Advertisement

Journal of Elasticity

, Volume 87, Issue 2–3, pp 95–108 | Cite as

On Formulating and Assessing Continuum Theories of Electromagnetic Fields in Elastic Materials

  • J. L. Ericksen
Article

Abstract

My aim is to explore some ideas about the foundations of electromagnetic theory for elastic materials and to suggest some ways of assessing theories of this kind. I will describe some old ideas that seem to have been forgotten, about forces exerted by matter and fields on each other, and a similar idea about energies. Among other things, I will trace Toupin’s thinking about elastic dielectrics, showing how he moved toward using these ideas, although he did not explicitly recognize them. Further, I will explain how his dynamical theory can be interpreted to be consistent with them, although this is not obvious from what he wrote.

Key words

elastic dielectrics foundations of electromagnetic theory 

Mathematics Subject Classifications (2000)

705xx 74A20 74F15 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Truesdell, C., Toupin, R.A.: The classical field theories. In: Flügge, S. (ed.) Handbuch der Physik, vol. III/I, pp. 226–793 (1960)Google Scholar
  2. 2.
    Kovetz, A.: Electromagnetic Theory. Oxford University Press, Oxford and New York (2000)MATHGoogle Scholar
  3. 3.
    Wang, C.C.: Mathematical principles of mechanics and electromagnetism. In: Miele, A. (ed.) (2 volumes). Plenum, New York and London (1979)Google Scholar
  4. 4.
    Brown, W.F.: Magnetoelastic Interactions. Springer, Berlin Heidelberg New York (1966)Google Scholar
  5. 5.
    Page, L.: Introduction to Theoretical Physics, 2nd ed., Van Nostrand, New York (1935)Google Scholar
  6. 6.
    Whittaker, E.T.: A History of the Theories of Aether and Electricity, ( 2 volumes). Harper & Brothers, New York (1960)Google Scholar
  7. 7.
    Hutter, K., van de Ven, A.F.: Field matter interactions in thermoelastic solids: lecture notes in physics. In: Ehlers, J., Hepp, K., Kippenhahn, R., Weidenmüller, H.A., Zittarz, J. (eds.) 88. Springer, Berlin Heidelberg New York (1978)Google Scholar
  8. 8.
    Toupin, R.A.: The elastic dielectric. J. Rational Mechanics Anal. 5, 849–915, (1956)MathSciNetGoogle Scholar
  9. 9.
    Toupin, R.A.: Stress tensors in elastic dielectrics. Arch. Ration. Mech. Anal. 5, 440–552, (1960)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Toupin, R.A.: A dynamical theory of elastic dielectrics. Int. J. Eng. Sci. 1, 101–126, (1963)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Ericksen, J.L.: Transformation theory for some continuum theories. Iran. J. Sci. Technol. 6, 113–124, (1977)Google Scholar
  12. 12.
    Ericksen, J.L.: On generalized momentum. Int. J. Solids Struct. 18, 315–317, (1982)MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Ericksen, J.L.: Theory of elastic dielectrics revisited. Arch. Ration. Mech. Anal. doi:10.1007/s00205-006-0042-4
  14. 14.
    Schlömerkemper, A.: Mathematical derivation of the continuum limit of the magnetic force between two parts of a rigid crystalline material. Arch. Ration. Mech. Anal. 176, 227–269, (2005)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Ericksen, J.L.: Electromagnetism in steadily rotating matter. Contin. Mech. Thermodyn. 17, 361–371, (2006)MATHCrossRefADSMathSciNetGoogle Scholar
  16. 16.
    Wilson, M., Wilson, H.A.: On the electric effect of rotating an electric insulator in a magnetic field. Proc. R. Soc. Lond. A89, 99–106, (1913)ADSGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  • J. L. Ericksen
    • 1
  1. 1.FlorenceUSA

Personalised recommendations