The constitutive equation of linear viscoelasticity, as applied to incompressible fluid materials, takes the form:
$$\tau \left( t \right) = \int\limits_0^\infty {f\left( s \right)C^t \left( s \right)ds}$$
where τ(t) is the extra-stress tensor at time t (i. e., the total stress tensor within an arbitrary additive isotropic tensor), while C′(s) is the Cauchy strain carrying the configuration at time ts into the configuration at time t (see Appendix). Eq. [1] is sometimes referred to as expressing the so-called Boltzmann superposition principle, but it has in fact a more precise logical status as an asymptotic form of the much more general constitutive equation of a simple fluid with fading memory (1).


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  1. 1).
    Coleman, B. D. and W. Noll, Revs. Mod. Phys. 33, 239 (1961).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  2. 2).
    Lodge, A. S., Rheol. Acta 7, 379 (1968).CrossRefzbMATHGoogle Scholar
  3. Lodge, A. S., Trans. Farad. Soc. 52, 20 (1956).CrossRefGoogle Scholar
  4. 3).
    Bernstein, B., E. A. Kearsley, and L. J. Zapas, Trans. Soc. Rheol. 7, 391 (1963).CrossRefzbMATHGoogle Scholar
  5. 4).
    Ward, A.F.H. and G. M. Jenkins, Rheol. Acta 1, 110 (1958).CrossRefGoogle Scholar
  6. 5).
    Zapas, L. J., J. Res. Natl. Bur. Stds. 70A, 525 (1966).Google Scholar
  7. 6).
    Tanner, R. I. and J. M. Simmons, Chem. Eng. Sci. 22, 1803 (1957).CrossRefGoogle Scholar
  8. 7).
    Tanner, R. I. and R. L. Ballman, Ind. Eng. Chem. Fund. 8, 588 (1969).CrossRefGoogle Scholar
  9. 8).
    Spriggs, T W., J. D. Muppler, and R. B. Bird, Trans. Soc. Rheol. 10, 191 (1966).CrossRefGoogle Scholar
  10. 9).
    Lodge, A. S., Elastic Liquids, p. 121 (London 1964).Google Scholar
  11. 10).
    Lodge, A. S., 1965, as quoted in (8).Google Scholar
  12. 11).
    Bird, R. B. and P. J. Carreau, Chem. Eng. Sci. 23, 427 (1968).CrossRefGoogle Scholar
  13. 12).
    Bogue, D. C., Ind. Eng. Chem. Fund. 5, 253 (1966).CrossRefGoogle Scholar
  14. 13).
    Carreau, P. J., Trans. Soc. Rheol. (in press).Google Scholar
  15. 14).
    Coleman, B. D., Arch. Ratl. Mech. Anal. 17, 1 (1964).Google Scholar
  16. Coleman, B. D., Arch. Ratl. Mech. Anal. 17, 230 (1964).zbMATHGoogle Scholar
  17. 15).
    White, J. L., Discussion at Euromech Colloquium 37 (Naples 1972).Google Scholar
  18. 16).
    Pearson, J. R. A., ibidem.Google Scholar
  19. 17).
    Philippoff, W., Trans. Soc. Rheol. 10, 317 (1966).CrossRefGoogle Scholar
  20. 18).
    Tanner, R. I., A.S.L.E. Trans. 8, 179 (1965).CrossRefGoogle Scholar
  21. 19).
    White, J. L. and A. B. Metzner, J. Pol. Sci. 7, 1867 (1963).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • G. Marrucci
    • 1
  • G. Astarita
    • 2
  1. 1.Cattedra di Principi di Ingegneria ChimicaUniversity of PalermoItaly
  2. 2.Istituto di Principi di Ingegneria ChimicaUniversity of NaplesItaly

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