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Issue M2AN Volume 37, Number 4, July-August 2003 Biological and Biomedical Applications Page(s) 725 - 739 DOI 10.1051/m2an:2003044

M2AN, Vol. 37, N°4, pp. 725-739
DOI: 10.1051/m2an:2003044

A three dimensional finite element method for biological active soft tissue FORMULATION IN CYLINDRICAL POLAR COORDINATES

Christian Bourdarias¹, Stéphane Gerbi¹ and Jacques Ohayon<sup>2

1</sup>  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.

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.

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

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