Page 508 - Introduction to Continuum Mechanics

492 Rivlin-Ericksen Tensor in Terms of Velocity Gradients - The Recursive Formulas

where Vv is the velocity gradient and D is the rate of deformation tensor.
We have, at any time r

That is, [see Eqs. (8.9.2)]

clearly, we also have

and

We now recall from Section 3.13, Eq. (3.13.6a), that

1 T
where D = :r[Vv + (Vv) ] is the rate of deformation tensor. Thus,
£

Next, from Eq. (8.10.4),