Skip to main content
SpringerLink
Log in

Variational treatment of the elastic constants of disordered materials

  • Published:
Zeitschrift für Physik A Hadrons and nuclei

Abstract

Using the method of Hill a variational principle is derived to obtain upper and lower bounds for the effective elastic constants of disordered materials, such as polycrystals or multiphase materials. All bounds previously known are rederived and especially new bounds are given being closer than the ones of Hashin and Shtrikman. In detail the elastic constants of polycrystals built of cubic single crystals and of multiphase materials are considered. The analogous bounds for the dielectric constant of polycrystals are also given.

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. Hill, R.: Proc. Phys. Soc. (London)A65, 349 (1952).

    Article  ADS  Google Scholar 

  2. Voigt, W.: Ann. Phys.33, 573 (1889).

    Article  Google Scholar 

  3. Reuss, A.: Z. Angew. Math. Mech.9, 49 (1929).

    Article  Google Scholar 

  4. Hashin, Z., Shtrikman, S.: J. Mech. Phys. Solids10, 335 (1962).

    Article  ADS  MathSciNet  Google Scholar 

  5. Hashin, Z., Shtrikman, S.: J. Mech. Phys. Solids10, 343 (1962).

    Article  ADS  MathSciNet  Google Scholar 

  6. Hashin, Z., Shtrikman, S.: J. Mech. Phys. Solids11, 127 (1963).

    Article  ADS  MathSciNet  Google Scholar 

  7. Beran, M. J.: Statistical continuum theories. New York: Interscience Publ. 1968.

    MATH  Google Scholar 

  8. Kröner, E.: Z. Physik151, 504 (1958).

    Article  ADS  Google Scholar 

  9. Kröner, E.: J. Mech. Phys. Solids15, 319 (1967).

    Article  ADS  Google Scholar 

  10. Zeller, R., Dederichs, P. H.: phys. stat. sol. (b)55 (1973).

  11. Dederichs, P. H., Zeller, R.: KFA-Jül-Report, JÜL-877-FF (1972).

  12. Hill, R.: J. Mech. Phys. Solids11, 357 (1963).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Festkörperforschung der Kernforschungsanlage Jülich, Jülich

    P. H. Dederichs & R. Zeller

Authors
  1. P. H. Dederichs
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. Zeller
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

It is a pleasure to thank Prof. G. Leibfried for helpful discussions and many comments.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dederichs, P.H., Zeller, R. Variational treatment of the elastic constants of disordered materials. Z. Physik 259, 103–116 (1973). https://doi.org/10.1007/BF01392841

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01392841

Search

Navigation