Page 517 - Introduction to Continuum Mechanics
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Non-Newtonian Fluids 501
A special nonlinear viscoelastic fluid defined by Eq. (8.15.3) with a memory function
dependent on the second invariant /2 of the tensor C, in the following way
is known as Tanner and Simmons network model fluid. The function/(s) is given by Eq. (8.4.9).
For this fluid, the network "breaks" when a scalar measure of the deformation / 2 reaches a
2
limiting value B + 3, where B is called the "strength" of the network.
Example 8.15.2
Show that for small deformations relative to the configuration at time t
where E is the infinitesimal strain tensor.
Solution. Let u denote the displacement vector measured from the configuration at time t.
Then
Thus,
Now, if u is infinitesimal, then
Also
Thus
