Summary
In this paper, different formulations of finite isotropic hyperelastic material laws for compressible solids are considered. Material laws with an additive split of the hyperelastic strain energy function into isochoric parts and volumetric parts are often used in the numerical treatment of nearly incompressible solids. It will be shown that this formulation leads to unphysical results in the simple tension problem when we do not restrict ourselves to nearly incompressible materials.
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Beatty, M. F.: Topics in finite elasticity: Hyperelasticity of rubber, elastomers, and biological tissues-with examples. Appl. Mech. Rev.40, 1699–1734 (1987).
Beatty, M. F., Stalnaker, D. O.: The Poisson function of finite elasticity. J. Appl. Mech.53, 807–813 (1987).
Ehlers, W.: Poröse Medien-ein kontinuumsmechanisches Modell auf der Basis der Mischungstheorie. Forschungsberichte aus dem Fachbereich Bauwesen der Universität-GH-Essen47, Essen 1989.
Flory, P. J.: Thermodynamic relations for high elastic materials. Trans. Faraday Soc.57, 829–838 (1961).
Gurtin, M. E.: An introduction to continuum mechanics. New York: Academic Press 1981.
Leipholz, H.: Einführung in die Elastizitätstheorie. Karlsruhe: G. Braun 1968.
Miehe, C.: Aspects of the formulation and finite element implementation of large strain isotropic elasticity. Int. J. Numer. Methods Eng.37, 1981–2004 (1994).
Mooney, M.: A theory of large elastic deformation. J. Appl. Phys.11, 582–592 (1940).
Ogden, R. W.: Large deformation isotropic elasticity: on the correlation of theory and experiment for compressible rubberlike solids. Proc. R. Soc. London Ser. A328, 567–583 (1972).
Ogden, R. W.: Volume changes associated with the deformation of rubber-like solids. J. Mech. Phys. Solids24, 323–338 (1976).
Ogden, R. W.: Non-linear elastic deformation. Chichester: Ellis Horwood 1984.
Peng, S. T. J., Landel, R. F.: Stored energy function and compressibility of rubberlike materials under large strain J. Appl. Phys.46, 2599–2604 (1975).
Penn, R. W.: Volume changes accompanying the extension of rubber. Trans. Soc. Rheol.14, 509–517 (1970).
Rivlin, R. S.: Large elastic deformations of isotropic materials. Proc. R. Soc. London Ser. A241, 379–397 (1948).
Simo, J. C., Pister, K. S.: Remarks on rate constitutive equations for finite deformation. Comput. Methods Appl. Mech. Eng.46, 201–215 (1984).
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Ehlers, W., Eipper, G. The simple tension problem at large volumetric strains computed from finite hyperelastic material laws. Acta Mechanica 130, 17–27 (1998). https://doi.org/10.1007/BF01187040
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DOI: https://doi.org/10.1007/BF01187040