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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.
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Submitted on : Friday, May 19, 2006 - 8:19:39 PM
Last modification on : Friday, February 4, 2022 - 3:10:23 AM
Long-term archiving on: : Sunday, April 4, 2010 - 9:05:13 PM

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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⟩

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