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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2023-07-01
|
| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.454/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| ISSN: | 1778-3569 |