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doc/Eqs/pair_gran_hertz.tex
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@ -7,7 +7,7 @@ $$
\sqrt{\delta} \sqrt{\frac{R_i R_j}{R_i + R_j}}
\Big[ (k_n \delta \mathbf{n}_{ij} -
m_{\mbox{\scriptsize{eff}}} \: \gamma_n \mathbf{ v}_n) -
(k_t \delta\mathbf{ \Delta s}_t +
(k_t \mathbf{ \Delta s}_t +
m_{\mbox{\scriptsize{eff}}} \: \gamma_t \mathbf{v}_t) \Big]
$$

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doc/Eqs/pair_gran_hooke.tex
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@ -5,7 +5,7 @@
$$
F_{hk} = (k_n \delta \mathbf{n}_{ij} -
m_{\mbox{\scriptsize{eff}}} \gamma_n\mathbf{ v}_n) -
(k_t \delta\mathbf{ \Delta s}_t +
(k_t \mathbf{ \Delta s}_t +
m_{\mbox{\scriptsize{eff}}} \gamma_t \mathbf{v}_t)
$$

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doc/Section_commands.html
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@ -366,7 +366,7 @@ full description:
<TR ALIGN="center"><TD ><A HREF = "pair_coul.html">coul/cut</A></TD><TD ><A HREF = "pair_coul.html">coul/debye</A></TD><TD ><A HREF = "pair_coul.html">coul/long</A></TD><TD ><A HREF = "pair_dipole.html">dipole/cut</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "pair_dpd.html">dpd</A></TD><TD ><A HREF = "pair_eam.html">eam</A></TD><TD ><A HREF = "pair_eam.html">eam/opt</A></TD><TD ><A HREF = "pair_eam.html">eam/alloy</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "pair_eam.html">eam/alloy/opt</A></TD><TD ><A HREF = "pair_eam.html">eam/fs</A></TD><TD ><A HREF = "pair_eam.html">eam/fs/opt</A></TD><TD ><A HREF = "pair_gayberne.html">gayberne</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "pair_gran.html">gran/hertzian</A></TD><TD ><A HREF = "pair_gran.html">gran/history</A></TD><TD ><A HREF = "pair_gran.html">gran/no_history</A></TD><TD ><A HREF = "pair_charmm.html">lj/charmm/coul/charmm</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "pair_gran_hertz_history.html">gran/hertz/history</A></TD><TD ><A HREF = "pair_gran_hooke.html">gran/hooke</A></TD><TD ><A HREF = "pair_gran_hooke_history.html">gran/hooke/history</A></TD><TD ><A HREF = "pair_charmm.html">lj/charmm/coul/charmm</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "pair_charmm.html">lj/charmm/coul/charmm/implicit</A></TD><TD ><A HREF = "pair_charmm.html">lj/charmm/coul/long</A></TD><TD ><A HREF = "pair_charmm.html">lj/charmm/coul/long/opt</A></TD><TD ><A HREF = "pair_class2.html">lj/class2</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "pair_class2.html">lj/class2/coul/cut</A></TD><TD ><A HREF = "pair_class2.html">lj/class2/coul/long</A></TD><TD ><A HREF = "pair_lj.html">lj/cut</A></TD><TD ><A HREF = "pair_lj.html">lj/cut/opt</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "pair_lj.html">lj/cut/coul/cut</A></TD><TD ><A HREF = "pair_lj.html">lj/cut/coul/debye</A></TD><TD ><A HREF = "pair_lj.html">lj/cut/coul/long</A></TD><TD ><A HREF = "pair_lj.html">lj/cut/coul/long/tip4p</A></TD></TR>

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doc/Section_commands.txt
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@ -504,9 +504,9 @@ full description:
"eam/fs"_pair_eam.html,
"eam/fs/opt"_pair_eam.html,
"gayberne"_pair_gayberne.html,
"gran/hertzian"_pair_gran.html,
"gran/history"_pair_gran.html,
"gran/no_history"_pair_gran.html,
"gran/hertz/history"_pair_gran_hertz_history.html,
"gran/hooke"_pair_gran_hooke.html,
"gran/hooke/history"_pair_gran_hooke_history.html,
"lj/charmm/coul/charmm"_pair_charmm.html,
"lj/charmm/coul/charmm/implicit"_pair_charmm.html,
"lj/charmm/coul/long"_pair_charmm.html,

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doc/fix_wall_gran.html
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@ -13,26 +13,33 @@
</H3>
<P><B>Syntax:</B>
</P>
<PRE>fix ID group-ID wall/gran wallstyle args keyword values ...
