Gauge field theory of a continuum with dislocations and disclinations
type: Item
instance of: scholarly article
title: Gauge field theory of a continuum with dislocations and disclinations
zbMATH Open document ID: 0587.73001
DOI: 10.1016/0020-7225(86)90042-X
author: B. George
published in: International Journal of Engineering Science
publication date: 1986-01-01T00:00:00Z
review text: In this work, by applying vielbein and gauge field theory, the authors studied the geometrical structure of a material manifold with dislocation and disclinations. In describing the characteristics of plastic imperfections, the affine and the gauge connections are introduced. They showed that the torsion tensor can be decomposed into a pure vielbein part and a gauge potential part. Taking the displacement fields, the vielbein and the connection as three basic parameters, through the use of a variational principle, the constitutive relations and the governing field equations are obtained. They emphasized that the physical quantities appearing in the Lagrangian density must be covariant not only in the coordinate transformation but also in the gauge transformation.. For practical applications they proposed two specific forms of internal energy density functions for a full description of a macroscopically isotropic material with dislocations and disclinations. This work might be useful for those researchers working on the mathematical theory of dislocations and disclinations.
Mathematics Subject Classification ID: 74A20
Mathematics Subject Classification ID: 74C99
Mathematics Subject Classification ID: 74A60
Mathematics Subject Classification ID: 74M25
Mathematics Subject Classification ID: 74A99
Mathematics Subject Classification ID: 81T99
zbMATH DE Number: 3943097
zbMATH Keywords: gauge connection
zbMATH Keywords: affine connection
zbMATH Keywords: geometrical structure of a material manifold
zbMATH Keywords: disclinations
zbMATH Keywords: plastic imperfections
zbMATH Keywords: torsion tensor
zbMATH Keywords: decomposed
zbMATH Keywords: pure vielbein part
zbMATH Keywords: gauge potential part
zbMATH Keywords: variational principle
zbMATH Keywords: constitutive relations
zbMATH Keywords: governing field equations
zbMATH Keywords: Lagrangian density
zbMATH Keywords: covariant
zbMATH Keywords: gauge transformation.
zbMATH Keywords: internal energy density functions
zbMATH Keywords: macroscopically isotropic material
reviewed by: Hilmi Demiray
MaRDI profile type: Publication
cites work: Q3234079
cites work: Q3253075
cites work: Q3263384
cites work: Q5564192
cites work: Modern differential geometric techniques in the theory of continuous distributions of dislocations
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cites work: Conservation of Isotopic Spin and Isotopic Gauge Invariance
cites work: Invariant Theoretical Interpretation of Interaction
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cites work: Q4042716
cites work: Nicht-lineare Elastizitätstheorie der Versetzungen und Eigenspannungen
full work available at URL: 0020-7225(86)90042-x
OpenAlex ID: W2017237882
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description: scientific article; zbMATH DE number 3943097