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.