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- W3106536110 abstract "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, $mathcal{M}_ntomathcal{M}$, 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." @default.
- W3106536110 created "2020-11-23" @default.
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- W3106536110 date "2016-03-30" @default.
- W3106536110 modified "2023-09-25" @default.
- W3106536110 title "Limits of elastic models of converging Riemannian manifolds" @default.
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- W3106536110 doi "https://doi.org/10.1007/s00526-016-0979-6" @default.
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