Page 515 - Introduction to Continuum Mechanics

Non-Newtonian Fluids 499

Eqs. (8.15.2) and (8.15.3) define two nonlinear viscoelastic fluids whose behavior at small
deformations are also different.

Example 8.15.1

For the nonlinear viscoelastic fluid defined by Eq. (8.15.2), find the stress components when
the fluid is under steady shearing flow defined by the velocity field:

Solution. The relative Cauchy-Green deformation tensor corresponding to this flow was
obtained in Example 8.8.1 as:

Thus,

Thus, from Eq. (8.15.2)

We see that for this fluid, the viscosity is given by

We also note that the normal stresses are not equal in the simple shearing flow. In fact,