Advertisement

A hyperelastic constitutive model for rubber-like materials

  • İsmail Doğan KülcüEmail author
Original
  • 251 Downloads

Abstract

In this contribution, a new form of the strain energy function is proposed to describe the hyperelastic behavior of rubber-like materials under various deformation. The proposed function represents an invariant-based model and contains two material parameters. The model was tested with the experimental data of vulcanized rubbers, collagen and fibrin. The material parameters are kept constant for a material subjected to different types of loading. Good agreement between model and experimental data was obtained for all materials.

Keywords

Hyperelasticity Strain energy Constitutive relation Rubber-like materials 

Notes

Acknowledgements

Author thanks the anonymous reviewers for their constructive and fruitful comments.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Arruda, E., Boyce, M.: A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. J. Mech. Phys. Solids 41, 389 (1993).  https://doi.org/10.1016/0022-5096(93)90013-6 CrossRefzbMATHGoogle Scholar
  2. 2.
    Boyce, M.C., Arruda, E.M.: Constitutive models of rubber elasticity: a review. Rubber Chem. Technol. 73(3), 504–523 (2000)CrossRefGoogle Scholar
  3. 3.
    Carroll, M.: A strain energy function for vulcanized rubbers. J. Elast. 103(2), 173–187 (2011)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Darijani, H., Naghdabadi, R.: Hyperelastic materials behavior modeling using consistent strain energy density functions. Acta Mech. 213(3–4), 235–254 (2010)CrossRefGoogle Scholar
  5. 5.
    Dobrynin, A.V., Carrillo, J.M.Y.: Universality in nonlinear elasticity of biological and polymeric networks and gels. Macromolecules 44(1), 140–146 (2010)CrossRefGoogle Scholar
  6. 6.
    Flory, P., Rehner, J.: Statistical mechanics of cross-linked polymer networks i. rubberlike elasticity. J. Chem. Phys. 11, 512 (1943).  https://doi.org/10.1063/1.1723791 CrossRefGoogle Scholar
  7. 7.
    Fung, Y.: Elasticity of soft tissues in simple elongation. Am. J. Physiol. Leg. Content 213(6), 1532–1544 (1967)CrossRefGoogle Scholar
  8. 8.
    Gent, A.: A new constitutive relation for rubber. Rubber Chem. Technol. 69, 59 (1996)CrossRefGoogle Scholar
  9. 9.
    Holzapfel, G.A.: Nonlinear Solid Mechanics: A Continuum Approach for Engineering. Wiley, Hoboken (2005)Google Scholar
  10. 10.
    Isihara, A., Hashitsume, N., Tatibana, M.: Statistical theory of rubber-like elasticity. iv.(two-dimensional stretching). J. Chem. Phys. 19(12), 1508–1512 (1951)MathSciNetCrossRefGoogle Scholar
  11. 11.
    James, H., Guth, E.: Theory of the elastic properties of rubbers. J. Chem. Phys. 11, 455 (1943)CrossRefGoogle Scholar
  12. 12.
    Mansouri, M., Darijani, H.: Constitutive modeling of isotropic hyperelastic materials in an exponential framework using a self-contained approach. Int. J. Solids Struct. 51(25–26), 4316–4326 (2014)CrossRefGoogle Scholar
  13. 13.
    Miehe, C., Göktepe, S., Lulei, F.: A micro–macro approach to rubber-like materials—part i: the non-affine micro-sphere model of rubber elasticity. J. Mech. Phys. Solids 52, 2617 (2004).  https://doi.org/10.1016/j.jmps.2004.03.011 MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Ogden, R.: Non-Linear Elastic Deformations. Dover Publications, New York (1997)Google Scholar
  15. 15.
    Ogden, R.W.: Large deformation isotropic elasticity-on the correlation of theory and experiment for incompressible rubberlike solids. Proc. R. Soc. Lond. A Math. Phys. Sci. 326(1567), 565–584 (1972)CrossRefGoogle Scholar
  16. 16.
    Sasso, M., Palmieri, G., Chiappini, G., Amodio, D.: Characterization of hyperelastic rubber-like materials by biaxial and uniaxial stretching tests based on optical methods. Polym. Test. 27(8), 995–1004 (2008)CrossRefGoogle Scholar
  17. 17.
    Steinmann, P., Hossain, M., Possart, G.: Hyperelastic models for rubber-like materials: consistent tangent operators and suitability for treloar’s data. Arch. Appl. Mech. 82(9), 1183–1217 (2012)CrossRefGoogle Scholar
  18. 18.
    Storm, C., Pastore, J.J., MacKintosh, F.C., Lubensky, T.C., Janmey, P.A.: Nonlinear elasticity in biological gels. Nature 435(7039), 191 (2005)CrossRefGoogle Scholar
  19. 19.
    Treloar, L.: Stress-strain data for vulcanized rubber under various types of deformation. Rubber Chem. Technol. 17(4), 813–825 (1944)CrossRefGoogle Scholar
  20. 20.
    Yeoh, O.H.: Characterization of elastic properties of carbon-black-filled rubber vulcanizates. Rubber Chem. Technol. 63(5), 792–805 (1990)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Faculty of EngineeringTurkish-German UniversityBeykoz/IstanbulTurkey

Personalised recommendations