Rivlin–Ericksen tensor explained

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)} = (\partial v _{i})/(+ \partial x _{j}) (\partial v _{j})/(\partial x _{i}) wherev _{i} is the fluid's velocity andA _{ij(n)} is n -th order Rivlin–Ericksen tensor.Higher-order tensor may be found iteratively by the expressionA _{ij(n+1)} = (l{D)/() }A_.

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

• Book: Truesdell, Clifford . Noll, Walter . amp . The Non-Linear Field Theories of Mechanics . Springer . 2004 . 978-3-662-10388-3.