  In non-linear incompatible elasticity, the configurations are maps from a
non-Euclidean body manifold into the ambient Euclidean space, $\mathbb{R}^k$.
We prove the $\Gamma$-convergence of elastic energies for configurations of a
converging sequence, $\mathcal{M}_n\to\mathcal{M}$, of body manifolds. This
convergence result has several implications: (i) It can be viewed as a general
structural stability property of the elastic model. (ii) It applies to certain
classes of bodies with defects, and in particular, to the limit of bodies with
increasingly dense edge-dislocations. (iii) It applies to approximation of
elastic bodies by piecewise-affine manifolds. In the context of
continuously-distributed dislocations, it reveals that the torsion field, which
has been used traditionally to quantify the density of dislocations, is
immaterial in the limiting elastic model.
