Small amplitude homogenization applied to models of non-periodic fibrous materials

David Manceau

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

  • Volume: 41, Issue: 6, page 1061-1087
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Manceau, David. "Small amplitude homogenization applied to models of non-periodic fibrous materials." ESAIM: Mathematical Modelling and Numerical Analysis 41.6 (2007): 1061-1087. <http://eudml.org/doc/250057>.

@article{Manceau2007,
abstract = { 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. },
author = {Manceau, David},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Non-periodic homogenization; fibrous material; small amplitude; low contrast; conduction; linear elasticity; H-measures.; non-periodic homogenization; -measures},
language = {eng},
month = {12},
number = {6},
pages = {1061-1087},
publisher = {EDP Sciences},
title = {Small amplitude homogenization applied to models of non-periodic fibrous materials},
url = {http://eudml.org/doc/250057},
volume = {41},
year = {2007},
}

TY - JOUR
AU - Manceau, David
TI - Small amplitude homogenization applied to models of non-periodic fibrous materials
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2007/12//
PB - EDP Sciences
VL - 41
IS - 6
SP - 1061
EP - 1087
AB - 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.
LA - eng
KW - Non-periodic homogenization; fibrous material; small amplitude; low contrast; conduction; linear elasticity; H-measures.; non-periodic homogenization; -measures
UR - http://eudml.org/doc/250057
ER -

References

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