| Issue |
ESAIM: M2AN
Volume 41, Number 6, November-December 2007
|
|
|---|---|---|
| Page(s) | 1061 - 1087 | |
| DOI | https://doi.org/10.1051/m2an:2007050 | |
| Published online | 15 December 2007 | |
Small amplitude homogenization applied to models of non-periodic fibrous materials
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
Received:
10
November
2006
Revised:
29
June
2007
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.
Mathematics Subject Classification: 35J25 / 74Q15 / 74B05
Key words: Non-periodic homogenization / fibrous material / small amplitude / low contrast / conduction / linear elasticity / H-measures.
© EDP Sciences, SMAI, 2007
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