On the meaning of the chosen set-averaging method within Eshelby-Kröner self-consistent scale transition model: the geometric mean versus the classical arithmetic average - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik Année : 2011

On the meaning of the chosen set-averaging method within Eshelby-Kröner self-consistent scale transition model: the geometric mean versus the classical arithmetic average

Résumé

Scale-transition models, such as Eshelby-Kröner self-consistent framework, which are often used for predicting the effective behavior of heterogeneous materials or estimating the distribution of local states from the knowledge of the corresponding macroscopic quantities, require the extensive use of set averages. In the present work, the fundamental formalism historically introduced by Kröner is, for the first time, considered from the point of view of both the geometric and the arithmetic set averages methods. It is demonstrated in this paper that the polarization tensors describing the relations existing between the local and the macroscopic mechanical states do have a strong physical meaning when expressed using the geometric average, instead of the classical arithmetic mean.

Dates et versions

hal-01011339 , version 1 (23-06-2014)

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Sylvain Fréour, Emmanuel Lacoste, Jamal Fajoui, Frédéric Jacquemin. On the meaning of the chosen set-averaging method within Eshelby-Kröner self-consistent scale transition model: the geometric mean versus the classical arithmetic average. Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 2011, 91 (9), pp.689-698. ⟨10.1002/zamm.201000167⟩. ⟨hal-01011339⟩
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