Abstract
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 |
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Article number | 40 |
Journal | Calculus of Variations and Partial Differential Equations |
Volume | 55 |
Issue number | 2 |
DOIs | |
State | Published - 1 Apr 2016 |
Bibliographical note
Funding 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.
Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.
Keywords
- 53Z05
- 74B20
- 74Q15