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

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We present a rigorous homogenization theorem for distributed edge-dislocations. We construct a sequence of locally-flat 2D 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.

Original languageAmerican English
Pages (from-to)361-387
Number of pages27
JournalJournal of Geometric Mechanics
Issue number3
StatePublished - 1 Sep 2015

Bibliographical note

Publisher Copyright:
© American Institute of Mathematical Sciences.


  • Dislocations
  • Gromov-Hausdorff convergence
  • Homogenization
  • Torsion


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