# characteristicVelocity

Submitted by NSalloum on Tue, 10/16/2018 - 09:42

hello,

I was wondering what is the exact physical meaning of the characteristic impact velocity, (i.e. characteristicVelocity), and how does it affect my simulation in LIGGGHTS.

Especially that I read in the documentations that it is basically introduced in the Hookean contact model, but it is rather involved in many scripts not dealing at all with Hook's contact model.

best wishes,
Nizar

### Forums:

Daniel Queteschiner | Tue, 10/16/2018 - 15:26

### characteristic velocity

To express the normal stiffness `k_n` in the Hooke model as a function of material parameters and relate it to the Hertz model, `k_n_Hooke` is chosen such that in the case of an undamped, perfectly elastic collision the maximum overlap `delta_n_Hooke = v_0 * sqrt(m*/k_n_Hooke)` is equal to the maximum overlap in the Hertz model. Here, `v_0` is the relative particle velocity at the beginning of the binary contact. (`k_n_Hooke = v_0^2 m* / delta_n_Hooke^2 = v_0^2 m* / delta_n_Hertz^2 `)
And that is how `v_0` gets introduced explicitly into the expression of `k_n_Hooke`. Since `k_n_Hooke` is an input parameter for all contacts in the simulation you have to specify an estimate of the average `v_0` in the system, i.e. a characteristic impact velocity.

Any tutorial script not using the Hooke contact model but specifying `characteristicVelocity` will just ignore that setting. It's not used for anything else.

NSalloum | Thu, 10/18/2018 - 12:38

### hello Daniel,

hello Daniel,

This was really very helpful clarifying.

But is their a way I can predicts its value for my system, as I am dealing with particles at the micro-scale? or am I simply supposed to tune it through calibration?

best wishes,