# American Institute of Mathematical Sciences

September  2015, 7(3): 361-387. doi: 10.3934/jgm.2015.7.361

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

 1 Institute of Mathematics, The Hebrew University, Jerusalem 91904, Israel, Israel

Received  September 2014 Revised  May 2015 Published  July 2015

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.
Citation: Raz Kupferman, Cy Maor. The emergence of torsion in the continuum limit of distributed edge-dislocations. Journal of Geometric Mechanics, 2015, 7 (3) : 361-387. doi: 10.3934/jgm.2015.7.361
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