Skip to main content
SpringerLink
Log in

Mechanics of Rubberlike Solids

  • Conference paper
Mechanics of the 21st Century

Abstract

In this paper we discuss: (i) the large deformation stress-strain response of rubberlike solids based on experimental observations, including both elastic and inelastic behaviour of particle-filled and unfilled rubber, (ii) the mathematical modelling of this behaviour through its phenomenological treatment using elasticity theory and extensions of the theory to account for inelastic responses such as the Mullins effect, stress softening and hysteretic stress-strain cycling, (iii) an introduction to the analysis of the coupling of mechanical and magnetic effects in so-called magneto-sensitive elastomers, which are being used as ‘active’ components in various applications where the mechanical properties of the material are changed rapidly when a suitable magnetic field is applied.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M.F. Beatty and S. Krishnaswamy, A theory of stress-softening in incompressible isotropic materials, J. Mech. Phys. Solids, 48, pp.1931–1965, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  2. D. Besdo, R.H. Schuster and J. Ihlemann, Constitutive Models for Rubber II, Balkema, 2001.

    Google Scholar 

  3. H. Bouasse and Z. Carrière, Courbes de traction du caoutchouc vulcanisé, Ann. Fac. Sciences de Toulouse, 5, pp.257–283, 1903.

    Google Scholar 

  4. M.C. Boyce and E.M. Arruda, Constitutive models of rubber elasticity: a review, Rubber Chem. Technol., 73, pp.504–523, 2000.

    Google Scholar 

  5. W.F. Brown, Magnetoelastic Interactions, Springer, 1966.

    Google Scholar 

  6. J.J.C. Busfield and A.H. Muhr, Constitutive Models for Rubber III, Balkema, 2003.

    Google Scholar 

  7. E.A. De Souza Neto, D. Perić and D.R. Owen, A phenomenological three-dimensional rate independent continuum model for highly filled polymers: formulation and computational aspects, J. Mech. Phys. Solids, 42, pp.1553–1550, 1994.

    Google Scholar 

  8. A. Dorfmann and A. Muhr, Constitutive Models for Rubber, Balkema, 1999.

    Google Scholar 

  9. A. Dorfmann and R.W. Ogden, A pseudo-elastic model for loading, partial unloading and reloading of particle-reinforced rubber, Int. J. Solids Structures, 40, pp.2699–2714, 2003.

    Article  MATH  Google Scholar 

  10. A. Dorfmann and R.W. Ogden, Magnetoelastic modelling of elastomers, European J. Mech. A/Solids, 22, pp.497–507, 2003.

    Article  MathSciNet  MATH  Google Scholar 

  11. A. Dorfmann and R.W. Ogden, A constitutive model for the Mullins effect with permanent set in particle-filled rubber, Int. J. Solids Structures, 41, pp.1855–1878, 2004.

    Article  MATH  Google Scholar 

  12. A. Dorfmann and R.W. Ogden, Nonlinear magnetoelastic deformations of elastomers, Acta Mechanica, 167, pp.13–28, 2003.

    Article  Google Scholar 

  13. A. Dorfmann and R.W. Ogden, Nonlinear magnetoelastic deformations. Q. J. Mech. Appl. Math., in press, 2004.

    Google Scholar 

  14. A. Dorfmann and R.W. Ogden, Some problems in nonlinear magnetoelasticity, ZAMP, in press, 2004.

    Google Scholar 

  15. A. Dorfmann, R.W. Ogden and G. Saccomandi, Universal relations for magnetoelastic solids, Int. J. Nonlinear Mech., 39, pp.1699–1708, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  16. A.N. Gent, A new constitutive relation for rubber, Rubber Chem. Technol., 69, pp.59–61, 1996.

    MathSciNet  Google Scholar 

  17. S. Govindjee and J.C. Simo, A micro-mechanically based continuum damage model for carbon black-filled rubbers incorporating the Mullins’ effect, J. Mech. Phys. Solids, 39, pp.87–112, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  18. M.E. Gurtin and E.C. Francis, Simple rate-independent model for damage, J. Spacecraft Rockets, 18, pp.285–286, 1981.

    Article  Google Scholar 

  19. G.A. Holzapfel, Nonlinear Solid Mechanics: a Continuum Approach for Engineering, 2nd ed. John Wiley & Sons Ltd, 2001.

    Google Scholar 

  20. C.O. Horgan, R.W. Ogden and G. Saccomandi, A theory of stress softening of elastomers based on finite chain extensibility, Proc. R. Soc. Lond. A, 460, pp.1737–1754, 2004.

    MathSciNet  MATH  Google Scholar 

  21. C.O. Horgan and G. Saccomandi, Constitutive modelling of rubberlike and biological materials with limiting chain extensibility, Math. Mech. Solids, 7, pp.353–371, 2002.

    MathSciNet  MATH  Google Scholar 

  22. C.O. Horgan and G. Saccomandi, Finite thermoelasticity with limiting chain extensibility, J. Mech. Phys. Solids, 51, pp.1127–1146, 2003.

    Article  MathSciNet  MATH  Google Scholar 

  23. C.O. Horgan and G. Saccomandi, A molecular-statistical basis for the Gent constitutive model of rubber elasticity, J. Elasticity, 68, pp.167–176, 2002.

    Article  MathSciNet  MATH  Google Scholar 

  24. K. Hutter and A.A.F. van de Ven, Field Matter Interactions in Thermoelastic Solids, Lecture Notes in Physics, vol. 88. Springer, 1978.

    Google Scholar 

  25. M.A. Johnson and M.F. Beatty, The Mullins effect in uniaxial extension and its influence on the transverse vibration of a rubber string, Continuum Mech. Thermodyn., 5, pp.83–115, 1993.

