Journal of Elasticity

, Volume 53, Issue 1, pp 37–45 | Cite as

A New Representation Theorem for Elastic Constitutive Equations of Cubic Crystals

Article

Abstract

The objective of this paper is to provide a new irreducible nonpolynomial representation for elastic constitutive equations of cubic crystals with the material symmetry group O or Td or Oh. The presented result is expressed in terms of a generating set composed of nine polynomial tensor generators. It is simpler and more compact than a recent result in terms of a generating set composed of ten tensor generators.

nonlinear elasticity constitutive equation invariance restriction cubic crystal nonpolynomial representation. 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M.E. Gurtin, An Introduction to Continuum Mechanics.Academic Press, New York (1981).MATHGoogle Scholar
  2. 2.
    A.C. Pipkin and A.S. Wineman, Material symmetry restrictions on non-polynomial constitutive equations. Arch. Rat. Mech. Anal. 12(1963) 420–426.MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    A.S. Wineman and A.C. Pipkin, Material symmetry restrictions on constitutive equations, Arch. Rat. Mech. Anal. 17(1964) 184-214.MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    A.J.M. Spencer, Theory of Invariants, In Continuum Physics(A.C. Eringen (ed.)), Vol. I. Academic Press, New York (1971).Google Scholar
  5. 5.
    H. Xiao, General irreducible representations for constitutive equations of elastic crystals and transversely isotropic elastic solids, J. Elasticity 39(1995) 47-73.MATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    H. Xiao, On anisotropic scalar functions of a single symmetric tensor, Proc. Roy. Soc. Lond. A452(1996) 1545-1561.ADSGoogle Scholar
  7. 7.
    H. Xiao, On constitutive equations of Cauchy elastic solids: all kinds of crystals and quasicrystals, J. Elasticity 48(1997) 241-283.MATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    H. Xiao, On anisotropic invariants of a symmetric tensor: crystal classes, quasicrystal classes and others, Proc. Roy. Soc. Lond. A454(1998) 1217-1240.ADSGoogle Scholar
  9. 9.
    A.E. Green and J.E. Adkins, Large Elastic Deformations.Clarendon Press, Oxford (1960).MATHGoogle Scholar
  10. 10.
    C. Truesdell and W. Noll, The Nonlinear Field Theories of Mechanics, In Handbuch der Physik, (S. Flügge (ed.)), Bd. III/3, Springer-Verlag, Berlin (1965).Google Scholar
  11. 11.
    G.F. Smith, Constitutive Equations for Anisotropic and Isotropic Materials. Elsevier, New York (1994).Google Scholar
  12. 12.
    J. Rychlewski and J.M. Zhang, On representations of tensor functions: a review, Advances in Mechanics 14(4) (1991) 75-94.MathSciNetGoogle Scholar
  13. 13.
    Q.S. Zheng, Theory of representations for tensor functions: a unified invariant approach to constitutive equations, Appl. Mech. Rev. 47(1994) 554-587.CrossRefGoogle Scholar
  14. 14.
    M. Basista, Tensor function representations as applied to deriving constitutive relations for skewed anisotropy, Zeits. Angew. Math. Mech. 65(1985) 151-158.MATHMathSciNetGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • H. Xiao
    • 1
  1. 1.Institute of Mechanics IRuhr-University BochumBochumGermany

Personalised recommendations