Reformulation of Continuum Defects in Terms of the General Teleparallel Geometry in the Language of Exterior Algebra

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. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.