Materials with Memory

  • R. S. Rivlin


The characteristic property of viscoelastic solids which distinguishes them from perfectly elastic solids is the fact that, if they are subjected to a deformation which varies with time, the stress measured at time t, say, depends not only on the instantaneous value of the deformation gradients, but also on the whole previous history of the deformation gradients. In a series of papers, Green and Rivlin1,2 and Green, Rivlin, and Spencer3 have developed constitutive equations for such materials, in which the stress is expressed in terms of the deformation in the form of series of multiple integrals. It is the object of this paper to recapitulate this development, with particular emphasis on the physical assumptions regarding the material which are implied by the mathematical assumptions made in the theory. Such a development is perhaps timely in view of the extensive attempts in recent years to represent the behavior of actual materials in the form given by the theory.


Constitutive Equation Deformation Gradient Viscoelastic Material Cauchy Stress Multiple Integral 
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  1. 1.
    Green, A. E., and Rivlin, R. S., Arch. Rat’l Mech. Anal., 1, 1 (1957).CrossRefGoogle Scholar
  2. 2.
    Green, A. E., and Rivlin, R. S., Arch. Rat’l Mech. Anal., 4, 387 (1960).CrossRefGoogle Scholar
  3. 3.
    Green, A. E., Rivlin, R. S., and Spencer, A.J.M., Arch. Rat’l Mech. Anal., 3, 82 (1959).CrossRefGoogle Scholar
  4. 4.
    Wineman, A. S., and Pipkin, A. C., Arch. Rat’l Mech. Anal., 17, 184 (1964).CrossRefGoogle Scholar
  5. 5.
    Coleman, B. D., and Noll, W., Arch. Rat’l Mech. Anal., 6, 355 (1960).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1973

Authors and Affiliations

  • R. S. Rivlin
    • 1
  1. 1.Center for the Application of MathematicsLehigh UniversityBethlehemUSA

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