Description of Several Models

Note this is again a shorthand notation for representing the six components of the stress tensor. For steady shear flow this model predicts no normal stresses and a constant viscosity. The material functions predicted by this model are summarized in Table 3.1. Obviously this model as it stands is wholly inadequate to describe the behavior of polymeric melts under processing conditions. 

By replacing the partial time derivative with a nonlinear time derivative, which is based on a codeforming and translating coordinate system, the constitutive equation given in Eq. 3.1 now becomes (Bird et al., 1987a)  

TABLE 3.1 Predictions of Viscoelastic Models for Steady Shear and Elongational Flow 

Phan-Thien-Tanner (single relaxation time) 

This constitutive equation is referred to as the upper converted Maxwell (UCM) model. In Example 3.1 this time derivative will be written out for simple shear and shear-free flows. The predictions of this model for steady shear 

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