Page 506 - Introduction to Continuum Mechanics

490 Calculations of the Relative Deformation Tensor

(c) The nonzero Rivlin Ericksen tensors are

Example 8.9.4
Given the velocity field of a sink flow in spherical coordinates:

(a) Obtain the motion using current time t as reference

(b) Compute the relative deformation tensor C t
(c) Find the Rivlin-Ericksen tensors.
Solution, (a) Let the motion be

then, from the given velocity field, we have

Integration of these equations with the conditions that at T = t, r'=r, 6' = 8 and <p' = 0, we
obtain

(b) Using Eq. (8.8.16), we obtain, with k = dv/dr