Some Topics in Finite Elasticity

  • R. S. Rivlin

Abstract

A Number of reviews of recent advances in finite elasticity theory have appeared in the past few years. Truesdell1 has given a comprehensive review of this and closely related topics, largely from a critical and historical point of view. Doyle and Ericksen2 have given an account of the fundamentals of the subject, employing the general tensor notation. The first few chapters of a book by Green and Zerna3 contain a connected account of the subject as it was at the time at which the book was written. This elegant presentation will have its main appeal to the more sophisticated readers, who are familiar with the use of convected co-ordinates and the associated general tensor calculus. An elementary account of finite elasticity theory, directed to readers whose main interest is in the physical aspects of the subject has been given by Rivlin4.

Keywords

Anisotropy Rubber Doyle Incompressibility Betti 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1a.
    Truesdell, C. J. Rat. Mech. Anal. Vol. 1, p. 125, 1952.Google Scholar
  2. 1b.
    . Truesdell, C. J. Rat. Mech. Anal. Vol. 2, p. 593, 1953.Google Scholar
  3. 2.
    Doyle, T. C. and Ericksen, J. L. Advances in Applied Mechanics, Vol. IV; Academic Press, New York, 1956.Google Scholar
  4. 3.
    Green, A. E. and Zerna, W. Theoretical Elasticity; Oxford University Press, Oxford, 1954.Google Scholar
  5. 4.
    Rivlin, R. S. Rheology, Theory and Applications. (Edited by Eirich, F. R.) Vol. 1; Academic Press, New York, 1956.Google Scholar
  6. 5.
    Rivlin, R. S. Phil. Trans. A Vol. 240, p. 491, 1948.CrossRefGoogle Scholar
  7. 6.
    Pearson, K. Quart. Appl. Math. Vol. 14, p. 133, 1956.Google Scholar
  8. 7.
    Green, A. E. and Spencer, A. J. M. Brown Univ. Report No. DA-3487/12.Google Scholar
  9. 8.
    Hill, R. J. Mech. and Phys. Solids Vol. 5, p. 229, 1957.CrossRefGoogle Scholar
  10. 9.
    Novozhilov, V. V. Foundations of the Nonlinear Theory of Elasticity (Translated by Bagemihl, F., Komm, H. and Seidel, W.) Graylock Press, Rochester, 1953.Google Scholar
  11. 10.
    Rivlin, R. S. and Saunders, D. W. Phil. Trans. A Vol. 243, p. 251, 1951.CrossRefGoogle Scholar
  12. 11.
    Gent, A. N. and Rivlin, R. S. Proc. Phys. Soc. B Vol. 65, p. 487, 1952.CrossRefGoogle Scholar
  13. 12.
    Gent, A. N. and Rivlin, R. S. Proc. Phys. Soc. B Vol. 65, p. 645, 1952.CrossRefGoogle Scholar
  14. 13.
    Smith, G. F. and Rivlin, R. S. Arch. Rat. Mech. Vol. 1, p. 107, 1957.CrossRefGoogle Scholar
  15. 14.
    Rivlin, R. S. Phil. Trans. A Vol. 240, p. 459, 1948.CrossRefGoogle Scholar
  16. 15.
    Ericksen, J. L. and Rivlin, R. S. J. Rat. Mech. Anal. Vol. 3, p. 281, 1954.Google Scholar
  17. 16.
    Smith, G. F. and Rivlin, R. S. Trans. Amer. Math. Soc. Vol. 88, p. 175, 1958.CrossRefGoogle Scholar
  18. 17.
    Adkins, J. E. Proc. Roy. Soc. A Vol. 229, p. 119, 1955.CrossRefGoogle Scholar
  19. 18.
    Murnaghan, F. D. Amer. J. Math. Vol. 59, p. 235, 1937.CrossRefGoogle Scholar
  20. 19.
    Voigt, W. Ann. Phys. Vol. 52, p. 536, 1893.Google Scholar
  21. 20.
    Mooney, M. J. Appl. Phys. Vol. 11, p. 582, 1940.CrossRefGoogle Scholar
  22. 21.
    Rivlin, R. S. Phil. Trans. A Vol. 240, p. 509, 1948.CrossRefGoogle Scholar
  23. 22.
    Treloar, L. R. G. The Physics of Rubber Elasticity; Oxford University Press, 1949.Google Scholar
  24. 23.
    Gumbrell, S. M., Mullins, L. and Rivlin, R. S. Trans. Faraday Soc. Vol. 49, p. 1495, 1953.CrossRefGoogle Scholar
  25. 24.
    Rivlin, R. S. Phil. Trans. A Vol. 241, p. 379, 1948.CrossRefGoogle Scholar
  26. 25.
    Rivlin, R. S. Phil. Trans. A Vol. 242, p. 173, 1949.CrossRefGoogle Scholar
  27. 26.
    Rivlin, R. S. Proc. Roy. Soc. A Vol. 195, p. 463, 1949.CrossRefGoogle Scholar
  28. 27.
    Green, A. E. and Shield, R. T. Proc. Roy. Soc. A Vol. 202, p. 407, 1950.CrossRefGoogle Scholar
  29. 28.
    Green, A. E. and Wilkes, E. W. J. Rat. Mech. Anal Vol. 3, p. 713, 1954.Google Scholar
  30. 29.
    Adkins, J. E. Proc. Roy. Soc. A Vol. 231, p. 75, 1955.CrossRefGoogle Scholar
  31. 30.
    Adkins, J. E. and Rivlin, R. S. Phil. Trans. A Vol. 244, p. 505, 1952.CrossRefGoogle Scholar
  32. 31.
    Murnaghan, F. D. Finite Deformation of an Elastic Solid; John Wiley, New York, 1951.Google Scholar
  33. 32.
    Green, A. E. and Wilkes, E. W. Quart. Appl. Math. Vol. 6, p. 240, 1953.CrossRefGoogle Scholar
  34. 33.
    Green, A. E. and Shield, R. T. Phil. Trans. A Vol. 244, p. 47, 1951.CrossRefGoogle Scholar
  35. 34.
    Adkins, J. E., Green, A. E. and Shield, R. T. Phil. Trans. A Vol. 246, p. 181, 1953.CrossRefGoogle Scholar
  36. 35.
    Adkins, J. E., Green, A. E. and Nicholas, G. C. Phil. Trans. A Vol. 247, p. 279, 1954.CrossRefGoogle Scholar
  37. 36.
    Rivlin, R. S. J. Rat. Mech. Anal. Vol. 2, p. 53, 1953.Google Scholar
  38. 37.
    Green, A. E., Rivlin, R. S. and Shield, R. T. Proc. Roy. Soc. A Vol. 211, p. 128, 1952.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • R. S. Rivlin
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityProvidence 12USA

Personalised recommendations