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 is
$$
\begin{cases}
\dot\gamma=0, & |\tau|\leq\sigma_y,\\
\tau=\sigma_y\operatorname{sgn}(\dot\gamma)+\eta\dot\gamma,
& |\tau|>\sigma_y.
\end{cases}
$$
Equivalently, in yielded material,
$$
\dot\gamma=\frac{|\tau|-\sigma_y}{\eta}\operatorname{sgn}\tau.
$$

Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2023/iii/paper-352/1/a/solution