<PRE>fix ID group-ID wall/gran Kn Kt gamma_n gamma_t xmu dampflag wallstyle args keyword values ...
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command
<LI>wall/gran = style name of this fix command
<LI>style = <I>xplane</I> or <I>yplane</I> or <I>zplane</I> or <I>zcylinder</I>
<LI>Kn = elastic constant for normal particle repulsion (force/distance units or pressure units - see discussion below)
<LI>Kt = elastic constant for tangential contact (force/distance units or pressure units - see discussion below)
<LI>gamma_n = damping coefficient for collisions in normal direction (1/time units or 1/time-distance units - see discussion below)
<LI>gamma_t = damping coefficient for collisions in tangential direction (1/time units or 1/time-distance units - see discussion below)
<LI>xmu = static yield criterion (unitless fraction between 0.0 and 1.0)
<LI>dampflag = 0 or 1 if tangential damping force is excluded or included
<LI>wallstyle = <I>xplane</I> or <I>yplane</I> or <I>zplane</I> or <I>zcylinder</I>
<LI>args = list of arguments for a particular style
<PRE> <I>xplane</I> or <I>yplane</I> or <I>zplane</I> args = lo hi gamma xmu
<LI> <I>xplane</I> or <I>yplane</I> or <I>zplane</I> args = lo hi
lo,hi = position of lower and upper plane (distance units), either can be NULL)
gamman = damping coeff for normal direction collisions with wall
xmu = friction coeff for the wall
<I>zcylinder</I> args = radius gamma xmu
<I>zcylinder</I> args = radius
radius = cylinder radius (distance units)
gamman = damping coeff for normal direction collisions with wall
xmu = friction coeff for the wall
</PRE>
<LI>zero or more keyword/value pairs may be appended to args
zero or more keyword/value pairs may be appended to args
<LI>keyword = <I>wiggle</I> or <I>shear</I>
@ -48,9 +55,9 @@
</UL>
<P><B>Examples:</B>
</P>
<PRE>fix 1 all wall/gran xplane -10.0 10.0 50.0 0.5
fix 2 all wall/gran zcylinder 15.0 50.0 0.5 wiggle z 3.0 2.0
fix 1 all wall/gran zplane 0.0 NULL 100.0 0.5
<PRE>fix 1 all wall/gran 200000.0 NULL 50.0 NULL 0.5 0 xplane -10.0 10.0
fix 1 all wall/gran 200000.0 NULL 50.0 NULL 0.5 0 zplane 0.0 NULL
fix 2 all wall/gran 100000.0 20000.0 50.0 30.0 0.5 1 zcylinder 15.0 wiggle z 3.0 2.0
</PRE>
<P><B>Description:</B>
</P>
@ -58,13 +65,48 @@ fix 1 all wall/gran zplane 0.0 NULL 100.0 0.5
wall. All particles in the group interact with the wall when they are
close enough to touch it.
</P>
<P>The first set of parameters (Kn, Kt, gamma_n, gamma_t, xmu, and
dampflag) have the same meaning as those specified with the
<A HREF = "pair_gran.html">pair_style granular</A> force fields. This means a NULL
can be used for either Kt or gamma_t as described on that page. If a
NULL is used for Kt, then a default value is used where Kt = 2/7 Kn.
If a NULL is used for gamma_t, then a default value is used where
gamma_t = 1/2 gamma_n.
</P>
<P>The nature of the wall/particle interactions are determined by which
pair_style is used in your input script: <I>hooke</I>, <I>hooke/history</I>, or
<I>hertz/history</I>. The equation for the force between the wall and
particles touching it is the same as the corresponding equation on the
<A HREF = "pair_gran.html">pair_style granular</A> doc page, in the limit of one of
the two particles going to infinite radius and mass (flat wall).
I.e. delta = radius - r = overlap of particle with wall, m_eff = mass
of particle, and sqrt(RiRj/Ri+Rj) becomes sqrt(radius of particle).
The units for Kn, Kt, gamma_n, and gamma_t are as described on that
doc page. The meaning of xmu and dampflag are also as described on
that page. Note that you can choose different values for these 6
wall/particle coefficients than for particle/particle interactions, if
you wish your wall to interact differently with the particles, e.g. if
the wall is a different material.
