Limits of elastic models of converging Riemannian manifolds

In non-linear incompatible elasticity, the configurations are maps from a non-Euclidean body manifold into the ambient Euclidean space, (Formula presented.). We prove the (Formula presented.) -convergence of elastic energies for configurations of a converging sequence, (Formula presented.) , 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.