Reformulation of continuum defects in terms of the general teleparallel geometry in the language of exterior algebra

TL;DR

This paper presents a new geometric formulation of continuum defects like dislocations and disclinations using general teleparallel geometry and exterior algebra, offering explicit continuity equations for defect densities.

Contribution

It introduces a novel formulation of continuum defects in terms of torsion and non-metricity within teleparallel geometry, expanding the geometric understanding of defects.

Findings

Derived explicit continuity equations for dislocation and disclination densities.

Reformulated defect theory using torsion, non-metricity, and exterior algebra.

Connected geometric defect descriptions with teleparallel geometry.

Abstract

We discuss the geometric formulation of continuum defects consisting of dislocations and disclinations. After reviewing the metric affine geometry and the present geometric formulation of dislocation and disclination written in terms of torsion and full curvature (together with vanishing non-metricity), we give a new formulation of them in a novel way in terms of torsion and non-metricity (together with vanishing full curvature), the so-called general teleparallel geometry. All calculations are performed by using the exterior algebra. We obtain continuity equations explicitly for dislocation density and disclination density.