yade-users team mailing list archive

[chiara modenese <c.modenese@xxxxxxxxx>]

2010/3/25 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.
>>
>> If I can give my opinion (very little since I still have quite a lot to
learn in the time yet to come) we know that from the contact mechanics when
two particles get in contact (let consider only the case of elastic
flattening) we can approximate the area of interaction as πa² (so a flat
surface), where a is the current contact area. It is an approximation since
we are neglecting the curvature, but it is a useful relation once we want to
work out the interaction force due to the interaction surface energy between
two particles (it is the so called derjiaguin approximation). In our case we
do not have any deformation at contact since we deal with rigid bodies, so I
cannot really see a clear connection. It was just to say why the cylinder
section.

Chia


>
>>
> 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
>
>
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