yade-dev team mailing list archive

[chiara modenese <c.modenese@xxxxxxxxx>]

2010/3/25 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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