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Towards improved Hashin–Shtrikman bounds on the effective moduli of random composites

Abstract : The celebrated bounds of Hashin and Shtrikman on the effective properties of composites are valid for a very wide class of materials. However, they incorporate only a very limited amount of information on the microstructure (volume fraction of each phase in the case of isotropic microstructures). As a result, they are generally not tight. In this work, we present an attempt at improving these bounds by incorporating explicitly the local volume fraction to the set of local descriptors of the microstructure. We show that, quite unexpectedly, the process fails in the sense that the classical bounds are retrieved. We further show that this negative result applies to so-called weakly isotropic local descriptors of the microstructure (to be defined in this paper). This suggests that improved bounds may be obtained with anisotropic descriptors.
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Contributeur : Sébastien Brisard <>
Soumis le : jeudi 23 février 2017 - 08:34:22
Dernière modification le : jeudi 1 juillet 2021 - 06:18:07
Archivage à long terme le : : mercredi 24 mai 2017 - 12:32:58


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This is the post-print (ie final draft post-refereeing) version of the article "Towards improved Hashin-Shtrikman bounds on the effective moduli of random composites" by Sébastien Brisard. The original publication is available at (doi:10.1051/meca/2016037).




Sébastien Brisard. Towards improved Hashin–Shtrikman bounds on the effective moduli of random composites. Mechanics & Industry, EDP Sciences, 2017, 18 (2), pp.214. ⟨10.1051/meca/2016037⟩. ⟨hal-01474668⟩



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