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

[math]\displaystyle{ \mathbf{A}_{ij(1)}= \frac{\partial v_i}{\partial x_j}+\frac{\partial v_j}{\partial x_i} }[/math]

where

[math]\displaystyle{ v_i }[/math] is the fluid's velocity and

[math]\displaystyle{ A_{ij(n)} }[/math] is [math]\displaystyle{ n }[/math]-th order Rivlin–Ericksen tensor.

Higher-order tensor may be found iteratively by the expression

[math]\displaystyle{ A_{ij(n+1)}=\frac{\mathcal{D}}{\mathcal{D}t}A_{ij(n)}. }[/math]

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

• Truesdell, Clifford; Noll, Walter (2004). The Non-Linear Field Theories of Mechanics. Springer. ISBN 978-3-662-10388-3.