Page 516 - Introduction to Continuum Mechanics

500 Special Single Integral Type Nonlinear Constitutive Equations

We see from this example that for the nonlinear viscoelastic fluid defined by Eq, (15.2), i.e.,

the viscosity function fi(k) is given by

and the two normal stress functions are given either by

or

The shear stress function, and the two normal stress functions (either
o { and 02, or <?]_ and t7 2) completely describe the material properties of this nonlinear vis-
coelastic fluid in the simple shearing flow. In part C we will show that these three material
functions completely describe the material properties of every simple fluid, of which the
present nonlinear fluid is a special case, in viscometric flows, of which the simple shearing flow
is a special case.
Similarly, for the nonlinear viscoelastic fluid defined by Eq. (8.15.3),

the viscosity function and the two normal stress functions can be obtained to be