An elastoplastic theory of dislocations as a physical field theory with torsion

2001/05/31 by Markus Lazar · 8 citations
Earth and Planetary Sciences · Engineering · Materials Science · Physics and Astronomy · #Elasticity and Material Modeling #High-pressure geophysics and materials #Nonlocal and gradient elasticity in micro/nano structures #cond-mat #gr-qc

paper · pdf · doi:10.1088/0305-4470/35/8/313

published as J.Phys.A35:1983-2004,2002 · 38 pages, 6 figures, RevTex

openalex publication_date 2002/02/18 · arxiv created 2002/02/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We consider a static theory of dislocations with moment stress in an anisotropic or isotropic elastoplastic material as a T (3) gauge theory. We obtain Yang-Mills-type field equations which express the force and the moment equilibrium. Additionally, we discuss several constitutive laws between the dislocation density and the moment stress. For a straight screw dislocation, we find the stress field which is modified near the dislocation core due to the appearance of moment stress. For the first time, we calculate the localized moment stress, the Nye tensor, the elastoplastic energy and the modified Peach-Koehler force of a screw dislocation in this framework. Moreover, we discuss the straightforward analogy between a screw dislocation and a magnetic vortex. The dislocation theory in solids is also considered as a three-dimensional effective theory of gravity.

Citations

• Theory of Group Representations and Applications
• On the Gauge Aspects of Gravity
• Some geometrical relations in dislocated crystals
• Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen
• Continuous distributions of dislocations: a new application of the methods of non-Riemannian geometry

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• Is spacetime curved? Assessing the underdetermination of general relativity and teleparallel gravity
• Geometric treatment of conduction electron scattering by crystal lattice strains and dislocations
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