I was setting parameters for pair_style gran/hertz/history kt and kn. And I cannot understand. In manual Kn=4G/3/(1-nu), in Zhang Phys Rev E72
Kn=4G/(1-nu). Besides if I place nu=0 kt/kn=1.5, nu=0.5 kt/kn=1. In Silbert Phys Rev E64 is said that for most materials kt/kn=2/3. In default value of lammps is 2/7. Could you please explain what is closer to the reality. And will it be absolutely inappropriate to set kn=E and kt=2/3E. And how can be physically interpreted mu>1?

You’re free to set those values to whatever you like. The pair gran
doc page explains what the default LAMMPS choices are and mentions
the Zhang paper.

A follow-up on Steve’s email to further clarify a few things.

LAMMPS for granular systems offers the possibility of a linear spring model, and a Hertzian one.

In the Hertzian case the spring is non-linear, and the relation between force and the overlap between two particles has been calculated after Hertz’s work, assuming that the particles are spherical and fully elastic in the normal direction. A good book for this I think is Contact Mechanics, by Johnson.

As for your question on the extra factor of 3 in the LAMMPS manual - I checked the formulae once more and they are equivalent. Zhang and Makse just have the extra 3 as part of their equation (1), whereas in the LAMMPS Manual the 3 has been transferred into the expression for kn. Note also that ksi (ξ) in Zhang and Makse is half of delta.

Anyway, in the Hertzian formula, as described by the manual you need to calculate Kn and Kt based on the stiffnesses and Poisson ratios of your grain material.

Please remember that all these are models of what happens in reality. For example grains in most applications are not fully elastic, or fully spherical. Grains are also frictional, which induces slip at parts of the contact area, making the tangential interaction even more difficult to describe.

So it always depends on you to decide whether the Hertz model is good for your problem. Many times I just go for a linear spring model for geomaterial grains.

Thank you very much for such a detailed explanation. Now I see my mistake. Though I am still confused with the fact that if I set nu=0.3, kt will be greater than kn. And do not quit understand xmu>1. I will study the book you recommend. And again thank you very much.