We derive a constitutive law for the myocardium from the description of both the geometrical arrangement ofcardiomyocytes and their individual mechanical behaviour. We model a set of cardiomyocytes by a quasiperiodic discretelattice of elastic bars interacting by means of moments. We work in a large displacement framework and we use a discretehomogenization technique. The macroscopic constitutive law is obtained through the resolution of anonlinear self-equilibrum system of the discrete lattice reference cell.