Tensor Function Theory and Classical Plastic Potential

  • J. Betten
Part of the International Centre for Mechanical Sciences book series (CISM, volume 292)


In the theory of elasticity an elastic potential (strain-energy function W) is assumed, from which the constitutive equations can be derived by using the relation σij = ∂W/∂εij, where are appropriately defined stress and strain tensors, respectively. In the isotropic special case, when the elastic constitutive equation can be represented as an isotropic tensor function
the elastic potential is a scalar-valued function only of the strain tensor and can be represented in the form W = W(S1, S2 S3), where S1, S2 S3 are the basic invariants of the strain tensor (finite or infinitesimal strain tensor). In [1] it has been shown in detail that the scalar coefficients in (1) can be expressed through the elastic potential:


Constitutive Equation Flow Rule Elastic Potential Tensor Function Integrity Basis 
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  1. 1.
    BETTEN, J., Elastizitäts-und Plastizitätslehre, Vieweg-Verlag, Braunschweig/Wiesbaden 1985.MATHGoogle Scholar
  2. 2.
    BETTEN, J., The Classical Plastic Potential Theory in Comparison with the Tensor Function Theory, International Symposium PLASTICITY TODAY on Current Trends and Results in Plasticity, Udine 1983, published in a special Olszak Memorial volume of the Engineering Fracture Mechanics 21 (1985): 641–652.Google Scholar
  3. 3.
    MURAKAMI, S. and SAWCZUK, A., On Description of rate-independent Be. haviour for prestrained Solids, Archives of Mechanics 31 (1979): 251–264.MATHMathSciNetGoogle Scholar
  4. 4.
    LEHMANN, Th., Einige Bemerkungen zu einer allgemeinen Klasse von Stoffgesetzen für große elasto-plastische Formänderungen, Ingenieur-Archiv 41 (1972): 297–310.CrossRefMATHGoogle Scholar
  5. 5.
    BETTEN, J., On the Representation of the Plastic Potential of Anisotropic Solids, Colloque International du CNRS n° 319, Comportement plastique des solides anisotropes, Grenoble 1981, published in the proceedings: Plastic Behavior of Anisotropic Solids (ed. J.P. Boehler) CNRS, Paris 1985, 213–228.Google Scholar
  6. 6.
    BOEHLER, J.P. and SAWCZUK, A., Application of Representation Theorems to describe Yielding of transversely isotropic Solids, Mech. Res. Comm. 3 (1976): 277–283.MATHGoogle Scholar
  7. 7.
    BOEHLER, R.P. and SAWCZUK, A., On Yielding of Oriented Solids, Acta Mechanica 27 (1977): 185–206.CrossRefGoogle Scholar
  8. 8.
    BETTEN, J., Net-Stress Analysis in Creep Mechanics, Ingenieur-Archiv 52 (1982): 405–419.CrossRefMATHGoogle Scholar
  9. 9.
    LITEWKA, A. and SAWCZUK, A., A Yield Criterion for Perforated Sheets, Ingenieur-Archiv 50 (1981): 393–400.CrossRefMATHGoogle Scholar
  10. 10.
    BETTEN, J., Damage Tensors in Continuum Mechanics, Euromech Colloquium 147 on “Damage Mechanics”, Paris VI, Cachan 1981, published in Journal de Mécanique théorique et appliquée 2 (1983): 13–32.MATHGoogle Scholar
  11. 11.
    BETTEN, J., Integrity Basis for a Second-Order and a Fourth-Order Tensor, International J. Math. and Math. Sci. 5 (1982): 87–96.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 1987

Authors and Affiliations

  • J. Betten
    • 1
  1. 1.Technical University AachenF.R. Germany

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