A gauge theory of defects in media with microstructure

DOI10.1016/0020-7225(89)90112-2zbMath0674.73007OpenAlexW2045641511MaRDI QIDQ1121684

Dimitris C. Lagoudas

Publication date: 1989

Published in: International Journal of Engineering Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0020-7225(89)90112-2

zbMATH Keywords

semisimple Lie groupgauge potentialsCovariant torsioncurvature quantitiesdefect densitiesexistence of conservation laws of linear and angular momentumminimal coupling constructsnon-semisimple internal symmetry groupset of deformable vector fieldsYang-Mills minimal replacement

Mathematics Subject Classification ID

Supersymmetric field theories in quantum mechanics (81T60) Nonlinear elasticity (74B20) Micromechanics of solids (74M25) Applications of Lie groups to the sciences; explicit representations (22E70) Micromechanical theories (74A60) Applications of global differential geometry to the sciences (53C80) Generalities, axiomatics, foundations of continuum mechanics of solids (74A99)

Related Items (4)

Pure gauge theory of the Cosserat surface ⋮ The \(T(3)\)-gauge model, the Einstein-like gauge equation, and Volterra dislocations with modified asymptotics. ⋮ Quasi-Abelian gauge theory of axisymmetric deformation of shells of revolution ⋮ A gauge theory of relaxing elastic materials containing dislocations

Cites Work

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• Matching the inner and outer solutions in the continuum theory of dislocations
• Differential geometry of defects in condensed systems of particles with only translational mobility
• Theories of elasticity with couple-stress
• Die Theorie der Disklinationen
• Conservation of Isotopic Spin and Isotopic Gauge Invariance
• Milestones in mathematical physics Noether's theorem

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