Rivlin–Ericksen tensor
# Rivlin–Ericksen tensor

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

    $\mathbf {A} _{ij(1)}={\frac {\partial v_{i}}{\partial x_{j}}}+{\frac {\partial v_{j}}{\partial x_{i}}}$

where

    $v_{i}$ is the fluid's velocity and
    $A_{ij(n)}$ is $n$-th order Rivlin–Ericksen tensor.

Higher-order tensor may be found iteratively by the expression

    $A_{ij(n+1)}={\frac {\mathcal {D}}{{\mathcal {D}}t}}A_{ij(n)}.$

The derivative chosen for this expression depends on convention. The upper-convected time derivative, lower-convected time derivative, and Jaumann derivative are often used.

