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: myocardium, constitutive law, homogenization, large deformations
@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: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {681--698},
year = {2003},
publisher = {EDP Sciences},
volume = {37},
number = {4},
doi = {10.1051/m2an:2003054},
mrnumber = {2018437},
zbl = {1070.74030},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an:2003054/}
}
TY - JOUR AU - Caillerie, Denis AU - Mourad, Ayman AU - Raoult, Annie TI - Cell-to-muscle homogenization. Application to a constitutive law for the myocardium JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2003 SP - 681 EP - 698 VL - 37 IS - 4 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an:2003054/ DO - 10.1051/m2an:2003054 LA - en ID - M2AN_2003__37_4_681_0 ER -
%0 Journal Article %A Caillerie, Denis %A Mourad, Ayman %A Raoult, Annie %T Cell-to-muscle homogenization. Application to a constitutive law for the myocardium %J ESAIM: Modélisation mathématique et analyse numérique %D 2003 %P 681-698 %V 37 %N 4 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an:2003054/ %R 10.1051/m2an:2003054 %G en %F 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: Modélisation mathématique et analyse numérique, Special issue on Biological and Biomedical Applications, Tome 37 (2003) no. 4, pp. 681-698. doi: 10.1051/m2an:2003054
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