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Small amplitude homogenization applied to models of non-periodic fibrous materials

Published online by Cambridge University Press:  15 December 2007

David Manceau
David Manceau*
Affiliation:
Centre de Mathématiques, I.N.S.A. de Rennes & I.R.M.A.R., 20 avenue des Buttes de Coëmes, CS 14315 - 35043 Rennes Cedex, France. dmanceau@insa-rennes.fr
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Abstract

In this paper, we compare a biomechanics empirical model of the heart fibrous structure to two models obtained by a non-periodic homogenization process. To this end, the two homogenized models are simplified using the small amplitude homogenization procedure of Tartar, both in conduction and in elasticity. A new small amplitude homogenization expansion formula for a mixture of anisotropic elastic materials is also derived and allows us to obtain a third simplified model.

Keywords

Non-periodic homogenizationfibrous materialsmall amplitudelow contrastconductionlinear elasticityH-measures.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 41 , Issue 6 , November 2007 , pp. 1061 - 1087
Copyright
© EDP Sciences, SMAI, 2007

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