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

Free access article

Issue		ESAIM: 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 Ohayon²

¹ 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

What is OpenURL?

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.

If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.