How to choose the friction coefficient between two granular with different friction coefficients

Dear LAMMPS Developers,

I am simulating granular spheres with two different friction coefficients (xmu_1 and xmu_2 respectively). I saw in the manual that when the friction between type 1 and type 2 particles is not specifically set, the geometric mean is used by default, set as sqrt(xmu_1 * xmu_2). This setting has a significant impact on my results. I would like to know the basis for this setting method, such as whether it comes from a certain book or a certain article.

Using the default settings, I got a result that looks good, so I want to know the source of this setting to rationalize our results.

I would guess that the default mixing rule was chosen since it is convenient.

Thanks for your reply, I also think this choice is very convenient. I’m just not sure how to prove to others that this choice is reasonable enough, so I’m wondering if there’s any materials out there that back this up.

A straightforward solution is to test all possible rules, and choose the rule that allow you to best reproduce a given properties.

Another possibility is to refer to the literature, the effect of combination rules is known and has been studied. I don’t know the literature of granular material, but see for instance this paper in the context of atomic simulations (I am sure that the same type of study was made for granular systems).

Finally, on the side note, the use of combination rules in simulation is something that is difficult to justify. We all use it, it is convenient because it does not require any additional parameters, but it is rarely (if ever?) based on solid fundamental arguments.


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Thanks for your reply. I have tried two different options, and the results are quite different. Due to the lack of experimental research on mixtures of granular materials with two different friction coefficients, I am not sure which option is more reasonable, so I am seeking some insights on simulation here. Thank you very much for providing this paper, it has deepened my understanding of combination rules. This might help me solve this problem. I sincerely appreciate your help.