Remarks on homogenization and $3D$-$2D$ dimension reduction of unbounded energies on thin films
We study periodic homogenization and $3D$-$2D$ dimension reduction by $\Gamma (\pi )$-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 necess...
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| Language: | English |
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Académie des sciences
2023-07-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.454/ |
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| author | Anza Hafsa, Omar Mandallena, Jean-Philippe |
| author_facet | Anza Hafsa, Omar Mandallena, Jean-Philippe |
| author_sort | Anza Hafsa, Omar |
| collection | DOAJ |
| description | We study periodic homogenization and $3D$-$2D$ dimension reduction by $\Gamma (\pi )$-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. |
| format | Article |
| id | doaj-art-297d356493ec42b6b1c36f3c0b6b36fe |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-07-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-297d356493ec42b6b1c36f3c0b6b36fe2025-02-07T11:08:08ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-07-01361G590391010.5802/crmath.45410.5802/crmath.454Remarks on homogenization and $3D$-$2D$ dimension reduction of unbounded energies on thin filmsAnza Hafsa, Omar0Mandallena, Jean-Philippe1Université de Nimes, Laboratoire MIPA, Site des Carmes, Place Gabriel Péri, 30021 Nîmes, FranceUniversité de Nimes, Laboratoire MIPA, Site des Carmes, Place Gabriel Péri, 30021 Nîmes, FranceWe study periodic homogenization and $3D$-$2D$ dimension reduction by $\Gamma (\pi )$-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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.454/ |
| spellingShingle | Anza Hafsa, Omar Mandallena, Jean-Philippe Remarks on homogenization and $3D$-$2D$ dimension reduction of unbounded energies on thin films Comptes Rendus. Mathématique |
| title | Remarks on homogenization and $3D$-$2D$ dimension reduction of unbounded energies on thin films |
| title_full | Remarks on homogenization and $3D$-$2D$ dimension reduction of unbounded energies on thin films |
| title_fullStr | Remarks on homogenization and $3D$-$2D$ dimension reduction of unbounded energies on thin films |
| title_full_unstemmed | Remarks on homogenization and $3D$-$2D$ dimension reduction of unbounded energies on thin films |
| title_short | Remarks on homogenization and $3D$-$2D$ dimension reduction of unbounded energies on thin films |
| title_sort | remarks on homogenization and 3d 2d dimension reduction of unbounded energies on thin films |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.454/ |
| work_keys_str_mv | AT anzahafsaomar remarksonhomogenizationand3d2ddimensionreductionofunboundedenergiesonthinfilms AT mandallenajeanphilippe remarksonhomogenizationand3d2ddimensionreductionofunboundedenergiesonthinfilms |