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Plasticity; Defects; Dislocations; Teleparallelism; Torsion; Contorsion; Curvature

arash_yavari's picture

On Nye's Lattice Curvature Tensor

We revisit Nye's lattice curvature tensor in the light of Cartan's moving frames. Nye's definition of lattice curvature is based on the assumption that the dislocated body is stress-free, and therefore, it makes sense only for zero-stress (impotent) dislocation distributions. Motivated by the works of Bilby and others, Nye's construction is extended to arbitrary dislocation distributions. We provide a material definition of the lattice curvature in the form of a triplet of vectors, that are obtained from the material covariant derivative of the lattice frame along its integral curves.

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