</P>
<P>IMPORTANT NOTE: As discussed on the doc page for <A HREF = "pair_gran.html">pair_style
granular</A>, versions of LAMMPS before 9Jan09 used a
different equation for Hertzian interactions. This means Hertizian
wall/particle interactions have also changed. They now include a
sqrt(radius) term which was not present before. Also the previous
versions used Kn and Kt from the pairwise interaction and hardwired
dampflag to 1, rather than letting them be specified directly. This
means you can set the values of the wall/particle coefficients
appropriately in the current code to reproduce the results of a
prevoius Hertzian monodisperse calculation. For example, for the
common case of a monodisperse system with particles of diameter 1, Kn,
Kt, gamma_n, and gamma_s should be set sqrt(2.0) larger than they were
previously.
</P>
<P>The <I>wallstyle</I> can be planar or cylindrical. The 3 planar options
specify a pair of walls in a dimension. Wall positions are given by
<I>lo</I> and <I>hi</I>. Either of the values can be specified as NULL if a
single wall is desired. For a <I>zcylinder</I> wallstyle, the cylinder's
axis is at x = y = 0.0, and the radius of the cylinder is specified.
For all wallstyles, a damping and friction coefficient for
particle-wall interactions are also specified.
</P>
<P>Optionally, the wall can be moving, if the <I>wiggle</I> or <I>shear</I>
keywords are appended. Both keywords cannot be used together.
@ -126,7 +168,7 @@ LAMMPS</A> section for more info.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "fix_wiggle.html">fix_wiggle</A>
<P><A HREF = "fix_wiggle.html<A HREF = "pair_gran.html">>fix_wiggle</A>, pair_style granular</A>
</P>
<P><B>Default:</B> none
</P>

65
doc/fix_wall_gran.txt
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@ -10,20 +10,22 @@ fix wall/gran command :h3
[Syntax:]
fix ID group-ID wall/gran wallstyle args keyword values ... :pre
fix ID group-ID wall/gran Kn Kt gamma_n gamma_t xmu dampflag wallstyle args keyword values ... :pre
ID, group-ID are documented in "fix"_fix.html command :ulb,l
wall/gran = style name of this fix command :l
style = {xplane} or {yplane} or {zplane} or {zcylinder} :l
Kn = elastic constant for normal particle repulsion (force/distance units or pressure units - see discussion below) :l
Kt = elastic constant for tangential contact (force/distance units or pressure units - see discussion below) :l
gamma_n = damping coefficient for collisions in normal direction (1/time units or 1/time-distance units - see discussion below) :l
gamma_t = damping coefficient for collisions in tangential direction (1/time units or 1/time-distance units - see discussion below) :l
xmu = static yield criterion (unitless fraction between 0.0 and 1.0) :l
dampflag = 0 or 1 if tangential damping force is excluded or included :l
wallstyle = {xplane} or {yplane} or {zplane} or {zcylinder} :l
args = list of arguments for a particular style :l
{xplane} or {yplane} or {zplane} args = lo hi gamma xmu
{xplane} or {yplane} or {zplane} args = lo hi
lo,hi = position of lower and upper plane (distance units), either can be NULL)
gamman = damping coeff for normal direction collisions with wall
xmu = friction coeff for the wall
{zcylinder} args = radius gamma xmu
{zcylinder} args = radius
radius = cylinder radius (distance units)
gamman = damping coeff for normal direction collisions with wall
xmu = friction coeff for the wall :pre
zero or more keyword/value pairs may be appended to args :l
keyword = {wiggle} or {shear} :l
{wiggle} values = dim amplitude period
@ -37,9 +39,9 @@ keyword = {wiggle} or {shear} :l
[Examples:]
fix 1 all wall/gran xplane -10.0 10.0 50.0 0.5
fix 2 all wall/gran zcylinder 15.0 50.0 0.5 wiggle z 3.0 2.0
fix 1 all wall/gran zplane 0.0 NULL 100.0 0.5 :pre
fix 1 all wall/gran 200000.0 NULL 50.0 NULL 0.5 0 xplane -10.0 10.0
fix 1 all wall/gran 200000.0 NULL 50.0 NULL 0.5 0 zplane 0.0 NULL
fix 2 all wall/gran 100000.0 20000.0 50.0 30.0 0.5 1 zcylinder 15.0 wiggle z 3.0 2.0 :pre
[Description:]
@ -47,13 +49,48 @@ Bound the simulation domain of a granular system with a frictional
wall. All particles in the group interact with the wall when they are
close enough to touch it.
