Kn and Kt (and damping) calculations for pair_style gran/hooke/history

Dear LAMMPS community,

I am setting up a granular simulation and I want to ensure I am calculating the normal and tangential elastic constants (K_n and K_t), as well as the damping parameters, correctly for pair_style gran/hooke/history.

I am trying to map my macroscopic material properties to the linear spring-dashpot model. My known parameters are:

  • Young’s modulus: E
  • Poisson’s ratio: \nu
  • Particle diameter: d (assuming two identical interacting particles)
  • Particle density: \rho
  • Coefficient of restitution: e
    Could you please suggest equation to calculate the K_n, gamma_n and K_t inputs for gran/hooke/history based on above material properties?