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

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 Weitzenböck 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 Weitzenböck manifolds, which is relevant to this class of homogenization problems.

See an erratum regarding Definition 4.1 and Lemma 4.8 in arxiv:1701.08903 (v3 is the same as v2 but for this comment)

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