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, Volume 37 (2003) no. 4, p. 725-739

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.

DOI : https://doi.org/10.1051/m2an:2003044
Classification:  65M60,  92C10,  92C50,  74L15,  74S05,  74B20
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {37},
     number = {4},
     year = {2003},
     pages = {725-739},
     doi = {10.1051/m2an:2003044},
     zbl = {1070.74045},
     mrnumber = {2018440},
     language = {en},
     url = {http://www.numdam.org/item/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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 37 (2003) no. 4, pp. 725-739. doi : 10.1051/m2an:2003044. http://www.numdam.org/item/M2AN_2003__37_4_725_0/

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