# coordination number

Asked by Chiara Modenese on 2011-01-11

Hello,

Does anyone know what is the minimum coordination number for a packing of spheres per which the system is considered stable? How do you compute it? I got quite low values of it from triaxial test simulations, say below 4, and I was wondering about the causes.

Thanks, Chiara

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2011-01-11
2011-01-14
 Bruno Chareyre (bruno-chareyre) said on 2011-01-11: #1

CN below 4 is quite common, and expected.

Think isostaticity :
-There are 6 equilibrium equations.
-One frictional contact is blocking 3 DOFs.
Then, strictly speaking, a particle can be stable with 2 contacts (in
fact 3, in order to block also rotations). CN=4 is impossible except in
very special cases.

If friction=0, the contact is blocking only one DOF : it needs 4
contacts to really block one particle (with 3 contacts, it could
detach). Rotations will never be blocked. So you would get exactly CN=4
in that case (modulo elastic deformation creating contact if the ratio
pressure/Young is high).

Note that CN gives no indication on the stability of a packing. You
can't say "it is stable because CN>something".

HTH.

Bruno

 Chiara Modenese (chiara-modenese) said on 2011-01-11: #2

Hi Bruno,

thanks for your answer! May I ask you how would you define the stability of the packing?
As for the CN, does not it also depend on the condition at which the system is found? For instance, the confining pressure should influence it, no?

Chiara

 Bruno Chareyre (bruno-chareyre) said on 2011-01-11: #3

The unbalanced force tells you. It normalizes with respect to confining pressure (mean contact force).

For instance, I prefer saying that it depends on the density of the packing, the denser it is, the higher is the CN.
Experimentally, A dense material is characterized by the polydispersity of grains size (low porosity)

-------- Message d'origine--------
De: <email address hidden> de la part de Chiara Modenese
Date: mar. 11/01/2011 23:46
Objet : Re: [Yade-users] [Question #141044]: coordination number

Chiara Modenese posted a new comment:
Hi Bruno,

thanks for your answer! May I ask you how would you define the stability of the packing?
As for the CN, does not it also depend on the condition at which the system is found? For instance, the confining pressure should influence it, no?

Chiara

--

_______________________________________________
Post to : <email address hidden>

 Bruno Chareyre (bruno-chareyre) said on 2011-01-14: #5

I didn't understand this part of the question : "As for the CN, does not it also depend on the condition at which the system is found? [...] For instance, the confining pressure should influence it, no?"

Yes, it can. See, "modulo elastic deformation creating contact" in first reply.
Still, I don't see a relation with packing stability. The minimum is 3, or 2 if you have rolling stiffness. But being higher than that doesn't guarantee stability.