A critical review of the recent phenomenological and experimental studies on the nonlinear viscoelastic phenomena in concentrated polymer systems is presented. Differential type constitutive equations are classified into three groups: the extension of the 3-dimensional linear Maxwell model, of the Jeffreys model and of the constitutive equation for general viscous fluid. Applicability and limitations of these equations are discussed. On the other hand, integral type constitutive equations are classified into two groups: multi-integral expansion type and approximate closed form type equations.
The last type equations are classified further into two groups: the one time (
t′)-single integral type (WJFLMB, Bird-Carreau, Yamamoto, BKZ, special forms of BKZ) and the two times (
t′,
t″)-single integral type (Carreau, Yamamoto, Takahashi-Masuda-Onogi). The memory function in the one time (
t′)-single integral type constitutive equation depends on the invariants of either the rate of strain tensor at
t′ or the relative strain tensor between
t′ and
t. It cannot express the dependences of relaxation times on the rate of strain or the relative strain. The memory function in the two times (
t′,
t″)-single integral type constitutive equation includes the time (
t″) integration of the function of the invariants of either the rate of strain tensor at
t″ (
t′≤
t″≤
t), the stress tensor at
t″, or the relative strain tensor between
t″ and
t′. It can express the dependences of relaxation times on the rate of strain, relative strain or stress.
Comparisons between recent experimental results and the predictions of the two times (
t′,
t″)-single integral type constitutive equations for specific flows (steady shear flow, stress overshoot, and interrupted flow) are discussed in detail. Among others, it is emphasized that the integral type constitutive equations with either the rate of strain or the relative strain dependent memory function cannot explain the recent experimental data obtained by van Es and Christensen.
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