Small amplitude homogenization applied to models of non-periodic fibrous materials
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 41 (2007) no. 6, p. 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
Keywords: 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},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {6},
     year = {2007},
     pages = {1061-1087},
     doi = {10.1051/m2an:2007050},
     zbl = {1126.92006},
     mrnumber = {2377107},
     language = {en},
     url = {http://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, Volume 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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