2010/3/25 chiara modenese <[email protected]>
> > > 2010/3/25 Bruno Chareyre <[email protected]> > > >> 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 >> >> >> _______________________________________________ >> Mailing list: >> https://launchpad.net/~yade-dev<https://launchpad.net/%7Eyade-dev> >> Post to : [email protected] >> Unsubscribe : >> https://launchpad.net/~yade-dev<https://launchpad.net/%7Eyade-dev> >> More help : https://help.launchpad.net/ListHelp >> > >
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