Rivlin–Ericksen tensor

{{Short description|Concept in physics}}

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

:$\backslash mathbf\{A\}\_\{ij(1)\}=\; \backslash frac\{\backslash partial\; v\_i\}\{\backslash partial\; x\_j\}+\backslash frac\{\backslash partial\; v\_j\}\{\backslash partial\; x\_i\}$

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

: $A\_\{ij(n+1)\}=\backslash frac\{\backslash mathcal\{D\}\}\{\backslash mathcal\{D\}t\}A\_\{ij(n)\}.$

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