Title :

Commutability of homogenization and linearization at identity in finite elasticity and applications

Author(s) :

Gloria, Antoine [Auteur]
SImulations and Modeling for PArticles and Fluids [SIMPAF]
Neukamm, Stefan [Auteur]
Max Planck Institute for Mathematics in the Sciences [MPI-MiS]

Journal title :

Annales de l'Institut Henri Poincaré C, Analyse non linéaire

Pages :

941-964

Publisher :

EMS

Publication date :

2011-08-22

ISSN :

0294-1449

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

In this note we prove under some general assumptions on elastic energy densities (namely, frame indifference, minimality at identity, non-degeneracy and existence of a quadratic expansion at identity) that homogenization ...
Show more >In this note we prove under some general assumptions on elastic energy densities (namely, frame indifference, minimality at identity, non-degeneracy and existence of a quadratic expansion at identity) that homogenization and linearization commute at identity. This generalizes a recent result by S.~Müller and the second author by dropping their assumption of periodicity. As a first application, we extend their $\Gamma$-convergence commutation diagram for linearization and homogenization to the stochastic setting under standard growth conditions. As a second application, we prove that the $\Gamma$-closure is local at identity for this class of energy densities.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL