shear modulus differs from singular dislocation models.

Dislocation core self-energy is expressed via quadratic torsion and curvature terms.

Abstract

Einstein-like Lagrangian field theory is developed to describe elastic solid containing dislocations with finite-sized core. The framework of the Riemann-Cartan geometry in three dimensions is used, and the core self-energy is expressed by the translational part of the general Lagrangian quadratic in torsion and curvature. In the Hilbert-Einstein case, the gauge equation plays the role of non-conventional incompatibility law. The stress tensor of the modified screw dislocations is smoothed out within the core. The renormalization of the elastic constants caused by proliferation of the dislocation dipoles is considered. The use of the singularityless dislocation solution modifies the renormalization of the shear modulus in comparison with the case of singular dislocations.