A Rivlin–Ericksen temporal evolution of the strain rate tensor such that the derivative translates and rotates with the flow field.  The first-order Rivlin–Ericksen is given by
where
: is the fluid's velocity and
: is -th order Rivlin–Ericksen tensor.
Higher-order tensor may be found iteratively by the expression
The derivative chosen for this expression depends on convention.  The upper-convected time derivative, lower-convected time derivative, and Jaumann derivative are often used.