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 -quasiconvexification.
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 -quasiconvexification arguments.
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@article{CRMATH_2007__344_5_343_0,
author = {Gargiulo, Giuliano and Zappale, Elvira and Zorgati, Hamdi},
title = {Mod\'elisation de films courb\'es non simples de second gradient},
journal = {Comptes Rendus. Math\'ematique},
pages = {343--347},
publisher = {Elsevier},
volume = {344},
number = {5},
year = {2007},
doi = {10.1016/j.crma.2007.01.018},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/j.crma.2007.01.018/}
}
TY - JOUR AU - Gargiulo, Giuliano AU - Zappale, Elvira AU - Zorgati, Hamdi TI - Modélisation de films courbés non simples de second gradient JO - Comptes Rendus. Mathématique PY - 2007 SP - 343 EP - 347 VL - 344 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2007.01.018/ DO - 10.1016/j.crma.2007.01.018 LA - fr ID - CRMATH_2007__344_5_343_0 ER -
%0 Journal Article %A Gargiulo, Giuliano %A Zappale, Elvira %A Zorgati, Hamdi %T Modélisation de films courbés non simples de second gradient %J Comptes Rendus. Mathématique %D 2007 %P 343-347 %V 344 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2007.01.018/ %R 10.1016/j.crma.2007.01.018 %G fr %F CRMATH_2007__344_5_343_0
Gargiulo, Giuliano; Zappale, Elvira; Zorgati, Hamdi. Modélisation de films courbés non simples de second gradient. Comptes Rendus. Mathématique, Tome 344 (2007) no. 5, pp. 343-347. doi : 10.1016/j.crma.2007.01.018. http://www.numdam.org/articles/10.1016/j.crma.2007.01.018/
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