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

Caillerie, Denis; Mourad, Ayman; Raoult, Annie

ESAIM: Modélisation mathématique et analyse numérique, Special issue on Biological and Biomedical Applications, Tome 37 (2003) no. 4, pp. 681-698.

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.

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