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

Christian Bourdarias; Stéphane Gerbi; Jacques Ohayon[1]

  • [1] Laboratoire TIMC-IMAG, Dynacell, UMR CNRS 5525, Domaine de la Merci, 38706 Grenoble, France

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2003)

  • Volume: 37, Issue: 4, page 725-739
  • ISSN: 0764-583X

Abstract

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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 to describe the biomechanical behavior of a thick-walled anisotropic cylinder under different active loading conditions.

How to cite

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Bourdarias, Christian, Gerbi, Stéphane, and Ohayon, Jacques. "A three dimensional finite element method for biological active soft tissue formulation in cylindrical polar coordinates." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 37.4 (2003): 725-739. <http://eudml.org/doc/245560>.

@article{Bourdarias2003,
abstract = {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 to describe the biomechanical behavior of a thick-walled anisotropic cylinder under different active loading conditions.},
affiliation = {Laboratoire TIMC-IMAG, Dynacell, UMR CNRS 5525, Domaine de la Merci, 38706 Grenoble, France},
author = {Bourdarias, Christian, Gerbi, Stéphane, Ohayon, Jacques},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {constitutive law; finite element method; biological tissue; hyperelasticity; nonlinear partial differential equations; anisotropic material; hyperelastic continuum medium; thick-walled anisotropic cylinder},
language = {eng},
number = {4},
pages = {725-739},
publisher = {EDP-Sciences},
title = {A three dimensional finite element method for biological active soft tissue formulation in cylindrical polar coordinates},
url = {http://eudml.org/doc/245560},
volume = {37},
year = {2003},
}

TY - JOUR
AU - Bourdarias, Christian
AU - Gerbi, Stéphane
AU - Ohayon, Jacques
TI - A three dimensional finite element method for biological active soft tissue formulation in cylindrical polar coordinates
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2003
PB - EDP-Sciences
VL - 37
IS - 4
SP - 725
EP - 739
AB - 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 to describe the biomechanical behavior of a thick-walled anisotropic cylinder under different active loading conditions.
LA - eng
KW - constitutive law; finite element method; biological tissue; hyperelasticity; nonlinear partial differential equations; anisotropic material; hyperelastic continuum medium; thick-walled anisotropic cylinder
UR - http://eudml.org/doc/245560
ER -

References

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