Rheological problems are non-homogeneous, aelotropic, non-linear and irreversible. If a start is made with the stress-tensor field, one soon runs into a number of difficulties. The strain tensor is defined for any type of medium-homogeneous, heterogeneous, isotropic, aelotropic and hence should be a suitable vehicle for investigation the yield condition. Again, the classical strain/strain rate, when used, makes the constitutive equation very complex. So the generalized strain measure should be used.


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  1. 1).
    Seth, B. R., Prikl. Math. Mech. 27, 380–382 (1963); Generalized strain and transition concepts for elastic-plastic deformation, creep and relaxation, Proc. XI Intern. Congress Applied Mech., Munich, pp. 383 to 389 (1964).MathSciNetGoogle Scholar
  2. Seth, B. R., Prikl. Math. Mech. ZAMM 50, 617–621 (1970).CrossRefzbMATHGoogle Scholar
  3. 2).
    Hill, R., The mathematical theory of plasticity, pp. 318-319 (Oxford 1950).Google Scholar
  4. 3).
    Hill, R., J. Mech. Phys. Solids 16, 229-242, 315–322 (1968).ADSCrossRefzbMATHGoogle Scholar
  5. 4).
    Olszak, W. and P. Peryna, J. Math. Phys. Sci. 2, 67–72 (1968).zbMATHGoogle Scholar
  6. 5).
    Stassi, F. D’Alls, J. Italian Assoc. Theo. Appl. Mech. 2, 178–195 (1967).Google Scholar
  7. 6).
    Haar, A. and T. Karman, Zur Theorie der Spannungszustände im plastischen und sandartigen Medien, S. 2 (Göttingen 1909).Google Scholar
  8. 7).
    Lippman, H., Sbovnik Perevodov Mechanika 1963, 3.Google Scholar
  9. 8).
    Thomas, T. Y., J. Math. Mech. 17, 987–1004 (1968).zbMATHGoogle Scholar
  10. 9).
    Love, A. E. H., Mathematical theory of elasticity, pp. 161-162 (1927).Google Scholar
  11. 10).
    Borah, B. N., Ind. J. Pur. Appl. Maths. 2, 335–343 (1971).zbMATHGoogle Scholar
  12. 11).
    Morgan, Int. J. Engg. Sci. 4, 155 (1966).CrossRefzbMATHGoogle Scholar
  13. 12).
    Fox, Acta Mech. 7, 248 (1969).CrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • B. R. Seth
    • 1
  1. 1.Birla Institute of TechnologyMesra, RanchiIndia

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