# Bingham plastic

A Bingham plastic is a material that behaves as a rigid body at low stresses but flows as a viscous fluid at high stress. It is used as a common mathematical model of mud flow in offshore engineering.

The material is rigid for shear stress, τ, less than a critical value, τ0. Once the critical shear stress is exceeded, the material flows as a Newtonian fluid with shear stress and shear rate, ∂u/∂y, (as defined in the article on viscosity) related by:

[itex]\frac {\partial u} {\partial y} = \left\{\begin{matrix} 0 &, \tau < \tau_0 \\ (\tau - \tau_0)/ {\mu} &, \tau \ge \tau_0 \end{matrix}\right.[itex]Template:Math-stub

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