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Abstract

The constitutive equation of linear viscoelasticity, as applied to incompressible fluid materials, takes the form:
$$\tau \left( t \right) = \int\limits_0^\infty {f\left( s \right)C^t \left( s \right)ds}$$
([1])
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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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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