Accéder directement au contenu Accéder directement à la navigation
Article dans une revue

Combining Galerkin approximation techniques with the principle of Hashin and Shtrikman to derive a new FFT-based numerical method for the homogenization of composites

Abstract : We report on the mathematical analysis of two different, FFT-based, numerical schemes for the homogenization of composite media within the framework of linear elasticity: the basic scheme of Moulinec and Suquet (1994, 1998) [9] and [10], and the energy-based scheme of Brisard and Dormieux (2010) [13]. Casting these two schemes as Galerkin approximations of the same variational problem allows us to assert their well-posedness and convergence. More importantly, we extend in this work their domains of application, by relieving some stringent conditions on the reference material which were previously thought necessary. The origins of the flaws of each scheme are identified, and a third scheme is proposed, which seems to combine the strengths of the basic and energy-based schemes, while leaving out their weaknesses. Finally, a rule is proposed for handling heterogeneous pixels/voxels, a situation frequently met when images of real materials are used as input to these schemes.
Liste complète des métadonnées

https://hal-enpc.archives-ouvertes.fr/hal-00722361
Contributeur : Sébastien Brisard <>
Soumis le : mardi 3 septembre 2013 - 11:18:35
Dernière modification le : vendredi 17 juillet 2020 - 17:09:09
Archivage à long terme le : : mercredi 4 décembre 2013 - 02:25:09

Fichier

bris2012a-postprint.pdf
Fichiers éditeurs autorisés sur une archive ouverte

Identifiants

Citation

Sébastien Brisard, Luc Dormieux. Combining Galerkin approximation techniques with the principle of Hashin and Shtrikman to derive a new FFT-based numerical method for the homogenization of composites. Computer Methods in Applied Mechanics and Engineering, Elsevier, 2012, 217-220, pp.197-212. ⟨10.1016/j.cma.2012.01.003⟩. ⟨hal-00722361⟩

Partager

Métriques

Consultations de la notice

661

Téléchargements de fichiers

551