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arXiv · 1410.2906

The emergence of torsion in the continuum limit of distributed edge-dislocations

Raz Kupferman·Cy Maor
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Abstract

We present a rigorous homogenization theorem for distributed dislocations. We construct a sequence of locally-flat Riemannian manifolds with dislocation-type singularities. We show that this sequence converges, as the dislocations become denser, to a flat non-singular Weitzenb\"ock manifold, i.e. a flat manifold endowed with a metrically-consistent connection with zero curvature and non-zero torsion. In the process, we introduce a new notion of convergence of Weitzenb\"ock manifolds, which is relevant to this class of homogenization problems.

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Raz Kupferman, Cy Maor. 2014-10-10. The emergence of torsion in the continuum limit of distributed edge-dislocations. https://doi.org/10.3934/jgm.2015.7.361

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