# About mixing of coefficients of pair_style granular

Dear all
hope you are all well recently, I hope to obtain some help for the mixing of coefficients of pair_style granular. I hope to have two different materials, but both the “hertz/material” model.

for material 2, i hope to have “rolling” part, while material 1 dose not have “rolling” part.
but this cannot really work in the lastest lammps by default mixing by lammps, therefore, i wish to give the “pair_coeff 1 2” by myself and want to give pair_coeff 1 2 without “rolling” part, but the remaining parameters just follow the equation for lammps documentations:
https://docs.lammps.org/pair_granular.html
however, i do meet a problem for Young’s modulus of pair_coeff 1 2. Firstly, for the equations of effective young’s modulus, there are two different equations for E_eff,ij; see equation 2 and 3 in the image.

i attached the image (from lammps documentations) for these two equations. I am not pretty sure whether this is a typo for the equation 3, whether the square is missing in the equation 3.
So I assume that the equation 2 is right. So in my case, i tried to check this without “rolling” part;
so input script 1, the mixing coefficients are automatically obtained by LAMMPS; input script 2, i give
the mixing coefficients based on the equations from LAMMPS documentations. I think i should get the 100% same results.

for my material 1, E1 = 7e6, v1 = 0.5; material 2, E2 = 7e10, v2 = 0.2, so based on equation 1, the Eeff,ij = 9.33e6; then i should give the suitable Eij so that i obtain the same Eeff,ij (9.33e6), based on my calculation from equation 2, when Eij is 1.68e7, the Eeff,ij is 9.33e6, which should be ok, but it seems that i got totally different simulations results for these input script 1 and input script 2:
see input 1, the key sentences are:

``````pair_coeff 2 2 hertz/material 7.0e10 0.1 0.2 tangential mindlin_rescale/force NULL 1.0 1.0
pair_coeff 1 1 hertz/material 7e6 0.5 0.5 tangential mindlin_rescale/force NULL 1.0 0.001
``````

see input 2, the key sentences are :

``````pair_coeff 2 2 hertz/material 7.0e10 0.1 0.2 tangential mindlin_rescale/force NULL 1.0 1.0
pair_coeff 1 1 hertz/material 7e6 0.5 0.5 tangential mindlin_rescale/force NULL 1.0 0.001
pair_coeff 1 2 hertz/material 1.68e7 0.316228 0.316228 tangential mindlin_rescale/force NULL 1.0 0.031623
``````

all parameters are geometric averaging, and Eij is calculated based on equation 1,2 and 3.

so does anyone has the idea that how should i correctly give the values for mixing of coefficients, i just want to obtain the same results compared to the default results obtained from lammps

hope you all have a nice day This looks like it’s just a typo in the documentation. There should be a square exponent in Eq. 3, which is present in the code.

This looks correct when compared to the code, so your argument for pair_coeff 1 2 should be 9.33e6 not 1.68e7. I’ll have to check with the primary author of pair granular whether there’s a disconnect in the documentation.

Should the mixed value of Poisson’s ratio be ~0.22?

Dear jtclemm

Thanks for your response, i have also checked the source code of pair_style granular, it seems that the equation 2 is the right one. it could be a typo for equation 3.

for the calculation of pair_coeff 1 2, it seems that the lammps automatically calculate the effective Eij based on equation 1 if we do not give the Eij.
so if we give the exact value of Eij, the effective Eij should be calculated based on equation 2.
it seems that the Eij is different compared to effective Eij.
but for the mixing, i have a idea for using mixing, i can use rolling sds 0 0 0. Although we have rolling command, do not really have this rolling