The simplified viscoelastic model is mainly an empirical construction. The key ingredient is the normal stress property that is introduced for the prediction of swelling. Although it is possible to qualitatively relate the swelling and the first normal stress difference, a quantitative relationship is not obvious. Methodologies have to be identified and developed for the determination of material functions and parameters. A stepwise technique is recommended for this purpose.

As a preliminary remark, it is worth mentioning that the simplified viscoelastic model has been developed and implemented mainly for the simulation of 3D extrusion flows, therefore including the prediction of extrudate swelling. In view of this, it should be considered acceptable to use cylindrical extrudate swelling data for the identification of the specific model properties.

As seen previously in Theory and Equations, the simplified viscoelastic model involves three material functions and a parameter: the shear viscosity , the normal viscosity , the relaxation time , and a weighting coefficient . Typically, standard viscosity data (shear viscosity vs. shear rate) should be used for identifying the shear viscosity function. In most situations, shear thinning is experimentally observed, and algebraic relationships such as the power law, the Bird-Carreau law, or the Cross law will be good candidates. However, you should consider a law that exhibits a zero-shear plateau if you expect regions in which there is no deformation in the flow domain.

Next, a function and material parameters should be selected for the normal viscosity . By default, a relationship identical to the selected shear viscosity is considered, as this appears to be a reasonable initial choice. Of course, this default selection can be revised subsequently.

When eventually selecting the relaxation time and the weighting factor, it is recommended that you perform a fast 2D simulation of the axisymmetric extrudate swelling, to examine the effects of the remaining degrees of freedom. Typically, the weighting coefficient will control the swelling intensity vs. flow rate, while the relaxation time function will control the development of the extrudate diameter along the jet, and may also have an influence on the developed extrudate geometric attributes. Usually, a constant value or a Bird-Carreau law can be selected for the relaxation time. The value or zero-shear value should preferably be in agreement with the typical times involved in the flow. On the other hand, a series of calculations should be performed with various values of the weighting coefficient via an evolution scheme, to examine the development of extrudate vs. flow rate. A comparison with experimental data on swelling should enable the selection of an appropriate numerical value for the weighting coefficient .