Modélisation de la loi de comportement hyperélastique transversalement isotrope des élastomères
DOI:
https://doi.org/10.13052/REMN%20%2016/2007//Keywords:
elastomer, hyperelasticity, isotropic, transversely isotropic, finit elementAbstract
This paper presents a detailed description of the computer implementation of a fully incompressible isotropic and transversely isotropic hyperelastic behavior. The approach is based on the fiber reinforced composites continuum theory. As an extension of the isotropic hyperelasticity, it is assumed that the strain energy function is decomposed into an isotropic and an anisotropic components. Closed form expressions for the elasticity tensors in incompressible plane stress are given for isotropic and transversely isotropic cases. Numerical examples are presented to illustrate the performance of these expressions.
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References
Aît Houcine N., Approche globale de la mécanique de la rupture appliquée aux élastomères,
Thesis, de l’Université des Sciences et Technologies de Lille, France, 1996.
Bonet J., Burton A. J., “A Simple Orthotropic, Transversely Isotropic Hyperelastic
Constitutive Equation for Large Strain Computations”, Computer Methods in Applied
Mechanics and Engineering, vol. 162, 1998, p. 151-164.
Cazacu O., “A new hyperelastic model for transversely isotropic solids”, Mathematik und
Physik ZAMP, vol. 53, 2002, p. 901-911.
Chevaugeon N., Verron E., Peseux B., « Construction d’une loi de Comportement Isotrope
Transverse pour la simulation du Thermoformage de Thermoplastiques Charges de
Fibres », XVe Congrés Français de Mécanique, France, 2001, p. 259-264.
Chevaugeon N., Verron E., Peseux B., “Finite element analyis of nonlinear transversely
isotropic hyperelastic membranes for thermoforging applications”, European Congres in
Computation Methods in Applied Science and Engineering, ECCOMAS 2000, Barcelona,
September 2000.
Ekh M., Runesson K., “Modeling and numerical issues in hyperelasto-plasticity with
anisotropy”, International Journal of Solids and Structures, vol. 38, 2001, p. 9461-9478.
Gasser T.C., Holzapfel G.A., “A rate-independent elastoplastic constitutive model for fiberreinforced
composites at finite strains: continuum basis, algorithmic formulation and
finite element implementation”, Computational Mechanics, 2002.
Gruttmann F., Taylor R. L., “Theory and Finite Element Formulation of Rubberlike
Membrane Shells Using Principal Stretches”, International Journal for Numerical
Methods in Engineering, vol. 35, 1992, p. 1111-1126.
Holzapfel G. A., Non linear solid mechanics, Wiley, 2000.
Holzapfel G. A., Eberlein R., Wiriggers P., Weizsäcker H. W., “Large strain analysis of soft
biological membranes: Formulation and finite element analysis”, Computer Methods in
Applied Mechanics and Engineering, vol. 132, 1996, p. 45-61.
Kyriacou S. K., Schwab C., Humphrey J. D., “Finite Element Analysis of Nonlinear
Orthotropic Hyperelastic Membranes”, Comput. Mech., vol. 18, 1996, p. 269-278.
Limbert G., Taylor M., “On the constitutive modeling of biological soft connective tissues, A
general theoretical framework and explicit forms of the tensors of elasticity for strongly
anisotropic continuum fiber-reincorced composites at finite strain”, International Journal
of Solids and Structures, vol. 39, 2002, p. 2343-2358.
Lürding D., Basar Y., Hanskötter U., “Application of transversly isotropic mateials to multilayer
shell elements undergoing finite rotations and large strains”, International Journal
of Solids and Structures, vol. 38, 2001, p. 9493-9503.
Marvalova B., Urban R., “Identification of orthotropic hyperelastic material properties of
cord-rubber cylindrical air-spring, Experimental Stress Analysis”, 39 International
Conference, Czech Republic, 2001.
Miehe C., “Aspect of the Formulation and Finite Element Implementation of Large Strain
Isotropic Elasticity”, International Journal for Numerical Methods in Engineering, 37,
vol. 37, 1994, p. 1981-2004.
Reese S., “Meso-macro modelling of fibre-reinforced rubber-like composites exhibiting large
elastoplastic deformation”, International Journal of Solids and Structures, vol. 40, 2003,
p. 951-980.
Reese S., Raible T., Wriggers P., “Finite element modelling of orthotropic material behaviour
in pneumatic membranes”, International Journal of Solids and Structures, vol. 38, 2001,
p. 9525-9544.
Simo J. C., Taylor R. L., “Quasi-incompressible finite elasticity in principal stretches:
Continuum basis and numerical algorithms”, Computer Methods in Applied Mechanics
and Engineering, vol. 85, 1991, p. 273-310.
Spencer A. J. M., “Constitutive Theory for Strongly Anisotropic Solids”, A. J. M. Spencer
(Ed.), Continuum Theory of the Mechanics of Fiber-Reinforced Composites, CISM
Courses and Lectures n° 282, International Center for Mechanical Sciences, Springer-
Verlag, Wien, 1984, p. 1-32.
Walton J. R., Wilber J. P., “Sufficient condition for strong ellipticity for a class of anisotropic
materials”, International Journal of Non-Linear Mechanics, vol. 38, 2003, p. 441-455.
Weiss J. A., Maker B. N., Govindjee S., “Finite Element Implementation of Incompressible,
Transversely Isotropic Hyperelasticity”, Computer Methods in Applied Mechanics and
Engineering, vol. 135, 1996, p. 107-128.
