Rivlin–Ericksen tensor

Template:Short description 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

${𝐀}_{ij(1)}=\frac{\partial v_i}{\partial x_j}+\frac{\partial v_j}{\partial x_i}$

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

$A_{ij(n+1)}=\frac{𝒟}{𝒟t}{A}_{ij(n)}.$

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

References

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