normal model hertz/stiffness

Purpose

Implement the normal contact model Hertz with user-defined non-linear stiffness and damping.

Syntax

model hertz/stiffness [other model_type/model_name pairs as described here ] settings keyword values

zero or more keyword/value pairs may be appended to the end (after all models are specified)

limitForce values = 'on' or 'off'
  on = ensures that the normal force is never attractive (an artefact that can occur at the end of a collision).
  off = standard implementation that might lead to attractive forces.
tangential_damping values = 'on' or 'off'
  on = activates tangential damping
  off = no tangential damping

Associated material properties

None.

Material interaction properties

kn ( $k_n$ ): modified elastic modulus for normal contact of the two materials [pressure]
kt ( $k_t$ ): modified elastic modulus for tangential contact of the two materials [pressure]
gamman ( $\gamma_n$ ): viscoelastic damping coefficient for normal contact of the two materials [pressure*time/mass]
gammat ( $\gamma_t$ ): viscoelastic damping coefficient for tangential contact of the two materials [pressure*time/mass]

Description

This model extends the normal contact model Hertz by allowing a non-linear normal stiffness $\tilde{k}_n$ and viscoelastic damping coefficient $\tilde{\gamma}_n$ , namely:

$\tilde{k}_n = k_n \sqrt{\delta_n r^*} \tilde{\gamma}_n = \gamma_n m^* \sqrt{\delta_n r^*}$

where $\delta_n$ is the particles’ overlap, $r^*$ is the effective radius and $m^*$ is the effective mass.

The model also defines the tangential stiffness $\tilde{k}_t$ and viscoelastic damping coefficient $\tilde{\gamma}_t$ to be used by the tangential models as follows:

$\tilde{k}_t = k_t \sqrt{\delta_n r^*} \tilde{\gamma}_t = \gamma_t m^* \sqrt{\delta_n r^*}$

Restrictions

None.

Coarse-graining information:

Using coarsegraining in combination with this command should lead to statistically equivalent dynamics and system state.

Default

tangential_damping = ‘on’, limitForce = ‘off’