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.

Note 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. Therefore, it is acceptable to use cylindrical extrudate swelling data for the identification of the specific model properties.

As seen above, the simplified viscoelastic model involves three material functions and a parameter: the shear viscosity , the first normal viscosity , the relaxation time , and a weighting coefficient . Typically, usual viscosity data should be used for identifying the shear viscosity function. In most situations, shear thinning is experimentally observed, and algebraic relationships such as power law, Bird-Carreau, or Cross laws will be good candidates. However, it is recommended that you consider a law that exhibits a zero-shear plateau if regions of no-deformation are expected over the flow domain.

Next, a function and material parameters should be selected for the first normal viscosity . By default, a relationship identical to the selected shear viscosity is considered, as this appears to be a reasonable choice, at least at first. Of course, this default selection can be revised subsequently. The power law, which exhibits unbounded values under zero deformation, should be avoided if large regions of no deformation are expected. Instead, functions that exhibit a plateau, such as the Bird-Carreau laws, should be preferred.

Eventually, for the relaxation time and the weighting coefficient , it is suggested to perform a fast 2D simulation of axisymmetric extrudate swelling, where the effects of the remaining degrees of freedom are examined. Typically, the weighting coefficient will control the swelling intensity versus the flow rate, while the relaxation time function will control the development of the extrudate diameter along the jet, and may have a possible influence also 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 , where the development of extrudate versus the flow rate is examined, via an evolution scheme. A comparison with experimental data on swelling should enable the selection of an appropriate numerical value for the weighting coefficient .