Skip to main content
SpringerLink
Log in

An energy function for transversely-isotropic elastic material and the Ponyting Effect

  • Published:
Korean Journal of Computational & Applied Mathematics Aims and scope Submit manuscript

Abstract

On the basis of the semi-linear material of John, invoking the theory of homogenization for heterogeneous media and the theory of invariants for isotropic scalar functions, an energy function is built for a transversely-isotropic medium in finite elastic deformation. The Ponyting Effect, for material in simple shear, is reviewed for this case of transversal isotropy. It is shown that this effect is apprehended by the constructed energy function.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. C.A. TruesdellThe Mechanical Foundation of Elasticity and Fluid Dynamics. International Science Review Series, Vol III. Gordon and Breach Science Publishers, NY. 1966.

    Google Scholar 

  2. A.I. LurieNonlinear Elasticity. Nauka Publishers, Moscow. 1980 (in Russian).

    Google Scholar 

  3. A. AkinolaAn Energy Function for transtropic Elastic Material. ICTP Preprint (1996) IC/96/281, 1–10.

  4. J.T. Oden and J.N. ReddyVariational Methods in Theoretical Mechanics 2nd edition. Springer-Verlag, NY. 1983.

    Book  Google Scholar 

  5. A.E. Green and J. AdkinsLarge Elastic Deformations. Oxford University Press. 1960.

  6. C.C. Wang and C.A. TruesdellIntroduction to Rational Elasticity. Noordhoff Inter Publishing, 1973.

  7. B.E. PobedriaMechanics of Composite Materials. Moscow State University Press, Moscow. 1984 (in Russian).

    Google Scholar 

  8. A. AkinolaFinite Deformations of Heterogeneous Elastic Body with Regular Structure. Dep. VINITI Academy of Sciences USSR, (1985) No.5069-85. (in Russian).

  9. A.E. Green and W. ZernaTheoretical Elasticity. Oxford University Press. 1968.

  10. F. JohnPlain Strain Problems for a Perfectly Elastic Material of Harmonic Type. Commun. Pure and Appl. Math. Vol.13 (1960) No.2, 139–196.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematics Department, Obafemi Awolowo University, ILE-IFE, Nigeria

    Ade Akinola

Authors
  1. Ade Akinola
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Akinola, A. An energy function for transversely-isotropic elastic material and the Ponyting Effect. Korean J. Comput. & Appl. Math. 6, 639–649 (1999). https://doi.org/10.1007/BF03009956

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03009956

AMS Mathematics Subject Classification

Key words and phrases

Search

Navigation