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.
|Original language||American English|
|Journal||Calculus of Variations and Partial Differential Equations|
|State||Published - 1 Apr 2016|
Bibliographical noteFunding Information:
Raz Kupferman is partially supported by the Israel-US Binational Foundation (Grant No. 2010129), by the Israel Science Foundation (Grant No. 661/13) and by a Grant from the Ministry of Science, Technology and Space, Israel and the Russian Foundation for Basic Research, the Russian Federation.
© 2016, Springer-Verlag Berlin Heidelberg.