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[Bruno Chareyre <bruno.chareyre@xxxxxxxxxxx>]

Hehe. If you want to understand Ip2_FrictMat_FrictMat_FrictPhys, you 
have to read Chareyre's thesis, not Hentz's thesis. ;)

Ip2_FrictMat_FrictMat_FrictPhys can't be wrong because it says nothing!

I can't explain the logic behind Hentz, what I know is what dimensional 
analysis says : The macroscopic (packing) stiffness E is proportional to 
k/D.
So, if I like (I could dislike) to get a constant E for different sizes 
D, I need k=E*/D, where E* is "a constant", or say a material parameter.
In that case, I can tell I have E=A.E*, where A is to be determined for 
each new packing density, size distribution, anisotropy, deposition 
method, ...
The point is to get the same elastic behaviour for a packing of size 
e.g. 1x1x1, whatever the number of element in the packing.

I never claimed E=E*, which is why it makes no sense to compare the 
equations as you did. In Hentz, E is really supposed to be the stiffness 
of the packing.

I could put, a factor 2,3,7,PI,sqrt(2) in front of Kn = ..., it would 
not change the fact that A is unknown. And currently, _there is no exact 
theory giving A_. If there was a theory for that, well, we could just 
quit DEM and go derive equations.


> is 1.57× smaller than one used by Hentz.
>
>   
1.57 is a joke, if you consider that for the same kn, E can vary from 1 
to 10 depending on packing density, etc. I'm actually spurprised that 
the difference is so small.
Note that, if I remember correctly, the funny factor in Hentz is not 
just for Poisson ratio. It also includes the number of contact per 
volume, which is a way to account for different densities (approximately).

That being said, with the current "FrictPhys" definition of Kn, and with 
a random mid-dense packing, with a narrow distribution of sizes, A will 
be close to one. But don't repeat that to anybody, because one day 
somebody will say "oh, I found E!=E*, your equation is wrong!", exactly 
like now.
So, the official answer is : E =A.E*, A undefined, nothing more.

Bruno