[LukeFullard]

Hi all. I am trying to write my own finite difference code to simulate a visco-plastic flow using the Bingham rule for shear

ShearStress=YieldStress + nu*ShearRate when abs(ShearStress)>YieldStress
and
ShearRate=0 when abs(ShearStress)<=YieldStress


It seems to me that abs(ShearStress)>YieldStress will always be true (assuming a positive ShearRate). Am I missing something? Should it be

nu*ShearRate>YieldStress ?

I am confused!

Thanks for any help

[prashant24983]

Originally Posted by LukeFullard

Hi all. I am trying to write my own finite difference code to simulate a visco-plastic flow using the Bingham rule for shear

ShearStress=YieldStress + nu*ShearRate when abs(ShearStress)>YieldStress
and
ShearRate=0 when abs(ShearStress)<=YieldStress


It seems to me that abs(ShearStress)>YieldStress will always be true (assuming a positive ShearRate). Am I missing something? Should it be

nu*ShearRate>YieldStress ?

I am confused!

Thanks for any help

Imagine a rectangular block of mayonnaise (as an example of bingham viscoplastic material) on a flat plate. The shear stress between the mayonnaise and the flat surface will be 0 as there is no lateral force acting on the mayonnaise. The only force acting on the mayonnaise is its own weight which does not produce any component in shear direction. But as you start to tilt the plate, a component of its weight starts to act in the shear direction which depends on the angle of tilt.

Till the shear force reaches the threshold value of YieldStress you will not see any deformation in your mayonnaise. But there is an angle at which the shear stress becomes larger than YieldStress and as soon as that happens, and based on your equation, the viscosity model changes & the material starts to deform based on the bingham model for condition abs(ShearStress)>YieldStress. (Note: I am assuming sufficiently large quantity of mayonnaise for this experiment to show the behavior described above )

Physics described above 'hopefully' illustrates what those equation and conditions signify and I guess something similar is what you are trying to model?

When you say "abs(ShearStress)>YieldStress will always be true", you are leaving out the fact that shear stress is simply the force acting on the mayonnaise in shear direction, which is dependent on the physics of the model.

In my experiment above, the shear stress changes from 0 and gradually increases based on tilt angle. So shear stress will not "always" be greater than yield stress. Dont look at the equation, the equation does not provide the definition of shear stress. The physics of your problem will help you determine the shear stress!

[LukeFullard]

Originally Posted by prashant24983

The physics of your problem will help you determine the shear stress!

I saw this and it clicked! Thanks very much!