Comptes Rendus
Problèmes mathématiques de la mécanique
Modélisation de films courbés non simples de second gradient
[Curved nonsimple grade-two thin films]
Comptes Rendus. Mathématique, Volume 344 (2007) no. 5, pp. 343-347.

The behavior of a curved thin film made of a nonsimple grade two material is described by a nonconvex bulk energy depending on the first and second order derivatives of the deformation. We show using Γ-convergence arguments that the quasiminimizers of the three-dimensional energy converge, when the thickness of the curved film vanishes, to the minimizers of an energy which is a function of a two-dimensional deformation and of a Cosserat vector. Part of the energy density is obtained by A-quasiconvexification arguments.

Le comportement d'un film courbé mince composé d'un matériau non simple de second gradient est décrit par une énergie interne non convexe dépendant des dérivées secondes de la déformation. On démontre en utilisant des arguments de Γ-convergence, que lorsque l'épaisseur du film tend vers zéro, les quasiminimiseurs de l'énergie tridimensionnelle convergent vers les minimiseurs d'une énergie dépendant d'une déformation bidimensionnelle et d'un vecteur de Cosserat. Une partie de la densité d'énergie est obtenue par des arguments de A-quasiconvexification.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2007.01.018
Giuliano Gargiulo 1; Elvira Zappale 2; Hamdi Zorgati 3

1 Dipartimento di Scienze biologiche ed ambientali, Universita' degli Studi del Sannio, 82100 Benevento, Italie
2 DIIMA, Università degli Studi di Salerno, via Ponte Don Melillo, 84084 Fisciano, Italie
3 Faculté des Sciences de Tunis, Campus Universitaire, 2092 Tunis, Tunisie
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     title = {Mod\'elisation de films courb\'es non simples de second gradient},
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Giuliano Gargiulo; Elvira Zappale; Hamdi Zorgati. Modélisation de films courbés non simples de second gradient. Comptes Rendus. Mathématique, Volume 344 (2007) no. 5, pp. 343-347. doi : 10.1016/j.crma.2007.01.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.01.018/

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