Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 352 / 1 / a / Solution

Letbe the rate-of-strain tensor and let $\dot{\mathbf{\gamma }}=2\mathbf{D}$. The invariant magnitude convention that reproduces the ordinary scalar rate in simple shear flow isThe tensor contraction makes this definition independent of a rigid rotation of coordinates.