Dislocation theory as a 3-dimensional translation gauge theory
TLDR
In this paper, the static elastoplastic theory of dislocations in an elastic material was considered and a Yang-Mills type Lagrangian and some Lagrangians with anisotropic constitutive laws were used to express the balance of force and moment.Abstract:
We consider the static elastoplastic theory of dislocations in an elastoplastic material We use a Yang-Mills type Lagrangian (the teleparallel equivalent of Hilbert-Einstein Lagrangian) and some Lagrangians with anisotropic constitutive laws The translational part of the generalized affine connection is utilized to describe the theory of elastoplasticity in the framework of a translation gauge theory We obtain a system of Yang-Mills field equations which express the balance of force and momentread more
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Gauge Theories Of Gravitation: A Reader With Commentaries
TL;DR: In this article, the authors present a case study of the rise of the Poincare group of gravity and its fallacies about torsion in the context of General Relativity Theory.
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Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity
Markus Lazar,Gérard A. Maugin +1 more
TL;DR: In this paper, the authors studied the elastic stress and strain fields of dislocations and disclinations in the framework of Mindlin's gradient elasticity and obtained exact analytical solutions for the stress and elastic strain fields.
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Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity
Markus Lazar,Gérard A. Maugin +1 more
TL;DR: In this article, the authors studied the elastic stress and strain fields of dislocations and disclinations in the framework of Mindlin's gradient elasticity and obtained exact analytical solutions for the stress and straining fields.
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Chiral Topological Elasticity and Fracton Order.
TL;DR: It is emphasized that the very structure of Riemann-Cartan geometry, which is used to formulate the theory, encodes some of the fracton phenomenology, suggesting that the Fracton order itself is geometric in nature.
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Gauge Theories of Gravitation
TL;DR: A survey of the literature on classical gauge theories of gravity can be found in this paper, where the authors provide a guide to the literature and a discussion of the most prominent contributors.
References
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Mathematical foundations of elasticity
TL;DR: In this article, the mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis are discussed. But the authors do not discuss the application of functional analysis to the problem of elasticity.
Book
A Gauge Theory of Dislocations and Disclinations
Aida Kadic,Dominic G.B. Edelen +1 more
TL;DR: In this paper, the gauge theory of deffects and linearization are discussed, as well as the phenomenology of de-ffects, and the history of the de-effect theory.
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On the Gauge Aspects of Gravity
Frank Gronwald,Friedrich W. Hehl +1 more
TL;DR: In this paper, it was shown that the Dirac equation in a non-inertial frame can be used to predict general relativity in a Riemann-Cartan spacetime with torsion and curvature.