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Cell-to-Muscle homogenization. Application to a constitutive law forthe myocardium

Published online by Cambridge University Press:  15 November 2003

Denis Caillerie ,
Ayman Mourad  and
Annie Raoult
Denis Caillerie
Affiliation:
Laboratoire Sols, Solides, Structures, BP 53, 38041 Grenoble Cedex 9, France. Denis.Caillerie@inpg.fr.
Ayman Mourad
Affiliation:
Laboratoire Sols, Solides, Structures, BP 53, 38041 Grenoble Cedex 9, France. Denis.Caillerie@inpg.fr. Laboratoire de Modélisation et Calcul, BP 53, 38041 Grenoble Cedex 9, France. Ayman.Mourad@imag.fr.
Annie Raoult
Affiliation:
Laboratoire de Modélisation et Calcul, BP 53, 38041 Grenoble Cedex 9, France. Ayman.Mourad@imag.fr. Laboratoire TIMC, Domaine de la Merci, 38076 La Tronche Cedex, France. Annie.Raoult@imag.fr.
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Abstract

We derive a constitutive law for the myocardium from the description of both the geometrical arrangement of cardiomyocytes and their individual mechanical behaviour. We model a set of cardiomyocytes by a quasiperiodic discrete lattice of elastic bars interacting by means of moments. We work in a large displacement framework and we use a discrete homogenization technique. The macroscopic constitutive law is obtained through the resolution of a nonlinear self-equilibrum system of the discrete lattice reference cell.

Keywords

Myocardiumconstitutive lawhomogenizationlarge deformations.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 4: Special issue on Biological and Biomedical Applications , July 2003 , pp. 681 - 698
Copyright
© EDP Sciences, SMAI, 2003

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