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.
@article{M2AN_2003__37_4_681_0,
author = {Caillerie, Denis and Mourad, Ayman and Raoult, Annie},
title = {Cell-to-muscle homogenization. Application to a constitutive law for the myocardium},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {37},
year = {2003},
pages = {681-698},
doi = {10.1051/m2an:2003054},
mrnumber = {2018437},
zbl = {1070.74030},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2003__37_4_681_0}
}
Caillerie, Denis; Mourad, Ayman; Raoult, Annie. Cell-to-muscle homogenization. Application to a constitutive law for the myocardium. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 37 (2003) pp. 681-698. doi : 10.1051/m2an:2003054. http://gdmltest.u-ga.fr/item/M2AN_2003__37_4_681_0/
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