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Issue ESAIM: M2AN
Volume 37, Number 4, July-August 2003
Biological and Biomedical Applications
Page(s) 681 - 698
DOI 10.1051/m2an:2003054

M2AN, Vol. 37, N°4, pp. 681-698
DOI: 10.1051/m2an:2003054

Cell-to-Muscle homogenization. Application to a constitutive law for the myocardium

Denis Caillerie1, Ayman Mourad2, 1 and Annie Raoult3, 2

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

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.


Mathematics Subject Classification. 74L15, 74Q05, 74Q15, 92B05.

Key words: Myocardium, constitutive law, homogenization, large deformations.


© EDP Sciences, SMAI 2003


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