lammps/doc/pair_gran.txt

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

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pair_style gran/hertzian command :h3
pair_style gran/history command :h3
pair_style gran/no_history command :h3

[Syntax:]

pair_style style Kn gamma_n xmu dampflag :pre

style = {gran/hertzian} or {gran/history} or {gran/no_history} :ulb,l
Kn = spring constant for particle repulsion (force/distance units) :l
gamma_n = damping coefficient for normal direction collisions (1/time units) :l
xmu = static yield criterion (unitless) :l
dampflag = 0 or 1 if tangential damping force is excluded or included :l,ule

[Examples:]

pair_style gran/history 200000.0 0.5 1.0 1 :pre

[Description:]

The {gran} styles use the following formula "(Silbert)"_#Silbert for
frictional force between two granular particles that are a distance r
apart when r is less than the contact distance d = Ri + Rj, where Ri
and Rj are the radii of the two particles:

:c,image(Eqs/pair_granular.jpg)

The 1st term is a normal force and the 2nd term is a tangential force.
The normal force has 2 parts: a contact force and a damping force.
The tangential force also has 2 parts: a shear force and a damping
force.  The shear force is included in pair styles {history} and
{Hertzian}, but is not included in pair style {no_history}.  The
tangential damping force is not included if {dampflag} is set to 0.
The other quantities in the equation are as follows:

delta = d - r
f(x) = 1 for Hookean contact used in pair styles {history} and {no_history}
f(x) = sqrt(x) for Hertzian contact used in pair style {hertzian}
Kn = elastic constant for normal contact
Kt = elastic constant for tangential contact = 2/7 of Kn
gamma_n = viscoelastic damping constant for normal contact
gamma_t = viscoelastic damping constant for tangential contact = 1/2 of gamma_n
m_eff = Mi Mj / (Mi + Mj) = effective mass of 2 particles of mass Mi and Mj
Delta St = tangential displacement vector between the 2 spherical particles \
      which is truncated to satisfy a frictional yield criterion
n_ij = unit vector along the line connecting the centers of the 2 particles
Vn = normal component of the relative velocity of the 2 particles
Vt = tangential component of the relative velocity of the 2 particles :ul

The Kn and gamma_n coefficients are set as parameters to the
pair_style command.  You can also think of Kn as being in mg/d units
where m is mass, g is the gravitational constant, and d is the
characteristic diameter of a particle.

Xmu is also specified in the pair_style command and is the upper limit
of the tangential force through the Coulomb criterion Ft = xmu*Fn.
The tangential force between 2 particles grows according to a
tangential spring and dash-pot model until Ft/Fn = xmu and is then
held at Ft = Fn*xmu until the particles lose contact.

For granular styles there are no individual atom type coefficients
that can be set via the "pair_coeff"_pair_coeff.html command.  All
global settings are made via the pair_style command.

See the citation below for more discussion of granular potentials.

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[Mixing, shift, table, tail correction, restart, rRESPA info]:

The "pair_modify"_pair_modify.html mix, shift, table, and tail options
are not relevant for granular pair styles.

These pair styles write their information to "binary restart
files"_restart.html, so a pair_style command does not need to be
specified in an input script that reads a restart file.

These pair styles can only be used via the {pair} keyword of the
"run_style respa"_run_style.html command.  They do not support the
{inner}, {middle}, {outer} keywords.

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[Restrictions:] none

All the granular pair styles are part of the "granular" package.  It
is only enabled if LAMMPS was built with that package.  See the
"Making LAMMPS"_Section_start.html#2_3 section for more info.

[Related commands:]

"pair_coeff"_pair_coeff.html

[Default:] none

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