Small amplitude homogenization applied to models of non-periodic fibrous materials
ESAIM: Mathematical Modelling and Numerical Analysis - 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 : https://doi.org/10.1051/m2an:2007050
Classification : 35J25,  74Q15,  74B05
Mots clés : non-periodic homogenization, fibrous material, small amplitude, low contrast, conduction, linear elasticity, $H$-measures
@article{M2AN_2007__41_6_1061_0,
author = {Manceau, David},
title = {Small amplitude homogenization applied to models of non-periodic fibrous materials},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
pages = {1061--1087},
publisher = {EDP-Sciences},
volume = {41},
number = {6},
year = {2007},
doi = {10.1051/m2an:2007050},
zbl = {1126.92006},
mrnumber = {2377107},
language = {en},
url = {www.numdam.org/item/M2AN_2007__41_6_1061_0/}
}
Manceau, David. Small amplitude homogenization applied to models of non-periodic fibrous materials. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 41 (2007) no. 6, pp. 1061-1087. doi : 10.1051/m2an:2007050. http://www.numdam.org/item/M2AN_2007__41_6_1061_0/

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