Comptes Rendus
On the effect of small fluctuations in the volume fraction of constituents on the effective properties of composites
Comptes Rendus. Mécanique, Volume 333 (2005) no. 3, pp. 219-226.

This study deals with three-scale composite materials comprised of nonlinear constituents. At the meso scale the composite can be considered as locally homogeneous with a macroscopic spatial variation of the constituents volume fraction. When these variations about a mean value are small, a Taylor expansion to second-order of the effective properties of the composite with respect to the fluctuations is given. This expansion can be used to discuss the beneficial or deleterious effects of clusters of inhomogeneities. It can also be used to derive new upper and lower bounds for the effective properties of nonlinear composites from dilute results.

Cette étude traite de composites à trois échelles nettement séparées. Ces matériaux peuvent être considérés comme localement homogènes à l'échelle mésoscopique, mais avec une fraction volumique des constituants qui varie d'un point à l'autre. Quand ces fluctuations de concentration sont faibles, un développement de Taylor des propriétés effectives macroscopiques du composite est établi. Ce développement est utilisé pour discuter l'effet des amas d'hétérogénéités. Il permet également d'obtenir des bornes supérieures et inférieures nouvelles sur les propriétés effectives macroscopiques de composites non linéaires.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crme.2004.12.004
Keywords: Computational solid mechanics, Homogenization, Composite materials, Nonlinear behavior
Mot clés : Mécanique des solides numérique, Homogénéisation, Matériaux composites, Comportement non linéaire

Pierre Suquet 1

1 Laboratoire de mécanique et d'acoustique, 31, chemin Joseph-Aiguier, 13402 Marseille cedex 20, France
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Pierre Suquet. On the effect of small fluctuations in the volume fraction of constituents on the effective properties of composites. Comptes Rendus. Mécanique, Volume 333 (2005) no. 3, pp. 219-226. doi : 10.1016/j.crme.2004.12.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.12.004/

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