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arXiv · 1410.2909

Riemannian surfaces with torsion as homogenization limits of locally-Euclidean surfaces with dislocation-type singularities

Raz Kupferman·Cy Maor
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Abstract

We reconcile between two classical models of edge-dislocations in solids. The first model, dating from the early 1900s models isolated edge-dislocations as line singularities in locally-Euclidean manifolds. The second model, dating from the 1950s, models continuously-distributed edge-dislocations as smooth manifolds endowed with non-symmetric affine connections (equivalently, endowed with torsion fields). In both models, the solid is modeled as a Weitzenböck manifold. We prove, using a weak notion of convergence [KM15], that the second model can be obtained rigorously as a homogenization limit of the first model, as the density of singular edge-dislocation tends to infinity.

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Raz Kupferman, Cy Maor. 2015-06-28. Riemannian surfaces with torsion as homogenization limits of locally-Euclidean surfaces with dislocation-type singularities. https://doi.org/10.1017/s0308210515000773

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