The first set of parameters (Kn, Kt, gamma_n, gamma_t, xmu, and
dampflag) have the same meaning as those specified with the
"pair_style granular"_pair_gran.html force fields. This means a NULL
can be used for either Kt or gamma_t as described on that page. If a
NULL is used for Kt, then a default value is used where Kt = 2/7 Kn.
If a NULL is used for gamma_t, then a default value is used where
gamma_t = 1/2 gamma_n.
The nature of the wall/particle interactions are determined by which
pair_style is used in your input script: {hooke}, {hooke/history}, or
{hertz/history}. The equation for the force between the wall and
particles touching it is the same as the corresponding equation on the
"pair_style granular"_pair_gran.html doc page, in the limit of one of
the two particles going to infinite radius and mass (flat wall).
I.e. delta = radius - r = overlap of particle with wall, m_eff = mass
of particle, and sqrt(RiRj/Ri+Rj) becomes sqrt(radius of particle).
The units for Kn, Kt, gamma_n, and gamma_t are as described on that
doc page. The meaning of xmu and dampflag are also as described on
that page. Note that you can choose different values for these 6
wall/particle coefficients than for particle/particle interactions, if
you wish your wall to interact differently with the particles, e.g. if
the wall is a different material.
IMPORTANT NOTE: As discussed on the doc page for "pair_style
granular"_pair_gran.html, versions of LAMMPS before 9Jan09 used a
different equation for Hertzian interactions. This means Hertizian
wall/particle interactions have also changed. They now include a
sqrt(radius) term which was not present before. Also the previous
versions used Kn and Kt from the pairwise interaction and hardwired
dampflag to 1, rather than letting them be specified directly. This
means you can set the values of the wall/particle coefficients
appropriately in the current code to reproduce the results of a
prevoius Hertzian monodisperse calculation. For example, for the
common case of a monodisperse system with particles of diameter 1, Kn,
Kt, gamma_n, and gamma_s should be set sqrt(2.0) larger than they were
previously.
The {wallstyle} can be planar or cylindrical. The 3 planar options
specify a pair of walls in a dimension. Wall positions are given by
{lo} and {hi}. Either of the values can be specified as NULL if a
single wall is desired. For a {zcylinder} wallstyle, the cylinder's
axis is at x = y = 0.0, and the radius of the cylinder is specified.
For all wallstyles, a damping and friction coefficient for
particle-wall interactions are also specified.
Optionally, the wall can be moving, if the {wiggle} or {shear}
keywords are appended. Both keywords cannot be used together.
@ -115,6 +152,6 @@ Any dimension (xyz) that has a granular wall must be non-periodic.
[Related commands:]
"fix_wiggle"_fix_wiggle.html
"fix_wiggle"_fix_wiggle.html, pair_style granular"_pair_gran.html
[Default:] none

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doc/pair_gran.html
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@ -17,21 +17,35 @@
</H3>
<P><B>Syntax:</B>
</P>
<PRE>pair_style style Kn gamma_n xmu dampflag
<PRE>pair_style style Kn Kt gamma_n gamma_t xmu dampflag
</PRE>
<UL><LI>style = <I>gran/hooke</I> or <I>gran/hooke/history</I> or <I>gran/hertz/history</I>
<LI>Kn = spring constant for particle repulsion (see units below)
<LI>Kn = elastic constant for normal particle repulsion (force/distance units or pressure units - see discussion below)
<LI>gamma_n = damping coefficient for collisions in normal direction (see units below)
<LI>Kt = elastic constant for tangential contact (force/distance units or pressure units - see discussion below)
<LI>gamma_n = damping coefficient for collisions in normal direction (1/time units or 1/time-distance units - see discussion below)
<LI>gamma_t = damping coefficient for collisions in tangential direction (1/time units or 1/time-distance units - see discussion below)
<LI>xmu = static yield criterion (unitless fraction between 0.0 and 1.0)
<LI>dampflag = 0 or 1 if tangential damping force is excluded or included
</UL>
<P>IMPORTANT NOTE: Versions of LAMMPS before 9Jan09 had different style
names for granular force fields. This is to emphasize the fact that
the Hertzian equation has changed to model polydispersity more
accurately. A side effect of the change is that the Kn, Kt, gamma_n,
and gamma_t coefficients in the pair_style command must be specified
with different values in order to reproduce calculations made with
earlier versions of LAMMPS, even for monodisperse systems. See the
NOTE below for details.
