Skip to main content
SpringerLink
Log in

A Strain Energy Function for Vulcanized Rubbers

  • Published:
Journal of Elasticity Aims and scope Submit manuscript

Abstract

A three-parameter strain energy function is developed to model the nonlinearly elastic response of rubber-like materials. The development of the model is phenomenological, based on data from the classic experiments of Treloar, Rivlin and Saunders, and Jones and Treloar on sheets of vulcanized rubber. A simple two-parameter version, similar to the Mooney-Rivlin and Gent-Thomas strain energies, provides an accurate fit with all of the data from Rivlin and Saunders and Jones and Treloar, as well as with Treloar’s data for deformations for which the principal deformation invariant I 1 has values in the range 3≤I 1≤20.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Treloar, L.R.G.: The Physics of Rubber Elasticity, 3rd edn. Clarendon, Oxford (1975)

    Google Scholar 

  2. Boyce, M.C., Arruda, E.M.: Constitutive models of rubber elasticity: a review. Rubber Chem. Technol. 73, 504–523 (2000)

    Article  Google Scholar 

  3. Treloar, L.R.G.: Stress-strain data for vulcanized rubber under various types of deformation. Trans. Faraday Soc. 40, 59–70 (1944)

    Article  Google Scholar 

  4. Rivlin, R.S., Saunders, D.S.: Large elastic deformation of isotropic materials—VII. Experiments on the deformation of rubber. Philos. Trans. R. Soc. Lond. Ser. A 243, 251–288 (1951)

    Article  ADS  MATH  Google Scholar 

  5. Jones, D.F., Treloar, L.R.G.: The properties of rubber in pure homogeneous strain. J. Phys. D, Appl. Phys. 27, 1285–1304 (1975)

    Article  ADS  Google Scholar 

  6. Valanis, K.C., Landel, R.F.: The strain-energy function of a hyperelastic material in terms of the extension ratios. J. Appl. Phys. 38, 2997–3002 (1967)

    Article  ADS  Google Scholar 

  7. Obata, Y., Kawabata, S., Kawai, H.: Mechanical properties of natural rubber vulcanizates in finite deformation. J. Polym. Sci. 8, 903–919 (1970)

    Google Scholar 

  8. Gent, A.N., Thomas, A.G.: Forms for the stored (strain) energy function for rubber. J. Polym. Sci. 28, 625–628 (1958)

    Article  ADS  Google Scholar 

  9. Sawyers, K.N.: On the possible values of the strain invariants for isochoric deformation. J. Elast. 7, 99–102 (1977)

    Article  Google Scholar 

  10. Agarwal, V.K., Carroll, M.M.: Admissibility conditions on principal strain invariants. Acta Mech. 177, 89–96 (2004)

    Article  Google Scholar 

  11. Klingbeil, W.W., Shield, R.T.: Some numerical investigations on empirical strain-energy functions in the large axisymmetric extensions of rubber membranes. J. Appl. Math. Phys. 15, 608–629 (1964)

    Article  Google Scholar 

  12. Gent, A.N.: A new constitutive relation for rubber. Rubber Chem. Technol. 69, 59–61 (1996)

    Article  MathSciNet  Google Scholar 

  13. Carroll, M.M.: Molecular chain networks and strain energy functions in rubber elasticity. Int. J. Eng. Sci. (submitted for publication)

  14. Criscione, J.C.: Rivlin’s representation formula is ill-conceived for the determination of response functions via biaxial testing. J. Elast. 70, 129–147 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  15. Carroll, M.M.: Compressible isotropic strain energies that support universal irrotational finite deformations. Q. J. Mech. Appl. Math. 58, 601–614 (2005)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering and Materials Science, Rice University, Mail Stop 321, P.O. Box 1892, Houston, TX, 77251-1892, USA

    M. M. Carroll

Authors
  1. M. M. Carroll
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. M. Carroll.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Carroll, M.M. A Strain Energy Function for Vulcanized Rubbers. J Elast 103, 173–187 (2011). https://doi.org/10.1007/s10659-010-9279-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10659-010-9279-0

Keywords

Mathematics Subject Classification

Search

Navigation