normal model hooke/stiffness

Purpose

Implement the normal contact model Hook with user-defined stiffnesses and dampings.

Syntax

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

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

absolute_damping values = 'on' or 'off'
  on = activates tangential damping
  off = no tangential damping
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

Material interaction properties

kn ( $k_n$ ): normal stiffness of the two materials in contact [force/length]
kt ( $k_t$ ): tangential stiffness of the two materials in contact [force/length]
gamman ( $\tilde{\gamma}_n$ ): normal damping of the two materials in contact per unit mass [force*time/(length*mass)]
gammat ( $\tilde{\gamma}_t$ ): tangential damping of the two materials in contact per unit mass [force*time/(length*mass)]
gamman_abs ( $\gamma_n$ ): normal damping of the two materials in contact [force*time/length] (only if absolute_damping on)
gammat_abs ( $\gamma_t$ ): tangential damping of the two materials in contact [force*time/length] (only if absolute_damping on)

Description

The model calculates the normal force between two particles in contact as follows:

$F_n = k_n \delta n_{ij} - \gamma_n v_{n,ij}$

where $k_n$ is the normal stiffness, $\delta$ is the overlap of the two particles, $n_{ij}$ is the contact normal, $\gamma_n$ is the damping coefficient, $v_{n,ij}$ is the relative normal velocity of the two particles. The overlap of spherical particles is defined as $\delta = r_i + r_j - r$ , where $r_i$ and $r_j$ are the particles’ radii and $r$ is the centroid distance.

This model defines also the stiffness and damping coefficient of the tangential force defined as:

$F_t = k_t \delta t_{ij} - \gamma_t v_{t,ij}$

where $\delta t_{ij}$ is the tangential overlap and $v_{t,ij}$ is the relative tangential velocity. Please, refer to the documentation relative to the tangential models for more information.

For the case of absolute_damping off (which is default), the specified damping coefficients $\tilde{\gamma}_n$ and $\tilde{\gamma}_t$ are multiplied by the effective mass $m^* = (m_i m_j)/(m_i + m_j)$ , where $m_i$ and $m_j$ are the particles’ masses.

$\gamma_n = m^* \tilde{\gamma}_n \gamma_t = m^* \tilde{\gamma}_t$

By setting tangential_damping off, $\gamma_t$ is automatically set to zero.

Force Limiting:

Note, that not using limitForce might lead to attractive forces between particles and walls, especially for very high dampings. Be sure you include this key word for the pair style and the wall model if you like to avoid this.

Restrictions

If using SI units, $Y$ must be bigger than 5e6. If using CGS units, $Y$ must be bigger than 5e5. When using limitForce on, the specified coefficient of restitution is only approximate. This might become problematic for low coefficients of restitution as showing in Schwager and Poschel.

Coarse-graining information:

Using coarsegraining in combination with this command might lead to different dynamics or system state and thus to inconsistencies.

Default

absolute_damping = ‘off’, tangential_damping = ‘on’, limitForce = ‘off’