The Strain-Energy Function for Anisotropic Elastic Materials

  • G. F. Smith
  • R. S. Rivlin


If we consider a body of perfectly elastic material to undergo deformation in which a point initially at X i in the rectangular Cartesian coordinate system x i moves to x i in the same coordinate system, then the strain-energy function W is a single-valued function of the quantities g ij defined by.


Reference System Polynomial Basis Displacement Gradient Monoclinic System Undeformed State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    F. Birch, Physical Review vol. 71 (1947) pp. 809–824.CrossRefGoogle Scholar
  2. 2.
    J. D. Dana and C. S. Hurlbut, Dana’s textbook of mineralogy, New York, John Wiley and Sons, 1952.Google Scholar
  3. 3.
    A. E. Green and E. W. Wilkes, Journal of Rational Mechanics and Analysis vol. 3 (1954) pp. 713–723.Google Scholar
  4. 4.
    A. E. Green and W. Zerna, Theoretical elasticity, Oxford, Clarendon Press, 1954.Google Scholar
  5. 5.
    F. D. Murnaghan, Finite deformation of an elastic solid, New York, John Wiley & Sons, 1951.Google Scholar
  6. 6.
    P. L. Sheng, Secondary eleasticity, Chinese Association for the Advancement of Science Monographs, no. 1, 1955.Google Scholar
  7. 7.
    C. Truesdell, Journal of Rational Mechanics and Analysis vol. 1 (1952) pp. 125–300.Google Scholar
  8. 8.
    W. Voigt, Lehrbuch der Kristallphysik, Leipzig, B. G. Teubner, 1910.Google Scholar
  9. 9.
    H. Weyl, The classical groups, their invariants and representations, Princeton, Princeton University Press, 1946.Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • G. F. Smith
    • 1
  • R. S. Rivlin
    • 1
  1. 1.Brown UniversityProvidenceUSA

Personalised recommendations