**THEORY OF VISCOPLASTIC FLOWS**

**The viscoplastic fluids are non-Newtonian fluids, it means that they
have a non-linear behaviour.**

**The viscous behaviour of most fluids is described by Stokes' law of
viscosity and such fluids are called Newtonian fluids.**

**The relation between the constrains and the deformation velocity
for a Newtonian fluid is linear and follows the equation :**
**where D is the deformation velocity tensor : **

**A lot of industrial flows are not Newtonian fluids so there is an important
bibliography on non-Newtonian flows.**

**Non-newtonian fluids don't follow the linear behaviour anymore,
the relation between viscosity and velocity depends of the fluid type :
pseudoplastic, viscoplastic, shear thinning, ... . There is several behaviour
laws to analyse the law of viscosity of non-Newtonian flows.**
**More precisely, Bingham fluids (see examples)
behaviour is modelised by :**

**For these type of flows, there is a yield value under which there
is no movement. Above it, they follow a Newtonian behaviour plus the constant
of yield value.**