Small amplitude homogenization applied to models of non-periodic fibrous materials
ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 6, pp. 1061-1087.

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.

DOI : 10.1051/m2an:2007050
Classification : 35J25, 74Q15, 74B05
Mots-clés : non-periodic homogenization, fibrous material, small amplitude, low contrast, conduction, linear elasticity, $H$-measures 
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     title = {Small amplitude homogenization applied to models of non-periodic fibrous materials},
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Manceau, David. Small amplitude homogenization applied to models of non-periodic fibrous materials. ESAIM: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 6, pp. 1061-1087. doi : 10.1051/m2an:2007050. http://www.numdam.org/articles/10.1051/m2an:2007050/

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