The emergence of torsion in the continuum limit of distributed edge-dislocations
Raz Kupferman, Cy Maor · The Journal of Geometric Mechanics · 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.