Gauge field theory of a continuum with dislocations and disclinations
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.
geometrical structure of a material manifold
scientific article; zbMATH DE number 3943097
scientific article