MG12 - Talk detail
 

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Abstract

Geometric theory of defects in solids

One attempt to construct a fundamental theory of defects (dislocations and disclinations) is based on Riemann-Cartan geometry where metric and torsion are considered as independent physical variables. The torsion two-form equals the surface density of Burgers vector for dislocations, and the curvature two-form yields the surface density of Frank vector for disclinations. The elasticity equations are replaced by Einstein's equations and enter the theory through the gauge conditions on the triad. In a similar way the Lorentz gauge for a SO(3)-connection yields the SO(3)-principle chiral field theory as the gauge condition. This geometric approach not only reproduces results obtained within the ordinary elasticity theory but also permits one to consider continuous distribution of defects.

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