normal model hertz/time_dependent

Purpose

Implement the normal contact model Hertz with a time-dependent Young’s modulus.

Syntax

model hertz/time_dependent [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)

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
heating_normal_hertz values = 'on' or 'off'
  on = model contributes to surface heating in the frame of enable_surface_heating
  off = model does not contribute to surface heating
disableNormalWhenBonded values = 'on' or 'off'
  on = if the cohesion bond model is used, then the normal force is only added if the two particles are not bonded
  of = the normal force is always added if two particles overlap
computeDissipatedEnergy values = 'on' or 'off'
  on = the normal model saves the dissipated energy for each contact for the
  use in fix calculate/dissipated_energy
  of = no values are saved
computeElasticPotential values = 'on' or 'off'
  on = the normal model saves the current elastic potential for each contact
  for the use in fix calculate/normal_elastic_energy
  of = no values are saved

Associated material properties

Material properties

youngsModulus ( $Y$ ): the Young’s modulus of a material, i.e. its stiffness [pressure]
poissonsRatio ( $\nu$ ): the Poisson’s ratio, i.e. the ratio of transverse to axial strain [ $\cdot$ ]
YModifier ( $\alpha_Y$ ): scaling factor for Young’s modulus [ $\cdot$ ]. It can be either a constant or a discrete function of time provided via look-up table.

Material interaction properties

coefficientRestitution ( $e$ ): The coefficient of restitution of two materials [ $\cdot$ ]

Description

This model extends the normal contact model Hertz by allowing a constant or a time-dependent scaling of the Young’s modulus, namely:

$Y_{new} = \alpha_Y Y$

where $\alpha_Y$ can be either a constant or a discrete function of time provided via look-up table (see material_properties command for more information).

Warning

No feature currently takes the scaling factor $\alpha_Y$ into account outside of this contact model. This can have unwanted side effects and the user must ensure that the parameter does not cause them. One example is the fix check/timestep/gran which will only consider $Y$ specified via the youngsModulus property. Thus, the user needs to ensure that the time-step restrictions are satisfied due to the varying $Y_{new}$ .

Restrictions

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

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’, heating_normal_hertz = ‘off’