A three dimensional finite element method for biological active soft tissue Formulation in cylindrical polar coordinates
Laboratoire de Mathématiques, Université
de Savoie, Savoie Technolac, 73376 Le Bourget
du Lac, France. Christian.Bourdarias@univ-savoie.fr., Stephane.Gerbi@univ-savoie.fr.
2 Laboratoire TIMC-IMAG, Dynacell, UMR CNRS 5525, Domaine de la Merci, 38706 Grenoble, France. Jacques.Ohayon@univ-savoie.fr.
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.
Mathematics Subject Classification: 65M60 / 92C10 / 92C50 / 74L15 / 74S05 / 74B20
Key words: Constitutive law / finite element method / biological tissue / hyperelasticity / nonlinear partial differential equations / anisotropic material.
© EDP Sciences, SMAI, 2003