Commutability of homogenization and ...
Document type :
Compte-rendu et recension critique d'ouvrage
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]
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 >
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
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