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ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Small amplitude homogenization applied to modelsof non-periodic fibrous materials
David Manceau
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 41 / Issue 6 / November 2007

Published online by Cambridge University Press:

15 December 2007, pp. 1061-1087

Print publication:

November 2007
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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.