yade-dev team mailing list archive

[Bruno Chareyre <bruno.chareyre@xxxxxxxxxxx>]

> I re-read my first post over to make sure; no reference to macroscopic
> (packing's) modulus was done.
Not you, but Hentz did (and Wenjie, Frederic, etc). That's how it comes 
into the discussion when it comes to comparisons.
>  I was merely expressing my surprise over
> the weird definition of contact area, since I thought it was generally
> accepted that it is cross-section of cylinder between particles
I never considered any contact area. For me contact area is 0, or 
something negligible versus size of particles. I don't see any cylinder 
either between grains. My vision is not better, it is just well suited 
for what I'm doing (uncemented materials).


> 	//Real Sinit 	= Mathr::PI * std::pow( std::min(Da,Db) , 2);
>
> I am wondering at which point it was commented -- it must have lead to
> packing stiffness change by that factor 1.57.
>
>   
My bad habit of taking one file, changing what I like, and keeping some 
old commented parts in case I want to know what was there before (I 
obviously coded the "basic" version starting from the law inherited from 
SDEC, and actually I think it was my first coding in Yade!).
For sure I'll remove that next time I commit a change in this file.

> > 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.
> >     
>
> Just because we don't define that, it means that anybody is free to
> change the logic in Ip2_FM_FM_FP; running the same simulation few weeks
> later will give you different results. That is not right. 
>   
That would be a problem, but I see no solution. The factor is 1 
currently, couldn't be simpler, and _should not_ be modified. Everybody 
should know (i.e. I'll have to document that) that in this law kn 
between spheres will be E.d.
Similar problem if somebody uses the default value of damping and one 
day somebody change it : different results. I'm sure we could find many 
situations less trivial than this.

> >  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.
> >     
> (FYI there is, for some special arrangements
> http://www.fisica.ufc.br/hans/p/256.pdf, but that is not our subject
> really)
>
>   
Equation (1) is wrong (for uncemented materials at least). I mean, not 
"a bit" wrong, totally wrong, as proved by Cambou and many others (cited 
in the paper), and it is easy to test with DEM (I did that and found 
dl=0.25*eps*l instead of eq. (1) in my case).

>  let me know over which
> points we disagree:
>   
Good!
> 1. Contact stiffness is something like a[N]/lengthOfContact[m]
>
>   
I don't have length of contact in mind more than area of contact. Or, 
perhaps, say length of contact is size of particles, and keep going.

> 2. a[N] is some quantity proportional to some particle-defined modulus
> (not saying it is E of continuous medium)
>
>   
Ok.
> 3. a is something like Young's modulus [Pa] * b[m²] (by dimensionality)
>
> 4. let us take (2r) as lengthOfContact (same radii, for simplicity) (the
> most obvious choice)
>
>   
Ok, we converge here. The thing is, in theorems of dimensional analysis 
(Buckingam), you really put the basic physical quantities, and size of 
particles is really the fundamental size in the system, not just an 
approximation of contact "length".
> 5. there is a thing Material::young [Pa] (note E below), defined in
> Material class; we take is as the value of Young's modulus [Pa] (the
> most obvious choice again)
>   
No. E is not "Young" modulus, it is the stiffness of contacts. It is 
called young because again, I adapted existing code the lazy way, and 
also because we have same data class for different laws, where the 
meaning of the data is not the same in each law.
For a similar reason, I renamed Poisson -> KsDivKs some time ago in 
preprocessors. I can't (or can I?) change the name in the data class though.
> 6. let's call this b[m²] "contact area", since it is area related to the
> contact (pure terminology thing)
>   
> 7. the current equation in yade is: kn=Er=E(2r²)/(2r), so "contact area"
> b[m²]=2r². Contrary to other obvious choices (4,5), it is very much
> non-obvious what is the geometrical meaning of 2r².
>   
Irrelevant for me : no area and no length.

However, adopting your philosophy (which is as correct as mine I think), 
I could say that contact area is obviously more than the  projection of 
the grain, since there is void around grains which should be associated 
to each interaction (the sum of interaction "volumes" should be the 
total volume of the packing right?).
If you consider a regular square packing, it gives a cube of size D for 
each grain (or each interaction), area = D². The fact that you see an 
apparent (2r²) instead of D² here is because you ignored the factor "2" 
multiplying the harmonic average. With that factor, you can write 
kn=E.D²/D, and the Young modulus of the cube is exactly the E used to 
define kn. In this special case, you have exactly E=E*.

> What I was saying was merely that it would be nicer to use πr² instead
> of 2r², which is cross-section area of cylinder between the particles.
>
>   
I'm happy with D² being the area of the bounding cube, and even more 
happy to justify the equations whatever the philosophy! :)
I really don't get what sort of cylinder should be considered, sorry.

Bruno