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[Jan Stránský <question403385@xxxxxxxxxxxxxxxxxxxxx>]

Question #403385 on Yade changed:
https://answers.launchpad.net/yade/+question/403385

Jan Stránský proposed the following answer:
Hi Mohsen,

please really provide a MWE :-) it would be much easier to determine the
source of problem..

First some explanation why the equivalence of micro and macro parameters is
almost never the case.

DEM is discrete, so what is really computed and important on contact is
f=k*u
f ... force [N]
u ... penetration depth [m]
k ... contat stiffness [N/m]

For easier definition of material models (and to make the elasticity
particle size independent, see Bruno's answer), it is possible to define a
contact law as stress=E*strain
For this, you need to convert the contact to **fictitious** truss,
assigning its length L and crosssection area A.
L can be easily defined as distance of particles' centers.
A is much more tricky, it is basically arbitrary value. It is covnenient to
make it proportional to particle size square. It is radius*radius in
FrictPhys models, but pi*radius*radius in CPM. So by changing this, you
change the explicit micro-macro relationship, preserving the model
consistency.
Another parameter is interaction ratio (aabbEnlargeFactor and
interactionDetectionFactor). With higher value, there is more trusses and
basically overall this more trusses makes higher stiffness.


Computed E and nu are calculated after axial loading (z axis) up to special
> strain (1e-2) as follows:
> E=slope of sigma-epsilon graph
> nu= - 0.5(epsx+epsy)/(epsz)


1e-2 is relatively high, there might be already some inelastic processes
(with the MWE I could tell if yes or no)


I could not set it till now. It may be because of high desired nu which is
> near 0.35. Setting inter-particle nu as 0.35 causes large values of E which
> seems correct; however it is not may case


nu=0.35 is relatively high and difficult to achieve with cohesive particle
models, this indeed might be the reason.


For cylinder with height to diameter ratio of two, I have not found such
geometry till now. Also it may be interesting for you to check [3]. They
could not achieve a set of inter particle parameters (E, nu, phi) that
matches the macro ones. I think it is also the case for [2].

What do you think am i right?
> Can we say: It is very hard to find a geometry satisfying this hypothesis:
> 'micro and macro parameters are the same'. If it is true then:


yes, it is hard, but there is no reason for it (see above).


'Is there any reference that can interpret the difference between micro
> and macro parameters theoretically '? Is it a usual case in DEM
> modeling?


It is a usual case in DEM modeling. The difference is intrinsic feature of
DEM models.

Anyway, my question finds still no answer: In references [1] and [2]
> have they compared values of micro and macro E and nu? I could not find
> any details about geometry in [2].


yes, macro E, nu and micro (young and poisson) parameters were compared.
Cubic periodic cell was used, bud the elastic parameters should be
independent on geometry.

There is another point that i forgot: why in CPM material the ratio of
> ks/kn is called Poisson ration? That is clear by increasing ks/kt (or
> inter particle nu), macro nu decreases as the lateral deformations are
> affected by shear relative movements. Hence such a physical definition
> (ks/kn) and terminology (nominating it as nu) are not consistent.


it is not only in CPM, but through almost all material models. I agree that
the name is not the best chosen, but on the other hand, it is the only
parameter influencing macroscopic Poisson's ratio :-)

You can observe (and theoretically prove) that changing poisson changes
both Poisson's ratio and Young's module, but changing young parameter does
change only Young's modulus, but not Poisson's ratio.

cheers
Jan


2016-10-25 16:27 GMT+02:00 Bruno Chareyre <
question403385@xxxxxxxxxxxxxxxxxxxxx>:

> Question #403385 on Yade changed:
> https://answers.launchpad.net/yade/+question/403385
>
> Bruno Chareyre proposed the following answer:
> Actually no, the micro-macro relations can always be put in a way such
> that they do NOT depend on particle sizes.
> In Yade, at least, it is the case (and it is obviously a good feature as
> you may found out). If you agree that cylinder size/aspect ratio should not
> play a role either, then interaction radius if any is the only remaining
> geometrical parameter, but it is in the end a contact parameter more than a
> geometrical parameter.
>
> What should bee kept the same in every geometry is porosity,
> coordination number, and fabric (an)isotropy. I think that's it.
>
> Bruno
>
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