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[Robert Caulk <question654408@xxxxxxxxxxxxxxxxxxxxx>]

Question #654408 on Yade changed:
https://answers.launchpad.net/yade/+question/654408

    Status: Open => Answered

Robert Caulk proposed the following answer:
Hello Hélvio,

It depends on your assignment of microparameters: tensile strength,
cohesion, and friction angle. Figure 2 [1] is going to help you
understand the answer to this question visually. The assignment of Mohr-
Coulomb criteria here is a fancy way to say that we are using the
equation of a straight line to describe the frictional behavior between
the particles. We truncate the line at FnMax.

Equation of the line: 
Fs = FsMax + Fn*tan(phi)
you are worried about Fs <= 0 when Fn is negative:
FsMax + (-Fn)*tan(phi) <= 0
FsMax <= Fn*tan(phi)
this only holds as long as Fn < FnMax = tA (line truncation, see Figure 2 [1]) and we know FsMax = cA
So the only way for Fs <=0 is for:
cA <= tA*tan(phi)

So as long as c > t*tan(phi) (which are all microparameters set by user)
then the model will never see a negative value for Fs. So taking Table
1[1] as an example: the tensile strength would need to be increased from
4.5 to 138 MPa for a negative Fs value to occur. I think most yade users
are micromechanically savy enough to avoid this kind of blunder, but to
answer your direct question "should this be allowed to occur?" Hmmm,
maybe it is worth adding an error message to protect users from
accidentally defining unphysical microparmeters.


[1]Scholtès, L., & Donzé, F.-V. (2012). Modelling progressive failure in fractured rock masses using a 3D discrete element method. International Journal of Rock Mechanics and Mining Sciences, 52, 18–30. http://doi.org/10.1016/j.ijrmms.2012.02.009

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