Skip to main content
SpringerLink
Log in

Global invariance and Lie-algebraic description in the theory of dislocations

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

The relationships between the Lie-algebraic description of continuously distributed dislocations and the global affine invariance of their tensorial density are studied. The affinely-invariant Lagrange description of static self-equilibrium distributions of dislocations is proposed and field equations describing distributions of internal stresses and couple stresses are formulated. The analogy between the proposed theory of dislocations and “3-fold electrodynamics” is formulated.

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

  • Barut, A. O., and Rączka, R. (1977).Theory of Group Representations and Applications, PWN, Warsaw.

    Google Scholar 

  • Bilby, B. A. (1960). InProgress in Solid Mechanics, I. N. Sneddon and R. H. Hill, eds., North-Holland, Amsterdam, p. 329.

    Google Scholar 

  • Bilby, B. A., Bullough, R., and Smith, E. (1955).Proceedings of the Royal Society A,231, 263.

    Google Scholar 

  • De Wit, R. (1973).Journal of Research of the National Bureau of Standards,77A, 49.

    Google Scholar 

  • Gairola, B. K. D. (1981). InContinuum Models of Discrete Systems, O. Brulin and R. K. T. Hsiek, eds., North-Holland, Amsterdam, p. 55.

    Google Scholar 

  • Hull, D., and Bacon, D. J. (1984).Introduction to Dislocations, Pergamon, Oxford.

    Google Scholar 

  • Kadić, A., and Edelen, D. G. B. (1983).A Gauge Theory of Dislocations and Disclinations, Springer-Verlag, Berlin.

    Google Scholar 

  • Post, E. J. (1980).Foundations of Physics,12, 169.

    Google Scholar 

  • Schouten, J. A. (1951).Tensor Analysis for Physicists, Clarendon Press, Oxford.

    Google Scholar 

  • Schouten, J. A. (1954).Ricci-Calculus, Springer-Verlag, Berlin.

    Google Scholar 

  • Sławianowski, J. J. (1985).Reports on Mathematical Physics,22, 323.

    Google Scholar 

  • Sławianowski, J. J. (1986).Reports on Mathematical Physics,23, 177.

    Google Scholar 

  • Trzęsowski, A. (1987a).International Journal of Theoretical Physics,26, 317.

    Google Scholar 

  • Trzęsowski, A. (1987b).International Journal of Theoretical Physics,26, 1059.

    Google Scholar 

  • Turski, Ł. (1966).Bulletin of the Polish Academy of Sciences, Technical Sciences,14, 289.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Fundamental Technological Research, Polish Academy of Sciences, 00-049, Warsaw, Poland

    Andrzej Trzęsowski & Jan J. Sławianowski

Authors
  1. Andrzej Trzęsowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jan J. Sławianowski
    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

Trzęsowski, A., Sławianowski, J.J. Global invariance and Lie-algebraic description in the theory of dislocations. Int J Theor Phys 29, 1239–1249 (1990). https://doi.org/10.1007/BF00672934

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00672934

Keywords

Search

Navigation