pair_style gran/hertzian command

pair_style gran/history command

pair_style gran/no_history command

Syntax:

pair_style style Kn gamma_n xmu dampflag 

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

Examples:

pair_style gran/history 200000.0 0.5 1.0 1 

Description:

The gran styles use the following formula (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:

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

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 command. All global settings are made via the pair_style command.

See the citation below for more discussion of granular potentials.

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

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

These pair styles write their information to binary restart files, 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 command. They do not support the inner, middle, outer keywords.

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 for more info.

Related commands:

pair_coeff

Default: none

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