</P>
<P><B>Examples:</B>
</P>
<PRE>pair_style gran/history 200000.0 50.0 0.5 1
<PRE>pair_style gran/hooke/history 200000.0 NULL 50.0 NULL 0.5 1
pair_style gran/hooke 200000.0 70000.0 50.0 30.0 0.5 0
</PRE>
<P><B>Description:</B>
</P>
@ -65,51 +79,67 @@ if <I>dampflag</I> is set to 0.
</P>
<UL><LI>delta = d - r = overlap distance of 2 particles
<LI>Kn = elastic constant for normal contact
<LI>Kt = elastic constant for tangential contact = 2/7 of Kn
<LI>Kt = elastic constant for tangential contact
<LI>gamma_n = viscoelastic damping constant for normal contact
<LI>gamma_t = viscoelastic damping constant for tangential contact = 1/2 of gamma_n
<LI>gamma_t = viscoelastic damping constant for tangential contact
<LI>m_eff = Mi Mj / (Mi + Mj) = effective mass of 2 particles of mass Mi and Mj
<LI>Delta St = tangential displacement vector between 2 spherical particles which is truncated to satisfy a frictional yield criterion
<LI>n_ij = 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 specified as parameters to the
pair_style command. The interpretation and units for these
coefficients are different in the Hookean versus Hertzian formulas.
<P>The Kn, Kt, gamma_n, and gamma_t coefficients are specified as
parameters to the pair_style command. If a NULL is used for Kt, then
a default value is used where Kt = 2/7 Kn. If a NULL is used for
gamma_t, then a default value is used where gamma_t = 1/2 gamma_n.
</P>
<P>The interpretation and units for these 4 coefficients are different in
the Hookean versus Hertzian equations.
</P>
<P>The Hookean model is one where the normal push-back force for two
overlapping particles is a linear function of the overlap distance.
Thus the specified Kn is in units of (force/distance). Note that this
push-back force is independent of absolute particle size (in the
monodisperse case) or the relative sizes of the two particles (in the
polydisperse case). This model also applies to the other terms in the
force equation so that the specified gamma_n is in units of (1/time),
Kt is in units of (force/distance), and gamma_t is in units of
(1/time).
monodisperse case) and of the relative sizes of the two particles (in
the polydisperse case). This model also applies to the other terms in
the force equation so that the specified gamma_n is in units of
(1/time), Kt is in units of (force/distance), and gamma_t is in units
of (1/time).
</P>
<P>The Hertzian model is one where the normal push-back force for two
overlapping particles is proportional to the area of overlap of the
two particles, and is thus a non-linear function of overlap distance.
Thus the specified Kn is in units of (force/area). The effects of
absolute particle size (monodispersity) and relative size
(polydispersity) are captured in the radii-dependent pre-factors.
When these pre-factors are carried through to the other terms in the
force equation it means that the specified gamma_n is in units of
(1/time-distance), Kt is in units of (force/area), and gamma_t is in
units of (1/time-distance).
Thus Kn has units of force per area and is thus specified in units of
(pressure). The effects of absolute particle size (monodispersity)
and relative size (polydispersity) are captured in the radii-dependent
pre-factors. When these pre-factors are carried through to the other
terms in the force equation it means that the specified gamma_n is in
units of (1/(time*distance)), Kt is in units of (pressure), and
gamma_t is in units of (1/(time*distance)).
</P>
<P>Note that in the Hookean case, Kn can be thought of as a spring
<P>Note that in the Hookean case, Kn can be thought of as a linear spring
constant with units of force/distance. In the Hertzian case, Kn is
like a non-linear spring constant with units of force/area, and as
shown in the <A HREF = "#Zhang">(Zhang)</A> paper, Kn = 4G / (3(1-nu)) where nu =
the Poisson ratio, G = shear modulus = E / (1(1+nu)), and E = Young's
modulus. Thus in the Hertzian case Kn can be set to a value that
like a non-linear spring constant with units of force/area or
pressure, and as shown in the <A HREF = "#Zhang">(Zhang)</A> paper, Kn = 4G /
(3(1-nu)) where nu = the Poisson ratio, G = shear modulus = E /
(1(1+nu)), and E = Young's modulus. Similarly, Kt = 8G / (2-nu).
