HOMOGENIZATION OF GRAPH-BASED ELASTIC STRUCTURES - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2017

HOMOGENIZATION OF 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.
Fichier principal
Vignette du fichier
Graph-HAL.pdf (539.69 Ko) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-01492589 , version 1 (20-03-2017)
hal-01492589 , version 2 (08-06-2017)
hal-01492589 , version 3 (27-12-2017)

Identifiers

  • HAL Id : hal-01492589 , version 1

Cite

H Abdoul-Anziz, Pierre Seppecher. HOMOGENIZATION OF GRAPH-BASED ELASTIC STRUCTURES. 2017. ⟨hal-01492589v1⟩
507 View
525 Download

Share

Gmail Mastodon Facebook X LinkedIn More