Page 505 - Introduction to Continuum Mechanics
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Non-Newtonian Fluids 489
Example 8.9.3
Consider the Couette flow with a velocity field given in cylindrical coordinates as
(a) Obtain the motion using current time t as reference.
(b) Compute the relative deformation tensor Q .
(c) Find the Rivlin-Ericksen tensors.
Solution, (a) From the given velocity field, one has
Integration of the above equation gives the pathline equations to be:
(b) Using Eqs. (8.8.9), one easily obtain the relative right Cauchy-Green deformation tensor
to be
