Limits of elastic models of converging Riemannian manifolds

Raz Kupferman, Cy Maor*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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 languageAmerican English
Article number40
JournalCalculus of Variations and Partial Differential Equations
Volume55
Issue number2
DOIs
StatePublished - 1 Apr 2016

Bibliographical note

Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.

Keywords

  • 53Z05
  • 74B20
  • 74Q15

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