    Article  MathSciNet  Google Scholar 

  26. M.A. Johnson and M.F. Beatty, A constitutive equation for the Mullins effect in stress controlled uniaxial extension experiments, Continuum Mech. Thermodyn., 5, pp.301–318, 1993.

    Article  MathSciNet  Google Scholar 

  27. M.R. Jolly, J.D. Carlson and B.C. Muñoz, A model of the behaviour of magnetorheological materials, Smart Mater. Struct., 5, pp.607–614, 1996.

    Article  Google Scholar 

  28. S.V. Kankanala and N. Triantafyllidis, On finitely strained magnetorheological elastomers, J. Mech. Phys. Solids, in press, 2004.

    Google Scholar 

  29. A. Kovetz, Electromagnetic Theory, Oxford University Press, 2000.

    Google Scholar 

  30. G. Marckmann, E. Verron, L. Gornet, G. Chagnon, P. Charrier and P. Fort, A theory of network alteration for the Mullins effect, J. Mech. Phys. Solids, 50, pp.2011–2028, 2002.

    Article  MATH  Google Scholar 

  31. G.A. Maugin, Continuum Mechanics of Electromagnetic Solids, North Holland, 1988.

    Google Scholar 

  32. L. Mullins, Effect of stretching on the properties of rubber, J. Rubber Res., 16, pp.275–289, 1947.

    Google Scholar 

  33. L. Mullins, Softening of rubber by deformation, Rubber Chem. Technol., 42, pp.339–362, 1969.

    Google Scholar 

  34. L. Mullins and N.R. Tobin, Theoretical model for the elastic behavior of filler-reinforced vulcanized rubbers, Rubber Chem. Technol., 30, pp.555–571, 1957.

    Google Scholar 

  35. A.H. Muhr, J. Gough and I.H. Gregory, Experimental determination of model for liquid silicone rubber: Hyperelasticity and Mullins’ effect. In Proceedings of the First European Conference on Constitutive Models for Rubber, pages 181–187, Vienna, 1999. Balkema, 1999.

    Google Scholar 

  36. R.W. Ogden, Large deformation isotropic elasticity: on the correlation of theory and experiment for incompressible rubberlike solids, Proc. R. Soc. Lond. A, 326, pp.565–584, 1972.

    MATH  Google Scholar 

  37. R.W. Ogden, Elastic deformation of rubberlike solids. In Mechanics of Solids, pages 499–537. The Rodney Hill 60th Anniversary Volume. Pergamon Press, 1982.

    Google Scholar 

  38. R.W. Ogden, Recent advances in the phenomenological theory of rubber elasticity, Rubber Chem. Technol., 59, pp.361–383, 1986.

    Google Scholar 

  39. R.W. Ogden, Non-linear Elastic Deformations, Dover Publications, 1997.

    Google Scholar 

  40. R.W. Ogden, Elements of the theory of finite elasticity. In Nonlinear Elasticity: Theory and Applications, London Mathematical Society Lecture Notes 283, pages 1–57. Cambridge University Press, 2001.

    Google Scholar 

  41. R.W. Ogden, Pseudo-elasticity and stress softening. In Nonlinear Elasticity: Theory and Applications, London Mathematical Society Lecture Notes 283, pages 491–522. Cambridge University Press, 2001.

    Google Scholar 

  42. R.W. Ogden and D.G. Roxburgh, A pseudo-elastic model for the Mullins effect in filled rubber, Proc. R. Soc. Lond. A, 455, pp.2861–2877, 1999.

    Article  MathSciNet  MATH  Google Scholar 

  43. R.W. Ogden and D.G. Roxburgh, An energy-based model of the Mullins effect. In Proceedings of the First European Conference on Constitutive Models for Rubber, pages 23–28, Vienna, 1999. Balkema, 1999.

    Google Scholar 

  44. K.R. Rajagopal and A.S. Wineman, A constitutive equation for nonlinear solids which undergo deformation induced microstructural changes, Int. J. Plasticity, 8, pp.385–395, 1992.

    Article  MATH  Google Scholar 

  45. A.J.M. Spencer, Theory of Invariants. In Continuum Physics Vol. 1, pages 239–353. Academic Press, 1971.

    Google Scholar 

  46. D.J. Steigmann Equilibrium theory for magnetic elastomers and magnetoelastic membranes, Int. J. Nonlinear Mech., 39, pp. 1193–1216, 2004.

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  48. L.R.G. Treloar, The Physics of Rubber Elasticity, 3rd edition, Oxford University Press, 1975.

    Google Scholar 

  49. G. Saccomandi and R.W. Ogden, Mechanics and Thermomechanics of Rubberlike Solids, CISM Courses and Lectures Series 452. Springer, 2004.

    Google Scholar 

  50. A.E. Zúñiga and M.F. Beatty, A new phenomenological model for stresssoftening in elastomers, ZAMP, 53, pp.794–814, 2002.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Glasgow, Glasgow, G12 8QW, UK

    Ray W. Ogden

Authors
  1. Ray W. Ogden
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Polish Academy of Sciences, Warsaw, Poland

    Witold Gutkowski  & Tomasz A. Kowalewski  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer

About this paper

Cite this paper

Ogden, R.W. (2005). Mechanics of Rubberlike Solids. In: Gutkowski, W., Kowalewski, T.A. (eds) Mechanics of the 21st Century. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3559-4_17

Download citation

  • DOI: https://doi.org/10.1007/1-4020-3559-4_17

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-3456-5

  • Online ISBN: 978-1-4020-3559-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation