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