Geodesic
Cell-to-muscle homogenization. Application to a constitutive law for the myocardium
ESAIM: Mathematical Modelling and Numerical Analysis , Special issue on Biological and Biomedical Applications, Tome 37 (2003) no. 4, pp. 681-698

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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.

DOI : 10.1051/m2an:2003054
Classification : 74L15, 74Q05, 74Q15, 92B05
Keywords: myocardium, constitutive law, homogenization, large deformations 
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     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 },
     pages = {681--698},
     publisher = {EDP-Sciences},
     volume = {37},
     number = {4},
     year = {2003},
     doi = {10.1051/m2an:2003054},
     mrnumber = {2018437},
     zbl = {1070.74030},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2003054/}
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Caillerie, Denis; Mourad, Ayman; Raoult, Annie. Cell-to-muscle homogenization. Application to a constitutive law for the myocardium. ESAIM: Mathematical Modelling and Numerical Analysis , Special issue on Biological and Biomedical Applications, Tome 37 (2003) no. 4, pp. 681-698. doi: 10.1051/m2an:2003054

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