Elongational flows kinematics

One may try to avoid the problem by the use of the upper-convected derivative, which ensures the coincidence of the principal axes of stress and strain. But doing that, it appears that any kinetics based on the stress amplitude is improper, since materials which exhibits thickening behaviour in elongation are, to the contrary, shear-thinning. Consequently no unique dependence can be expected for these two kinematics. The determination of a single set of parameters in various flows in then bound to be a compromise. 

Figure 9.3. Kinematics of separation of two material points during laminar flow in the uniaxial elongation and in the simple shear.

The choice of the kinematics used for probing non-Newtonian behavior is arbitrary, and hence, the number of choices is infinite. However, the rheological community has settled on a small number of standard flows. These standard flows are simple and realizable by experimentalists. Classic flows are simple shear and simple shear-free elongation [2]. 

---