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.
Mots clés : constitutive law, finite element method, biological tissue, hyperelasticity, nonlinear partial differential equations, anisotropic material
@article{M2AN_2003__37_4_725_0,
author = {Bourdarias, Christian and Gerbi, St\'ephane and Ohayon, Jacques},
title = {A three dimensional finite element method for biological active soft tissue formulation in cylindrical polar coordinates},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {725--739},
publisher = {EDP-Sciences},
volume = {37},
number = {4},
year = {2003},
doi = {10.1051/m2an:2003044},
mrnumber = {2018440},
zbl = {1070.74045},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2003044/}
}
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: Modélisation mathématique et analyse numérique PY - 2003 SP - 725 EP - 739 VL - 37 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2003044/ DO - 10.1051/m2an:2003044 LA - en ID - M2AN_2003__37_4_725_0 ER -
%0 Journal Article %A Bourdarias, Christian %A Gerbi, Stéphane %A Ohayon, Jacques %T A three dimensional finite element method for biological active soft tissue formulation in cylindrical polar coordinates %J ESAIM: Modélisation mathématique et analyse numérique %D 2003 %P 725-739 %V 37 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2003044/ %R 10.1051/m2an:2003044 %G en %F M2AN_2003__37_4_725_0
Bourdarias, Christian; Gerbi, Stéphane; Ohayon, Jacques. A three dimensional finite element method for biological active soft tissue formulation in cylindrical polar coordinates. ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 4, pp. 725-739. doi : 10.1051/m2an:2003044. http://www.numdam.org/articles/10.1051/m2an:2003044/
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