It is known that the first normal stress difference is mainly responsible for enhanced extrudate swelling in extrusion flow. This is typically a viscoelastic property. With respect to this fact, the simplified viscoelastic model is an extension of existing Newtonian fluid models, in which a normal stress difference has been incorporated into the force balance. In other words, in simple shear flow along the first axis and with a shear rate , the total extra-stress tensor is given by:

(11–66)

In this tensor, the shear stress component is given by , which involves the shear rate dependent viscosity . Several algebraic relationships are available for describing the shear viscosity, and can be found in Generalized Newtonian Flow. In the present context, the following laws can be considered:

The first normal stress is given by the quantity . This quantity involves the viscoelastic variable , a quantity (which can be referred to as normal viscosity), and a weighting factor (which can be positive or zero).

The viscoelastic variable obeys a transport equation involving a characteristic or relaxation time , which is given by:

(11–67)

The equation is such that the solution is recovered in simple shear flow. The normal viscosity found in Equation 11–66 is described by means of functions similar to those available for the shear viscosity , where is replaced by . In order to facilitate the setup of a flow simulation involving the simplified viscoelastic model, identical dependences for and are considered by default. However, it is important to note that different functions can be selected for the shear and normal viscosities.

Finally, for nonisothermal flows, temperature dependence can be selected for the shear and normal viscosities. Here, the Arrhenius law (Equation 10–18), the approximate Arrhenius law (Equation 10–20), and the WLF law (Equation 10–22) can be selected. When defining a nonisothermal case, a single function is used for describing the temperature dependence of the material functions , , , and optionally .

As far as the other features are concerned, the situation does not differ from that available for Newtonian or viscoelastic flows. In particular, 2D and 3D flows can be defined, and may include attributes such as inertia, gravity, viscous and wall friction heating, and so on. Also, in terms of boundary conditions, the situation does not differ from general viscoelastic flows. Free surfaces can be defined, as this is the primary motivation for the simplified viscoelastic model. The transport equation (Equation 11–67) for the viscoelastic variable requires boundary conditions at the inlet of the computational domain. They are automatically selected and imposed along boundary sides where the inflow condition is selected.