Shell theories arising as low energy $\Gamma$-limit of 3d nonlinear elasticity
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 2, pp. 253-295.

We discuss the limiting behavior (using the notion of $\Gamma$-limit) of the 3d nonlinear elasticity for thin shells around an arbitrary smooth 2d surface. In particular, under the assumption that the elastic energy of deformations scales like ${h}^{4}$, $h$ being the thickness of a shell, we derive a limiting theory which is a generalization of the von Kármán theory for plates.

Classification : 74K20,  74B20
@article{ASNSP_2010_5_9_2_253_0,
author = {Lewicka, Marta and Mora, Maria Giovanna and Pakzad, Mohammad Reza},
title = {Shell theories arising as low energy $\mathbf{\Gamma }$-limit of 3d nonlinear elasticity},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {253--295},
publisher = {Scuola Normale Superiore, Pisa},
volume = {Ser. 5, 9},
number = {2},
year = {2010},
zbl = {05791996},
mrnumber = {2731157},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2010_5_9_2_253_0/}
}
Lewicka, Marta; Mora, Maria Giovanna; Pakzad, Mohammad Reza. Shell theories arising as low energy $\mathbf{\Gamma }$-limit of 3d nonlinear elasticity. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 9 (2010) no. 2, pp. 253-295. http://www.numdam.org/item/ASNSP_2010_5_9_2_253_0/

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