Thus in the Hertzian case Kn and Kt can be set to values that
corresponds to properties of the material being modeled. This is also
true in the Hookean case, except that a spring constant must be chosen
that is appropriate for the size of particles in the model. Since
relative particle sizes are not accounted for, the Hookean styles may
not be a suitable model for polydisperse systems.
that is appropriate for the absolute size of particles in the model.
Since relative particle sizes are not accounted for, the Hookean
styles may not be a suitable model for polydisperse systems.
</P>
<P>IMPORTANT NOTE: In versions of LAMMPS before 9Jan09, the equation for
Hertzian interactions did not include the sqrt(RiRj/Ri+Rj) term and
thus was not as accurate for polydisperse systems. For monodisperse
systems, sqrt(RiRj/Ri+Rj) is a constant factor that effectively scales
all 4 coefficients: Kn, Kt, gamma_n, gamma_t. Thus you can set the
values of these 4 coefficients appropriately in the current code to
reproduce the results of a previous Hertzian monodisperse calculation.
For example, for the common case of a monodisperse system with
particles of diameter 1, all 4 of these coefficients should now be set
2x larger than they were previously.
</P>
<P>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,

86
doc/pair_gran.txt
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@ -12,17 +12,29 @@ pair_style gran/hertz/history command :h3
[Syntax:]
pair_style style Kn gamma_n xmu dampflag :pre
pair_style style Kn Kt gamma_n gamma_t xmu dampflag :pre
style = {gran/hooke} or {gran/hooke/history} or {gran/hertz/history} :ulb,l
Kn = spring constant for particle repulsion (see units below) :l
gamma_n = damping coefficient for collisions in normal direction (see units below) :l
Kn = elastic constant for normal particle repulsion (force/distance units or pressure units - see discussion below) :l
Kt = elastic constant for tangential contact (force/distance units or pressure units - see discussion below) :l
gamma_n = damping coefficient for collisions in normal direction (1/time units or 1/time-distance units - see discussion below) :l
gamma_t = damping coefficient for collisions in tangential direction (1/time units or 1/time-distance units - see discussion below) :l
xmu = static yield criterion (unitless fraction between 0.0 and 1.0) :l
dampflag = 0 or 1 if tangential damping force is excluded or included :l,ule
IMPORTANT NOTE: Versions of LAMMPS before 9Jan09 had different style
names for granular force fields. This is to emphasize the fact that
the Hertzian equation has changed to model polydispersity more
accurately. A side effect of the change is that the Kn, Kt, gamma_n,
and gamma_t coefficients in the pair_style command must be specified
with different values in order to reproduce calculations made with
earlier versions of LAMMPS, even for monodisperse systems. See the
NOTE below for details.
[Examples:]
pair_style gran/history 200000.0 50.0 0.5 1 :pre
pair_style gran/hooke/history 200000.0 NULL 50.0 NULL 0.5 1
pair_style gran/hooke 200000.0 70000.0 50.0 30.0 0.5 0 :pre
[Description:]
@ -56,9 +68,9 @@ The other quantities in the equations are as follows:
delta = d - r = overlap distance of 2 particles
Kn = elastic constant for normal contact
Kt = elastic constant for tangential contact = 2/7 of Kn
Kt = elastic constant for tangential contact
gamma_n = viscoelastic damping constant for normal contact
gamma_t = viscoelastic damping constant for tangential contact = 1/2 of gamma_n
gamma_t = viscoelastic damping constant for tangential contact
m_eff = Mi Mj / (Mi + Mj) = effective mass of 2 particles of mass Mi and Mj
Delta St = tangential displacement vector between 2 spherical particles \
which is truncated to satisfy a frictional yield criterion
@ -66,42 +78,58 @@ 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 specified as parameters to the
pair_style command. The interpretation and units for these
coefficients are different in the Hookean versus Hertzian formulas.
The Kn, Kt, gamma_n, and gamma_t coefficients are specified as
parameters to the pair_style command. If a NULL is used for Kt, then
a default value is used where Kt = 2/7 Kn. If a NULL is used for
gamma_t, then a default value is used where gamma_t = 1/2 gamma_n.
The interpretation and units for these 4 coefficients are different in
the Hookean versus Hertzian equations.
The Hookean model is one where the normal push-back force for two
overlapping particles is a linear function of the overlap distance.
