Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 352 / 1 / a / Solution

A Bingham plastic is a yield-stress fluid, and hence a non-Newtonian fluid. It is also an instantaneous generalized-Newtonian model after yielding. It cannot describe memory-dependent viscoelasticity, including stress relaxation, elastic recoil, and time-dependent normal-stress effects.

For scalar shear stress $\tau$ and shear rate $\dot{\gamma }$, its complete ideal constitutive law isEquivalently, in yielded material,