The stress tensor



The elastic properties of materials relate the applied stress tensor to the resulting strain tensor via the stiffness tensor or its inverse, the compliance tensor. They are the topics of Chaps. 11, 12 and 13. In the present chapter, the stress tensor at a point in the material is defined. The basic relations which must be verified by its spatial derivatives are then determined, and they lead to the condition that this tensor must be symmetric.


Stress Tensor Direction Cosine Component Parallel Small Cube Compliance Tensor 
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  1. 1.
    D. Calecki, Physique des milieux continus, vol. 1, Mécanique et thermodynamique (Hermann, Paris, 2007)Google Scholar
  2. 2.
    L.D. Landau and E.M. Lifshitz, Course of Theoretical Physics, vol. 7, Theory of Elasticity, 3rd edn. (Elsevier, Oxford, 1986)Google Scholar

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© 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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