Skip to main content
Log in

Compressible rubber materials: experiments and simulations

  • Special Issue
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

Porous rubber materials are often used in automotive industries. In this paper, a carbon black-filled one is investigated, which is used, for example, as sealing. Such materials are distinguished by viscoelastic behaviour and by a structural compressibility induced by the porous structure. To identify the material behaviour, uniaxial tension tests and hydrostatic compression tests are performed. Therein the main focus of attention lies on the basic elasticity and on the viscoelasticity in the whole loading range. An important observation of these tests is the viscoelastic behaviour under hydrostatic compression, which has to be included in the material model. Because of the two-phase character of cellular rubber, the theory of porous media is taken into account. To model the structural compressibility, a volumetric–isochore split of the deformation gradient is used. Therein the volumetric part includes the aspect of the point of compaction. Finally, the concept of finite viscoelasticity is applied introducing an intermediate configuration. Because of the viscoelastic behaviour under hydrostatic compression, the volumetric–isochore split is taken into account for the nonequilibrium parts, too. Nonlinear relaxation functions are used to model the process-dependent relaxation times and the highly nonlinear behaviour with respect to the deformation and feedrate. The material parameters of the model are estimated using a stochastic identification algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Avril S., Bonnet M., Bretelle A.: Overview of identification methods of mechanical parameters based on full-field measurements. Exp. Mech. 48, 381–402 (2008)

    Article  Google Scholar 

  2. de Boer R.: Theory of Porous Media. Springer, Berlin (2000)

    Book  MATH  Google Scholar 

  3. Bowen R.M.: Incompressible porous media models by use of the theory of mixtures. Int. J. Eng. Sci. 18, 1129–1148 (1980)

    Article  MATH  Google Scholar 

  4. Coleman B.D., Gurtin M.E.: Thermodynamics with internal variables. J. Chem. Phys. 47, 597–613 (1967)

    Article  Google Scholar 

  5. Coleman B.D., Noll W.: The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Ration. Mech. Anal. 13, 167–178 (1963)

    Article  MathSciNet  MATH  Google Scholar 

  6. Diebels S.: A micropolar theory of porous media: constitutive modelling. Transp. Porous Med. 34, 193–208 (1999)

    Article  Google Scholar 

  7. Ehlers, W.: Constitutive equations for granular materials in geomechanical context. In: Hutter, K. (ed.) Continuum Mechanics in Environmental Sciences, CISM International Centre for Mechanical Sciences, vol. 337, pp. 313–402. Springer, Berlin (1993)

  8. Eipper, G.: Theorie und Numerik finiter elastischer Deformationen in fluidgesättigten porösen Festkörpern. Dissertation, Institut für Mechanik (Bauwesen), Lehrstuhl II, Universität Stuttgart (1998)

  9. Koprowski-Theiss, N., Johlitz, M., Diebels, S.: Experiments and theoretical modelling of a carbon black filled solid rubber. Rubber Chem. Technol. (submitted) (2010)

  10. Koprowski-Theiss, N., Johlitz, M., Diebels, S.: Modelling of a cellular rubber with nonlinear viscosity functions. Exp. Mech. Published online (2010)

  11. Koprowski-Theiss, N., Johlitz, M., Diebels, S.: Pressure dependent properties of a compressible polymer. Exp. Mech. (submitted) (2010)

  12. Lion A.: On the large deformation behaviour of reinforced rubber at different temperatures. J. Mech. Phys. Solids 45, 1805–1834 (1997)

    Article  Google Scholar 

  13. Mooney M.: A theory of large elastic deformation. J. Appl. Phys. 11, 582–592 (1940)

    Article  MATH  Google Scholar 

  14. Rechenberg I.: Evolutionsstrategie ’94. Fromann-Holzboog, Stuttgart (1994)

    Google Scholar 

  15. Reese S., Govindjee S.: Theoretical and numerical aspects in the thermo-viscoelastic material behaviour of rubber-like polymers. Mech. Time-Depend. Mater. 1, 357–396 (1998)

    Article  Google Scholar 

  16. Rivlin R.S.: Large elastic deformation of isotropic materials IV: further developments of the general theory. Phil. Trans. R. Soc. Lond. A A241, 379–397 (1948)

    MathSciNet  Google Scholar 

  17. Scheday, G.: Theorie und Numerik der Parameteridentifikation von Materialmodellen der finiten Elastizität und Inelastizität auf der Grundlage optischer Feldmessmethoden. Dissertation, Bericht-Nr. I-11 des Instituts für Mechanik, Lehrstuhl I, Universität Stuttgart (2003)

  18. Schwefel H.P.: Evolution and Optimum Seeking. Wiley, New York, NY (1995)

    Google Scholar 

  19. Sedlan, K. Viskoelastisches Materialverhalten von Elastomerwerkstoffen, Experimentelle Untersuchung und Modellbildung. Dissertation, Berichte des Instituts für Mechanik (2/2001). Universität Gesamthochschule Kassel (2001)

  20. Seibert, H.: Echtzeitfähige Regelung eines hydrostatischen Druckversuchs zur Untersuchung des Kompressionsverhaltens poröser Elastomere. Diplomarbeit, Institut für Technische Mechanik, Universität des Saarlandes (2010)

  21. Sidoroff F.: Un modèle viscoélastique non lineaire avec configuration intermédiaire. Journal de Mécanique 13, 679–713 (1974)

    MathSciNet  Google Scholar 

  22. Truesdell C.: Sulle basi delle termomeccanica. Rend. Lincei 22, 33–38 (1957)

    MathSciNet  MATH  Google Scholar 

  23. Truesdell, C.A., Toupin, R.: The classical field theories. In: Flügge, S. (Herausgeber), Handbuch der Physik III/1. Springer, Berlin (1960)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. Koprowski-Theiß.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Koprowski-Theiß, N., Johlitz, M. & Diebels, S. Compressible rubber materials: experiments and simulations. Arch Appl Mech 82, 1117–1132 (2012). https://doi.org/10.1007/s00419-012-0616-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-012-0616-6

Keywords

Navigation