Displaying similar documents to “Cell-to-muscle homogenization. Application to a constitutive law for the myocardium”

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

Denis Caillerie, Ayman Mourad, Annie Raoult (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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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...

A model of macroscale deformation and microvibration in skeletal muscle tissue

Bernd Simeon, Radu Serban, Linda R. Petzold (2009)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper deals with modeling the passive behavior of skeletal muscle tissue including certain microvibrations at the cell level. Our approach combines a continuum mechanics model with large deformation and incompressibility at the macroscale with chains of coupled nonlinear oscillators. The model verifies that an externally applied vibration at the appropriate frequency is able to synchronize microvibrations in skeletal muscle cells. From the numerical analysis point of view,...

A three dimensional finite element method for biological active soft tissue formulation in cylindrical polar coordinates

Christian Bourdarias, Stéphane Gerbi, Jacques Ohayon (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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A hyperelastic constitutive law, for use in anatomically accurate finite element models of living structures, is suggested for the passive and the active mechanical properties of incompressible biological tissues. This law considers the passive and active states as a same hyperelastic continuum medium, and uses an activation function in order to describe the whole contraction phase. The variational and the FE formulations are also presented, and the FE code has been validated and applied...

Molecular modelling of stresses and deformations in nanostructured materials

Gwidon Szefer (2004)

International Journal of Applied Mathematics and Computer Science

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A molecular dynamics approach to the deformation and stress analysis in structured materials is presented. A new deformation measure for a lumped mass system of points is proposed. In full consistency with the continuum mechanical description, three kinds of stress tensors for the discrete system of atoms are defined. A computer simulation for a set of 10^5 atoms forming a sheet undergoing tension (Case 1) and contraction (Case 2) is given. Characteristic microstress distributions evoked...

Multiscale Materials Modelling: Case Studies at the Atomistic and Electronic Structure Levels

Emilio Silva, Clemens Först, Ju Li, Xi Lin, Ting Zhu, Sidney Yip (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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Although the intellectual merits of computational modelling across various length and time scales are generally well accepted, good illustrative examples are often lacking. One way to begin appreciating the benefits of the multiscale approach is to first gain experience in probing complex physical phenomena at one scale at a time. Here we discuss materials modelling at two characteristic scales separately, the atomistic level where interactions are specified through classical potentials...