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In the material science literature we find two continuum models forcrystalline defects: (i) A body with (finite) isolated defects is typicallymodeled as a Riemannian manifold with singularities, and (ii) a body withcontinuously distributed defects, which is modeled as a smooth (non-singular)Riemannian manifold with an additional structure of an affine connection. Inthis work we show how continuously distributed defects may be obtained as alimit of singular ones . The defect structure is represented by layering1-forms and their singular counterparts - de-Rham (n-1) currents. We then showthat every smooth layering $1$-form may be obtained as a limit, in the sense ofcurrents, of singular layering forms, corresponding to arrays of edgedislocations. As a corollary, we investigated manifolds with full materialstructure, i.e., a complete co-frame for the co-tangent bundle. We define thenotion of singular torsion current for manifolds with a parallel structure andprove its convergence to the regular smooth torsion tensor at homogenizationlimit. Thus establishing the so-called emergence of torsion at thehomogenization limit.

Homogenization of edge-dislocations as a weak limit of de-Rham currents