Small amplitude homogenization applied to models of non-periodic fibrous materials
Manceau, David
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 41 (2007), p. 1061-1087 / Harvested from Numdam
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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.

Publié le : 2007-01-01
DOI : https://doi.org/10.1051/m2an:2007050
Classification:  35J25,  74Q15,  74B05 
@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},
     volume = {41},
     year = {2007},
     pages = {1061-1087},
     doi = {10.1051/m2an:2007050},
     mrnumber = {2377107},
     zbl = {1126.92006},
     language = {en},
     url = {http://dml.mathdoc.fr/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) pp. 1061-1087. doi : 10.1051/m2an:2007050. http://gdmltest.u-ga.fr/item/M2AN_2007__41_6_1061_0/

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