Remarks on homogenization and $3D$-$2D$ dimension reduction of unbounded energies on thin films

Omar Anza Hafsa; Jean-Philippe Mandallena

doi:10.5802/crmath.454

Équations aux dérivées partielles, Mécanique

Remarks on homogenization and

3 D

-

2 D

dimension reduction of unbounded energies on thin films

Omar Anza Hafsa ¹ ; Jean-Philippe Mandallena ¹

¹ Université de Nimes, Laboratoire MIPA, Site des Carmes, Place Gabriel Péri, 30021 Nîmes, France

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 903-910.

Résumé

We study periodic homogenization and $3 D$ - $2 D$ dimension reduction by $Γ (π)$ -con-vergence of heterogeneous thin films whose the stored-energy densities have no polynomial growth. In particular, our results are consistent with one of the basic facts of nonlinear elasticity, namely the necessity of an infinite amount of energy to compress a finite volume of matter into zero volume. However, our results are not consistent with the noninterpenetration of the matter.

Reçu le : 2022-02-12
Accepté le : 2022-12-12
Publié le : 2023-07-18

DOI : 10.5802/crmath.454

Affiliations des auteurs :

Omar Anza Hafsa ¹ ; Jean-Philippe Mandallena ¹

¹ Université de Nimes, Laboratoire MIPA, Site des Carmes, Place Gabriel Péri, 30021 Nîmes, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Remarks on homogenization and $3D$-$2D$ dimension reduction of unbounded energies on thin films},
     journal = {Comptes Rendus. Math\'ematique},
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     year = {2023},
     doi = {10.5802/crmath.454},
     language = {en},
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Omar Anza Hafsa; Jean-Philippe Mandallena. Remarks on homogenization and $3D$-$2D$ dimension reduction of unbounded energies on thin films. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 903-910. doi : 10.5802/crmath.454. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.454/

Bibliographie
Cité par

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Barbora Benešová; Daniel Campbell; Stanislav Hencl; Martin Kružík Non-interpenetration of rods derived by $Γ$ -limits, M $^{3}$ AS. Mathematical Models Methods in Applied Sciences, Volume 35 (2025) no. 1, pp. 1-38 | DOI:10.1142/s0218202525500010 | Zbl:8005752

Cité par 1 document. Sources : zbMATH

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