Implémentation éléments finis du modèle hyperélastique anisotrope HGO
DOI:
https://doi.org/10.13052/EJCM.19.441-464Keywords:
biomechanics, anisotropic hyperelasticity, HGO model, finite elementAbstract
Anisotropic hyperelastic constitutive laws are often used to determine strain and stress in biological soft tissues such as ligaments, tendons or arterial walls. In this paper, the implementation of the HGO model in the finite element code FER is presented. Three numerical examples are studied: homogeneous uniaxial tension test where analytical solutions are available; uniaxial tension test highlighting the anisotropic behavior (contracting and swelling of the section in two perpendicular directions); contact and impact between hand and soft biological tissues in the framework of application using a virtual mannequin generator.
Downloads
References
ANSYS HTML Online Documentation, Release 11.0 Documentation for ANSYS, 2007.
Balzani D., Neff P., Schröder J., Holzapfel G.A, “A polyconvex framework for soft biological
tissues. Adjustment to experimental data”, International Journal of Solids and Structures,
n° 43, 2006, p. 6052-6070.
Bathe K.J., Finite element procedures in engineering analysis, Englewood Cliffs, NJ:
Prentice-Hall, 1982.
Chamoret D., Peyraut F., Gomes S., Mahdjoub M., Chevriau S., Feng Z.-Q., « Du mannequin
numérique au calcul éléments finis – application à la modélisation en biomécanique », 11e
Colloque National AIP PRIMECA de La Plagne, 22-24 avril 2009.
De Saxcé G., Feng Z.-Q., “New inequality and functional for contact with friction: the
implicit standard material approach”, Mech. Struct. Mach., n° 19, 1991, p. 301-325.
De Saxcé G., Feng Z.-Q., “The bi-potential method: a constructive approach to design the complete
contact law with friction and improved numerical algorithms”, Math. Comput. Model, Special
issue: Recent Advances in Contact Mechanics, n° 28 (4–8), 1998, p. 225-245.
Feng Z.-Q., “2D or 3D frictional contact algorithms and applications in a large deformation
context”, Commun. Numer. Methods Eng., n° 11, 1995, p. 409-416.
Feng Z.-Q., “Some test examples of 2D and 3D contact problems involving coulomb friction
and large slip”, Math. Comput. Model. Special issue: Recent Advances in Contact
Mechanics, n° 28 (4–8), 1998, p. 469-477.
Feng Z.-Q., Cros J.-M., “FER/SUBDomain an integrated environment for finite element
analysis using object-oriented approach”, Mathematical Modelling and Numerical
Analysis, vol. 36, n° 5, 2002, p. 773-781.
FER Online Documentation, http://lmee.univ-evry.fr/~feng/FerSystem.html, 2009.
Fung Y.C., Fronek K., Patitucci P., “Pseudoelasticity of arteries and the choice of its
mathematical expression”, Am. J. Physiol., n° 237, 1979, p. 620-631.
Gasser T.C., Ogden R.W., Holzapfel G.A., “Hyperelastic modelling of arterial layers with
distributed collagen fibre orientations”, J. R. Soc. Interface, n° 3, 2006, p. 15-35.
Gomes S., Sagot J.-C., Koukam A., Leroy N., “MANERCOS, a new tool providing ergonomics
in a concurrent engineering design life cycle”, 4th Annual Scientific Conference on Web
Technology, New Media, Communications and Telematics - Theory, Methods, Tools and
Applications, EUROMEDIA 99, Munich, 25-28 April 1999, p. 237-24.
Guo Z.Y., Peng X.Q., Moran B., “A composites-based hyperelastic constitutive model for
soft tissue with application to the human annulus fibrosus” J. Mech. Phys. Solids, n° 54,
, p. 1952-1971.
Holzapfel G.A., Gasser T.C., Ogden R.W., “A new constitutive framework for arterial wall
mechanics and a comparative study of material models”, Journal of Elasticity, n° 61,
, p. 1-48.
Holzapfel G.A., “Determination of material models for arterial walls from uniaxial extension
tests and histological structure”, Journal of Theoretical Biology, 238, 2006, p. 290-302.
Newmark N.M., “A method of computation for structural dynamics”, Journal of the
Engineering Mechanics Division, ASCE, 85, 1959, p. 67-94.
Peyraut F., Renaud C., Labed N., Feng Z.-Q., “Modélisation de tissus biologiques en
hyperélasticité anisotrope – Etude théorique et approche éléments finis”, Comptes Rendus
Mécanique, vol. 337, n° 2, 2009, p. 101-106.
Schröder J., Neff P., Balzani D., “A variational approach for materially stable anisotropic
hyperelasticity”, International Journal of Solids and Structures, n° 42, 2005, p. 4352-
Scovazzi G., Love E., Shashkov M.J., “Multi-scale Lagrangian shock hydrodynamics on
Q1/P0 finite elements: Theoretical framework and two-dimensional computations”,
Computer methods in applied mechanics and engineering, n° 197, 2008, p. 1056-1079.
Spencer A.J.M., Isotropic polynomial invariants and tensor functions, Boehler, J.P. (Ed.),
Applications of Tensor Functions in Solids Mechanics, CISM Course No. 282. Springer
Verlag, 1987.
Talbi N., Résolution du contact frottant entre objets déformables en temps réel et avec retour
haptique, Thèse de Doctorat, Université d’Evry Val d’Essonne, 2008.
Weiss J.A., Maker B.N., Govindjee S., “Finite element implementation of incompressible,
transversely isotropic hyperelasticity”, Computer methods in applied mechanics and
engineering, n° 135, 1996, p. 107-128.
