"LIGGGHTS WWW Site"_liws - "LAMMPS WWW Site"_lws - "LIGGGHTS Documentation"_ld - "LIGGGHTS Commands"_lc :c

:link(liws,http://www.cfdem.com)
:link(lws,http://lammps.sandia.gov)
:link(ld,Manual.html)
:link(lc,Section_commands.html#comm)

:line

gran model hooke/stiffness :h3

[Syntax:]

model hertz keyword values :pre
zero or more keyword/value pairs may be appended :l
  {absolute_damping} values = 'on' or 'off'
    on = activates tangential damping
    off = no tangential damping :pre
  {tangential_damping} values = 'on' or 'off'
    on = activates tangential damping
    off = no tangential damping :pre

[LIGGGHTS vs. LAMMPS Info:]

This part of "pair gran"_pair_gran.html and 
"fix wall/gran"_fix_wall_gran.html
is not availabe in LAMMPS.

[Description:]

This granular model uses the following formula for the frictional force between two granular 
particles, when the distance r between two particles of radii Ri and Rj is less than their 
contact distance d = Ri + Rj. There is no force between the particles when r > d.

For the case of {absolute_damping} = 'off' (which is default), the specified damping 
coefficient is multiplied by the effective mass. The forces are implemented as

:c,image(Eqs/pair_gran_html_m566a9984.png)

For the case of {absolute_damping} = 'on', this multiplication is omitted and the forces become

:c,image(Eqs/pair_gran_html_m76cd8bd9.png)

In the first term is the normal force between the two particles and the second term is the 
tangential force. The normal force has 2 terms, a spring force and a damping force. The 
tangential force also has 2 terms: a shear force and a damping force. The shear force is 
a "history" effect that accounts for the tangential displacement ("tangential overlap") 
between the particles for the duration of the time they are in contact.
This term is controlled by the "tangential model"_Section_gran_models.html in action
Keyword {tangential_damping} can be used to eliminate the second part of the force in 
tangential direction. The way how the Coulomb friction limit acts is also controlled
by the "tangential model"_Section_gran_models.html chosen by the user.

The quantities in the equations are as follows:

delta_n = d - r = overlap distance of 2 particles  :ulb,l
k_n = elastic constant for normal contact :l
k_t = elastic constant for tangential contact :l
gamma_n = viscoelastic damping constant for normal contact :l
gamma_t = viscoelastic damping constant for tangential contact :l
delta_t = tangential displacement vector between 2 spherical particles which is truncated to satisfy a frictional yield criterion :l
rmu = coefficient of rolling friction :l
contactradius = contact radius, equal to particle radius - 0.5 * delta_n :l
v_n = normal component of the relative velocity of the 2 particles :l
v_t = tangential component of the relative velocity of the 2 particles :l
w_r = relative rotational velocity of the 2 particles :l
:ule

To define those k_n_specified, k_t_specified, gamma_n_specified, and gamma_t_specified coefficients
(material properties), it is mandatory to use multiple "fix property/global"_fix_property.html commands:

fix id all property/global kn peratomtypepair n_atomtypes value_11 value_12 .. value_21 value_22 .. .
    (value_ij=value for k_n between atom type i and j; n_atomtypes is the number of atom types you want to use in your simulation)
fix id all property/global kt peratomtypepair n_atomtypes value_11 value_12 .. value_21 value_22 .. .
    (value_ij=value for k_t between atom type i and j; n_atomtypes is the number of atom types you want to use in your simulation)
fix id all property/global gamman peratomtypepair n_atomtypes value_11 value_12 .. value_21 value_22 .. .
    (value_ij=value for gamma_n between atom type i and j; n_atomtypes is the number of atom types you want to use in your simulation)
fix id all property/global gammat peratomtypepair n_atomtypes value_11 value_12 .. value_21 value_22 .. .
    (value_ij=value for gamma_t between atom type i and j; n_atomtypes is the number of atom types you want to use in your simulation) :pre

If the absolute damping implementation is used ({absolute_damping} = 'on'), the damping coefficients
 must be named gamman_abs and gammat_abs instead of gamman, gammat as follows:

fix id all property/global gamman_abs peratomtypepair n_atomtypes value_11 value_12 .. value_21 value_22 .. .
    (value_ij=value for gamma_n between atom type i and j; n_atomtypes is the number of atom types you want to use in your simulation)
fix id all property/global gammat_abs peratomtypepair n_atomtypes value_11 value_12 .. value_21 value_22 .. .
    (value_ij=value for gamma_t between atom type i and j; n_atomtypes is the number of atom types you want to use in your simulation) :pre

IMPORTANT NOTE: You have to use atom styles beginning from 1, e.g. 1,2,3,...

The coefficient of friction cof is the upper limit of the tangential force through 
the Coulomb criterion Ft = cof*Fn, where Ft and Fn are the total tangential and normal 
force components in the formulas above. Thus in the Hookean case, the tangential force 
between 2 particles grows according to a tangential spring and dash-pot model until 
Ft/Fn = cof and is then held at Ft = Fn*cof until the particles lose contact. 
In the Hertzian case, a similar analogy holds, though the spring is no longer linear.

[Restrictions:]

If using SI units, youngsModulus must be > 5e6
If using CGS units, youngsModulus must be > 5e5

[Default:] 

{tangential_damping} = 'on'

[(Di Renzo)] Alberto Di Renzo, Francesco Paolo Di Maio, CES, 59 (3), p 525–541 (2004).

[(Ai)] Jun Ai, Jian-Fei Chen, J. Michael Rotter, Jin Y. Ooi, Powder Technology, 206 (3), p 269-282 (2011).

[(Brilliantov)] Brilliantov, Spahn, Hertzsch, Poschel, Phys Rev E, 53, p 5382-5392 (1996).

[(Silbert)] Silbert, Ertas, Grest, Halsey, Levine, Plimpton, Phys Rev E, 64, p 051302 (2001).

[(Zhang)] Zhang and Makse, Phys Rev E, 72, p 011301 (2005). 

