# coordination number

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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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

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

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

Hadda (hadda) said : | #4 |

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)

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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

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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.

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