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The Cauchy Relations in Linear Elasticity Theory

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Abstract

In linear elasticity, we decompose the elasticity tensor into two irreducible pieces with 15 and 6 independent components, respectively. The vanishing of the piece with 6 independent components corresponds to the Cauchy relations. Thus, for the first time, we recognize the group-theoretical underpinning of the Cauchy relations.

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References

  1. L. Brillouin, Cours de Physique Théorique: les Tenseur en Mécanique et en Élasticité. Masson, Paris (1938).

    Google Scholar 

  2. R.L. Fosdick, private communications (May 2002).

  3. S. Haussühl, Die Abweichungen von den Cauchy-Relationen. Phys. kondens. Materie 6 (1967) 181–192.

    Google Scholar 

  4. S. Haussühl, Kristallphysik. Physik-Verlag, Weinheim (1983); (the 2nd edn is in preparation).

    Google Scholar 

  5. F.W. Hehl, Yu.N. Obukhov and G.F. Rubilar, On a possible new type of a T odd skewon field linked to electromagnetism. In: A. Macias, F. Uribe and E. Diaz (eds), Developments in Mathematical and Experimental Physics, Vol. A: Cosmology and Gravitation. Kluwer Academic/Plenum Publishers, New York (2002) pp. 241–256. Eprint archive http://www.arXiv. org/abs/gr-qc/0203096.

    Google Scholar 

  6. G. Leibfried, Gittertheorie der mechanischen und thermischen Eigenschaften der Kristalle. In: S. Flügge (ed.), Handbuch der Physik, Vol. VII/1, Kristallphysik I. Springer, Berlin (1955) pp. 104–324.

    Google Scholar 

  7. A.E.H. Love, A Treatise on the Mathematical Theory of Elasticity, 4th edn. Cambridge University Press, Cambridge, UK (1927).

    Google Scholar 

  8. J.E. Marsden, T.J.R. Hughes, Mathematical Foundations of Elasticity. Prentice-Hall, Englewoods Cliffs, NJ (1983).

    Google Scholar 

  9. J.A. Schouten, Tensor Analysis for Physicists, 2nd edn. Dover, Mineola, New York (1989).

    Google Scholar 

  10. I.S. Sokolnikoff, Tensor Analysis. Wiley, New York (1951).

    Google Scholar 

  11. A. Sommerfeld, Mechanik deformierbarer Medien, Vorlesungen über Theoretische Physik, Vol. II, 5th edn. Akademische Verlagsgesellschaft Geest & Portig, Leipzig (1964).

    Google Scholar 

  12. I. Todhunter, A History of the Theory of Elasticity and the Strength of Materials, from Galilei to Lord Kelvin, edited and completed by K. Pearson, Vol. I: Galilei to Saint-Venant 1639-1850. Dover, New York (1960) pp. 496–505; (1st edn 1886).

    Google Scholar 

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Authors and Affiliations

  1. Institute for Theoretical Physics, University of Cologne, 50923, Köln, Germany

    Friedrich W. Hehl

  2. Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, 91904, Israel, and Jerusalem College of Engineering, Jerusalem 91035, Israel

    Yakov Itin

Authors
  1. Friedrich W. Hehl
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  2. Yakov Itin
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Hehl, F.W., Itin, Y. The Cauchy Relations in Linear Elasticity Theory. Journal of Elasticity 66, 185–192 (2002). https://doi.org/10.1023/A:1021225230036

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