Skip to Main content Skip to Navigation
Journal articles

A direct approach to numerical homogenization in finite elasticity

Antoine Gloria 1
1 MICMAC - Methods and engineering of multiscale computing from atom to continuum
Inria Paris-Rocquencourt, ENPC - École des Ponts ParisTech
Abstract : We describe, analyze, and test a direct numerical approach to a homogenized problem in nonlinear elasticity at finite strain. The main advantage of this approach is that it does not modify the overall structure of standard softwares in use for computational elasticity. Our analysis includes a convergence result for a general class of energy densities and an error estimate in the convex case. We relate this approach to the multiscale finite element method and show our analysis also applies to this method. Microscopic buckling and macroscopic instabilities are numerically investigated. The application of our approach to some numerical tests on an idealized rubber foam is also presented. For consistency a short review of the homogenization theory in nonlinear elasticity is provided.
Document type :
Journal articles
Complete list of metadatas

https://hal.inria.fr/inria-00070383
Contributor : Rapport de Recherche Inria <>
Submitted on : Friday, May 19, 2006 - 8:19:39 PM
Last modification on : Wednesday, April 17, 2019 - 4:07:59 PM
Long-term archiving on: : Sunday, April 4, 2010 - 9:05:13 PM

Identifiers

  • HAL Id : inria-00070383, version 1

Collections

Citation

Antoine Gloria. A direct approach to numerical homogenization in finite elasticity. Networks and Heterogeneous Media, AIMS-American Institute of Mathematical Sciences, 2006, 1 (1), pp.109-141. ⟨inria-00070383⟩

Share

Metrics

Record views

446

Files downloads

404