Thus the specified Kn is in units of (force/distance). Note that this
push-back force is independent of absolute particle size (in the
monodisperse case) or the relative sizes of the two particles (in the
polydisperse case). This model also applies to the other terms in the
force equation so that the specified gamma_n is in units of (1/time),
Kt is in units of (force/distance), and gamma_t is in units of
(1/time).
monodisperse case) and of the relative sizes of the two particles (in
the polydisperse case). This model also applies to the other terms in
the force equation so that the specified gamma_n is in units of
(1/time), Kt is in units of (force/distance), and gamma_t is in units
of (1/time).
The Hertzian model is one where the normal push-back force for two
overlapping particles is proportional to the area of overlap of the
two particles, and is thus a non-linear function of overlap distance.
Thus the specified Kn is in units of (force/area). The effects of
absolute particle size (monodispersity) and relative size
(polydispersity) are captured in the radii-dependent pre-factors.
When these pre-factors are carried through to the other terms in the
force equation it means that the specified gamma_n is in units of
(1/time-distance), Kt is in units of (force/area), and gamma_t is in
units of (1/time-distance).
Thus Kn has units of force per area and is thus specified in units of
(pressure). The effects of absolute particle size (monodispersity)
and relative size (polydispersity) are captured in the radii-dependent
pre-factors. When these pre-factors are carried through to the other
terms in the force equation it means that the specified gamma_n is in
units of (1/(time*distance)), Kt is in units of (pressure), and
gamma_t is in units of (1/(time*distance)).
Note that in the Hookean case, Kn can be thought of as a spring
Note that in the Hookean case, Kn can be thought of as a linear spring
constant with units of force/distance. In the Hertzian case, Kn is
like a non-linear spring constant with units of force/area, and as
shown in the "(Zhang)"_#Zhang paper, Kn = 4G / (3(1-nu)) where nu =
the Poisson ratio, G = shear modulus = E / (1(1+nu)), and E = Young's
modulus. Thus in the Hertzian case Kn can be set to a value that
like a non-linear spring constant with units of force/area or
pressure, and as shown in the "(Zhang)"_#Zhang paper, Kn = 4G /
(3(1-nu)) where nu = the Poisson ratio, G = shear modulus = E /
(1(1+nu)), and E = Young's modulus. Similarly, Kt = 8G / (2-nu).
Thus in the Hertzian case Kn and Kt can be set to values that
corresponds to properties of the material being modeled. This is also
true in the Hookean case, except that a spring constant must be chosen
that is appropriate for the size of particles in the model. Since
relative particle sizes are not accounted for, the Hookean styles may
not be a suitable model for polydisperse systems.
that is appropriate for the absolute size of particles in the model.
Since relative particle sizes are not accounted for, the Hookean
styles may not be a suitable model for polydisperse systems.
IMPORTANT NOTE: In versions of LAMMPS before 9Jan09, the equation for
Hertzian interactions did not include the sqrt(RiRj/Ri+Rj) term and
thus was not as accurate for polydisperse systems. For monodisperse
systems, sqrt(RiRj/Ri+Rj) is a constant factor that effectively scales
all 4 coefficients: Kn, Kt, gamma_n, gamma_t. Thus you can set the
values of these 4 coefficients appropriately in the current code to
reproduce the results of a previous Hertzian monodisperse calculation.
For example, for the common case of a monodisperse system with
particles of diameter 1, all 4 of these coefficients should now be set
2x larger than they were previously.
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,

2
doc/region.html
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@ -59,7 +59,7 @@
</P>
<PRE>region 1 block -3.0 5.0 INF 10.0 INF INF
region 2 sphere 0.0 0.0 0.0 5 side out
region void cylinder y 2 3 5 -5.0 INF units box
region void cylinder y 2 3 5 -5.0 EDGE units box
region 1 prism 0 10 0 10 0 10 2 0 0
region outside union 4 side1 side2 side3 side4
</PRE>

2
doc/region.txt
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@ -50,7 +50,7 @@ keyword = {side} or {units} :l
region 1 block -3.0 5.0 INF 10.0 INF INF
region 2 sphere 0.0 0.0 0.0 5 side out
region void cylinder y 2 3 5 -5.0 INF units box
region void cylinder y 2 3 5 -5.0 EDGE units box
region 1 prism 0 10 0 10 0 10 2 0 0
region outside union 4 side1 side2 side3 side4 :pre