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<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
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<H3>pair_style gran/hertizian command
</H3>
<H3>pair_style gran/history command
</H3>
<H3>pair_style gran/no_history command
</H3>
<P><B>Syntax:</B>
</P>
<PRE>pair_style style Kn gamma_n xmu dampflag
</PRE>
<UL><LI>style = <I>gran/hertzian</I> or <I>gran/history</I> or <I>gran/no_history</I>
<LI>Kn = spring constant for particle repulsion
<PRE> (mg/d units where m is mass, g is the gravitational constant, d is diameter of a particle)
</PRE>
<LI>gamma_n = damping coefficient for normal direction collisions (sqrt(g/d) units)
<LI>xmu = static yield criterion
<LI>dampflag = flag (0/1) for whether to (no/yes) include tangential damping
</UL>
<P><B>Examples:</B>
</P>
<PRE>pair_style gran/history 200000.0 0.5 1.0 1
</PRE>
<P><B>Description:</B>
</P>
<P>The <I>gran</I> styles use the following formula <A HREF = "#Silbert">(Silbert)</A> for
frictional force between two granular particles that are a distance r
apart when r is less than the contact distance d.
</P>
<CENTER><IMG SRC = "Eqs/pair_granular.jpg">
</CENTER>
<P>The 1st term is a normal force and the 2nd term is a tangential force.
The other quantites are as follows:
</P>
<UL><LI>delta = d - r
<LI>f(x) = 1 for Hookean contacts used in pair styles <I>history</I> and <I>no_history</I>
<LI>f(x) = sqrt(x) for pair style <I>hertzian</I>
<LI>Kn = elastic constant for normal contact
<LI>Kt = elastic constant for tangential contact = 2/7 of Kn
<LI>gamma_n = viscoelastic constants for normal contact
<LI>gamma_t = viscoelastic constants for tangential contact = 1/2 of gamma_n
<LI>m_eff = Mi Mj / (Mi + Mj) = effective mass of 2 particles of mass Mi and Mj
<LI>Delta St = tangential displacement vector between the 2 spherical particles which is truncated to satisfy a frictional yield criterion
<LI>n = a unit vector along the line connecting the centers of the 2 particles
<LI>Vn = normal component of the relative velocity of the 2 particles
<LI>Vt = tangential component of the relative velocity of the 2 particles
</UL>
<P>The Kn and gamma_n coefficients are set as parameters to the
pair_style command. Xmu is also specified which 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 then is held at Ft =
Fn*xmu until the particles lose contact.
</P>
<P>For granular styles there are no individual atom type coefficients
that can be set. All global settings are made via the pair_style
command.
</P>
<P>See the citation for more discussion of the granular potentials.
</P>
<P><B>Restrictions:</B> none
</P>
<P>All of these styles are part of the "granular" package. It is only
enabled if LAMMPS was built with that package. See the <A HREF = "Section_start.html#2_3">Making
LAMMPS</A> section for more info.
</P>
<P>You must use <A HREF = "atom_style.html">atom style</A> <I>granular</I> with these pair
styles.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "pair_coeff.html">pair_coeff</A>
</P>
<P><B>Default:</B> none
</P>
<HR>
<A NAME = "Silbert"></A>
<P><B>(Silbert)</B> Silbert, Ertas, Grest, Halsey, Levine, Plimpton, Phys Rev
E, 64, p 051302 (2001).
</P>
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