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Licensed Unlicensed Requires Authentication Published by De Gruyter June 18, 2015

Isotropic incompressible hyperelastic models for modelling the mechanical behaviour of biological tissues: a review

  • Cora Wex , Susann Arndt , Anke Stoll , Christiane Bruns and Yuliya Kupriyanova EMAIL logo

Abstract

Modelling the mechanical behaviour of biological tissues is of vital importance for clinical applications. It is necessary for surgery simulation, tissue engineering, finite element modelling of soft tissues, etc. The theory of linear elasticity is frequently used to characterise biological tissues; however, the theory of nonlinear elasticity using hyperelastic models, describes accurately the nonlinear tissue response under large strains. The aim of this study is to provide a review of constitutive equations based on the continuum mechanics approach for modelling the rate-independent mechanical behaviour of homogeneous, isotropic and incompressible biological materials. The hyperelastic approach postulates an existence of the strain energy function – a scalar function per unit reference volume, which relates the displacement of the tissue to their corresponding stress values. The most popular form of the strain energy functions as Neo-Hookean, Mooney-Rivlin, Ogden, Yeoh, Fung-Demiray, Veronda-Westmann, Arruda-Boyce, Gent and their modifications are described and discussed considering their ability to analytically characterise the mechanical behaviour of biological tissues. The review provides a complete and detailed analysis of the strain energy functions used for modelling the rate-independent mechanical behaviour of soft biological tissues such as liver, kidney, spleen, brain, breast, etc.


Corresponding author: Yuliya Kupriyanova, Clinic for General, Visceral and Vascular Surgery, University Clinic Magdeburg, Leipziger Strasse 44, Building 60a, 39120 Magdeburg, Germany, Phone: +49 391 6117133, Fax: +49 391 6175570, E-mail:

Acknowledgments

This research is supported financially by Saxony Anhalt, Germany. The authors thank M.Sc. Alexander Russell of the Institute of Process Engineering, Otto von Guericke University Magdeburg, for the useful discussions and proofreading of the manuscript.

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Received: 2014-10-30
Accepted: 2015-5-7
Published Online: 2015-6-18
Published in Print: 2015-12-1

©2015 by De Gruyter

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