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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...
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...
A corrector theory for the strong approximation of gradient fields inside periodic composites made from two materials with different power law behavior is provided. Each material component has a distinctly different exponent appearing in the constitutive law relating gradient to flux. The correctors are used to develop bounds on the local singularity strength for gradient fields inside micro-structured media. The bounds are multi-scale in nature and can be used to measure the amplification of applied...
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