HOMOGENIZATION OF PERIODIC GRAPH-BASED ELASTIC STRUCTURES

Abstract : In the framework of Γ-convergence and periodic homogenization of highly contrasted materials, we study cylindrical structures made of one material and voids. Interest in high contrast homogenization is growing rapidly but assumptions are generally made in order to remain in the framework of classical elasticity. On the contrary, we obtain homogenized energies taking into account second gradient (i.e. strain gradient) effects. We first show that we can reduce the study of the considered structures to discrete systems corresponding to frame lattices. Our study of such lattices differs from the literature in the fact that we must take into account the different orders of magnitude of the extensional and flexural stiffnesses. This allows us to consider structures which would have been floppy when considering only extensional stiffness and completely rigid when considering flexural stiffnesses of the same order of magnitude than the extensional ones. At our knowledge, this paper provides the first rigorous homogenization result with a complete second gradient limit energy.
Liste complète des métadonnées

https://hal-univ-tln.archives-ouvertes.fr/hal-01492589
Contributeur : Pierre Seppecher <>
Soumis le : jeudi 8 juin 2017 - 22:16:16
Dernière modification le : jeudi 22 juin 2017 - 11:06:03
Document(s) archivé(s) le : samedi 9 septembre 2017 - 13:29:32

Fichier

Graph-based-structures-2.0.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-01492589, version 2

Citation

H Abdoul-Anziz, Pierre Seppecher. HOMOGENIZATION OF PERIODIC GRAPH-BASED ELASTIC STRUCTURES. 2017. 〈hal-01492589v2〉

Partager

Métriques

Consultations de
la notice

97

Téléchargements du document

109