The stiffness and compliance tensors, which relate the stress tensor to the resulting strain tensor, are symmetric tensors of rank 4. This chapter shows how the intrinsic symmetry of the strain and stress tensors reduces the number of independent components of the compliance and stiffness tensors, and then how the symmetry of the crystal, described by its point group, can further reduce this number. A short notation, called Voigt’s notation, is often used for these tensors. It represents the stress and the strain tensors through 6-component vectors, and the compliance and stiffness tensors by symmetric 6 × 6 matrices which are inverse to each other.


Burger Vector Isotropic Material Dislocation Line Uniaxial Stress Relative Elongation 
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Further reading

  1. 1.
    D. Hull, D. J. Bacon, Introduction to Dislocations, 5th edn. (Elsevier, 2011)Google Scholar
  2. 2.
    H. Foll, website on crystal defects (2001) ge/index.html


  1. 1.
    D. Calecki, Physique des milieux continus, vol. 1, Mécanique et thermodynamique (Hermann, Paris, 2007)Google Scholar
  2. 2.
    A. Yeganeh-Haerl, D.J. Weidner, J.B. Parise, Science 257, 650–652 (1992)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, case 115, 4 place JussieuUniversité Pierre et Marie CurieParisFrance
  2. 2.Laboratoire Matériaux et Phénomènes Quantiques, Bâtiment Condorcet, case 7021Université Paris Diderot-Paris 7Paris CedexFrance
  3. 3.Grenoble-INP et Institut Néel du CNRS, B.P. 166Université Grenoble-AlpesGrenobleFrance

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