Tangential contact - gnomeCreative/HYBIRD GitHub Wiki

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Tangential contact

HYBIRD allows the user to choose between two models: a fully developed frictional model, and a simpler viscous model. The former is necessary when the granular system is in a static or quasi-static state, but is much more computationally demanding. The latter is a simpler model, which can be used in highly dynamic systems as a first approximation. The command staticFrictionSolver allows the user to control which model to use.

The viscous model

This is the simplaset model, which is triggered if the command staticFrictionSolver is deactivated. The tangential contact force is in this case assumed to be proportional to the component of the relative velocity of the two spheres lying on the contact surface as

$F_\textrm{t,coll}=- \textrm{min}\left(2\alpha_\textrm{t}\sqrt{k_\textrm{t} \tilde{m}} u_\textrm{t,coll}, \textrm{tan} (\phi_d) F_\textrm{n,coll}\right)$,

where $k_\textrm{t}$ is a tangential stiffness, whose definition depends on the normal contact model:

  • If the normal model is linear, $k_\textrm{t}=k_\textrm{n,L}$
  • If the normal model is Hertzian $k_\textrm{t}=\frac{2 E_\textrm{p}}{(2-\nu_\textrm{p})(1+\nu_\textrm{p})} \sqrt{\tilde{r}} \left(F_\textrm{n,coll}\right)^{-1/3}$.

This model applies a dissipative force proportional to the shear between the two particles, an approach that mimics the viscous behavior of a fluid. The maximum force is given by a Coulomb friction criterion. This model simplifies the frictional behavior by implementing only the dynamic component of friction, and thus only the dynamic friction coefficient $\textrm{tan}(\phi_d)$ appears. It was originally developed by Haff & Werner (1986) and has been successfully used in many situations (Poschel & Schawer, 2005).

The viscous model

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