  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.
