A Rivlin–Ericksen temporal evolution of the

strain rate tensor In continuum mechanics, the strain-rate tensor or rate-of-strain tensor is a physical quantity that describes the rate of change of the deformation of a material in the neighborhood of a certain point, at a certain moment of time. It can be defi ...

such that the derivative translates and rotates with the flow field. The first-order Rivlin–Ericksen is given by :

\mathbf_= \frac+\frac

where :

v_i

is the fluid's velocity and :

A_

n

-th order Rivlin–Ericksen tensor. Higher-order tensor may be found iteratively by the expression :

A_=\fracA_.

The derivative chosen for this expression depends on convention. The

upper-convected time derivative In continuum mechanics, including fluid dynamics, an upper-convected time derivative or Oldroyd derivative, named after James G. Oldroyd, is the rate of change of some tensor property of a small parcel of fluid that is written in the coordinate ...

, lower-convected time derivative, and Jaumann derivative are often used.

References

* {{DEFAULTSORT:Rivlin-Ericksen tensor Multivariable calculus Fluid dynamics Non-Newtonian fluids