Exponential Shear: A Strong Flow

The recent development of new types of sliding‐plate rheometers for concentrated polymeric liquids makes it possible to generate a shearing deformation in which the strain is exponential in time. Such a deformation is a strong flow in the sense that the deformation kinematics have a strong tendency to stretch out the molecules of a polymeric liquid. Previous applications of the concept of strong flows have been limited to motions with constant stretch history, that is, deformations where the components of the strain rate tensor are constant with respect to time. For example, steady simple extension is a strong flow that has attracted much attention because of its ability to generate a high level of molecular stretching. However, it is a deformation that is difficult to generate in the laboratory. We make use of both a kinematic criterion for strong flows and one based on the elastic dumbbell model to show that exponential shear is likely to generate a high degree of molecular stretching. In addition, we propose the definition of a material function for representing data from exponential shear experiments. We also show that in the nonlinear viscoelastic range, exponential shear is likely to exhibit an unbounded growth in an appropriately defined function similar to the strain‐hardening behavior observed in the tensile stress growth coefficient of polymeric liquids with a branched molecular structure.