A gauge-theoretical approach to elasticity with microrotations

DOI10.1098/rspa.2011.0718zbMath1364.74017arXiv1012.5951OpenAlexW2102534584MaRDI QIDQ5345950

Yuri N. Obukhov, Christian G. Böhmer

Publication date: 7 June 2017

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.5951

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Applications of local differential geometry to the sciences (53B50)

Related Items (6)

Soliton-like solutions based on geometrically nonlinear Cosserat micropolar elasticity ⋮ Soliton solutions in geometrically nonlinear Cosserat micropolar elasticity with large deformations ⋮ New classes of modified teleparallel gravity models ⋮ Rotational elasticity and couplings to linear elasticity ⋮ Disclinations in the geometric theory of defects ⋮ Compatibility conditions of continua using Riemann–Cartan geometry

Cites Work

• Cartan's spiral staircase in physics and, in particular, in the gauge theory of dislocations
• Exact theory of stress and strain in rods and shells
• Elastic materials with couple-stresses
• Contributo per una formulazione di tipo integrale della meccanica dei continui di Cosserat
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• Theory of defects in solids and three-dimensional gravity
• Elasticita asimmetrica
• Wedge dislocation in the geometric theory of defects
• On the Fundamentals of the Three-dimensional Translation Gauge Theory of Dislocations
• Rotational Elasticity
• Cosserat continuum modelling of grain size effects in metal polycrystals
• A non-linear field theory
• Representation formulae of general solutions in the theory of hemitropic elasticity
• Transmission problems in the theory of elastic hemitropic materials
• The gauge theory of dislocations: a uniformly moving screw dislocation
• The EinsteinianT(3)-gauge approach and the stress tensor of the screw dislocation in the second order: avoiding the cut-off at the core
• On the structure of the theory of polar elasticity
• Analysis der Motorfelder im Cosserat‐Kontinuum
• Das Cosserat Kontinuum
• The stationary Weyl equation and Cosserat elasticity
• The \(T(3)\)-gauge model, the Einstein-like gauge equation, and Volterra dislocations with modified asymptotics.

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