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Comptes Rendus Mathématique
Volume 348, n° 9-10
pages 529-534 (mai 2010)
Doi : 10.1016/j.crma.2010.03.001
Received : 12 June 2009 ;  accepted : 3 Mars 2010
Homogénéisation d’un matériau périodique faiblement perturbé aléatoirement
Homogenization of a weakly randomly perturbed periodic material

Arnaud Anantharaman 1 , Claude Le Bris
Université Paris Est, CERMICS, Équipe projet MICMAC, INRIA-École des ponts, 6 & 8 avenue Pascal, 77455 Marne-la-Vallée cedex 2, France 


Nous proposons dans la présente Note une méthode pour calculer au premier ordre le comportement homogénéisé d’un milieu consistant en un matériau périodique de référence perturbé de manière stochastique. L’approche, très efficace en termes de coût calcul, admet une justification rigoureuse dans certains cas, et a été testée numériquement avec succès pour des cas plus généraux.

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We present in this Note an approach aiming at computing the first-order homogenized behaviour of a medium consisting of a randomly perturbed periodic reference material. The approach, which proves to be very efficient from a computational point of view, is rigorously founded in a certain class of settings and has been successfully numerically tested for more general settings.

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1  A. Anantharaman tient à remercier EADS IW pour son soutien financier.

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