Material and spatial gauge theories of solids I. Gauge constructs, geometry, and kinematics
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A gauge-theoretic approach for modeling continuous distributions of defects in solids is undertaken, based on local internal and external symmetries of an appropriate Lagrangian for those materials. The invariance of the Lagrangian under global action of internal (spatial) and external (material) symmetry groups is extended to invariance under local action of both groups of symmetries through an application of the minimal replacement construct of gauge theory. This is achieved by introduction of nontrivial spatial and material gauge connections. Both connections are used for the construction of two sets of Cartan equations of structure with two different types of torsion and curvature (spatial and material). The spatial torsion and curvature are shown to model "microcracks" and "microrotations", while the material torsion and curvature model dislocations, disclinations, and energy dissipation mechanisms. 1989.
International Journal of Engineering Science
author list (cited authors)
Lagoudas, D. C., & Edelen, D.