2007-02-10 05:40:32 +08:00
|
|
|
<HTML>
|
|
|
|
|
<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>
|
|
|
|
|
</CENTER>
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<HR>
|
|
|
|
|
|
|
|
|
|
<H3>compute stress/atom command
|
|
|
|
|
</H3>
|
|
|
|
|
<P><B>Syntax:</B>
|
|
|
|
|
</P>
|
2007-12-01 07:16:45 +08:00
|
|
|
<PRE>compute ID group-ID stress/atom keyword ...
|
2007-02-10 05:40:32 +08:00
|
|
|
</PRE>
|
2007-12-01 07:16:45 +08:00
|
|
|
<UL><LI>ID, group-ID are documented in <A HREF = "compute.html">compute</A> command
|
|
|
|
|
<LI>stress/atom = style name of this compute command
|
|
|
|
|
<LI>zero or more keywords may be appended
|
2009-03-06 05:17:05 +08:00
|
|
|
<LI>keyword = <I>ke</I> or <I>pair</I> or <I>bond</I> or <I>angle</I> or <I>dihedral</I> or <I>improper</I> or <I>fix</I> or <I>virial</I>
|
2007-02-10 05:40:32 +08:00
|
|
|
</UL>
|
|
|
|
|
<P><B>Examples:</B>
|
|
|
|
|
</P>
|
2008-02-07 23:17:25 +08:00
|
|
|
<PRE>compute 1 mobile stress/atom
|
|
|
|
|
compute 1 all stress/atom pair bond
|
2007-07-03 03:59:42 +08:00
|
|
|
</PRE>
|
2007-02-10 05:40:32 +08:00
|
|
|
<P><B>Description:</B>
|
|
|
|
|
</P>
|
2007-12-01 07:16:45 +08:00
|
|
|
<P>Define a computation that computes the symmetric per-atom stress
|
|
|
|
|
tensor for each atom in a group. The tensor for each atom has 6
|
2009-12-04 07:58:11 +08:00
|
|
|
components and is stored as a 6-element vector in the following order:
|
|
|
|
|
xx, yy, zz, xy, xz, yz. See the <A HREF = "compute_pressure.html">compute
|
2007-12-01 07:16:45 +08:00
|
|
|
pressure</A> command if you want the stress tensor
|
2009-12-04 07:58:11 +08:00
|
|
|
(pressure) of the entire system.
|
2007-02-10 05:40:32 +08:00
|
|
|
</P>
|
2007-12-01 07:36:27 +08:00
|
|
|
<P>The stress tensor for atom <I>I</I> is given by the following formula,
|
|
|
|
|
where <I>a</I> and <I>b</I> take on values x,y,z to generate the 6 components of
|
|
|
|
|
the symmetric tensor:
|
2007-02-10 05:40:32 +08:00
|
|
|
</P>
|
|
|
|
|
<CENTER><IMG SRC = "Eqs/stress_tensor.jpg">
|
|
|
|
|
</CENTER>
|
2007-07-03 03:59:42 +08:00
|
|
|
<P>The first term is a kinetic energy contribution for atom <I>I</I>. The
|
2007-12-01 07:36:27 +08:00
|
|
|
second term is a pairwise energy contribution where <I>n</I> loops over the
|
2007-12-01 07:16:45 +08:00
|
|
|
<I>Np</I> neighbors of atom <I>I</I>, <I>r1</I> and <I>r2</I> are the positions of the 2
|
2007-12-01 07:36:27 +08:00
|
|
|
atoms in the pairwise interaction, and <I>F1</I> and <I>F2</I> are the forces on
|
|
|
|
|
the 2 atoms resulting from the pairwise interaction. The third term
|
|
|
|
|
is a bond contribution of similar form for the <I>Nb</I> bonds which atom
|
2008-01-10 05:57:06 +08:00
|
|
|
<I>I</I> is part of. There are similar terms for the <I>Na</I> angle, <I>Nd</I>
|
2007-12-01 07:36:27 +08:00
|
|
|
dihedral, and <I>Ni</I> improper interactions atom <I>I</I> is part of.
|
2008-01-10 05:57:06 +08:00
|
|
|
Finally, there is a term for the <I>Nf</I> <A HREF = "fix.html">fixes</A> that apply
|
|
|
|
|
internal constraint forces to atom <I>I</I>. Currently, only the <A HREF = "fix_shake.html">fix
|
|
|
|
|
shake</A> and <A HREF = "fix_rigid.html">fix rigid</A> commands
|
|
|
|
|
contribute to this term.
|
2007-12-01 07:16:45 +08:00
|
|
|
</P>
|
2007-12-01 07:36:27 +08:00
|
|
|
<P>As the coefficients in the formula imply, a virial contribution
|
|
|
|
|
produced by a small set of atoms (e.g. 4 atoms in a dihedral or 3
|
|
|
|
|
atoms in a Tersoff 3-body interaction) is assigned in equal portions
|
|
|
|
|
to each atom in the set. E.g. 1/4 of the dihedral virial to each of
|
2008-01-10 05:57:06 +08:00
|
|
|
the 4 atoms, or 1/3 of the fix virial due to SHAKE constraints applied
|
|
|
|
|
to atoms in a a water molecule via the <A HREF = "fix_shake.html">fix shake</A>
|
|
|
|
|
command.
|
2007-12-01 07:16:45 +08:00
|
|
|
</P>
|
|
|
|
|
<P>If no extra keywords are listed, all of the terms in this formula are
|
|
|
|
|
included in the per-atom stress tensor. If any extra keywords are
|
2009-03-06 05:17:05 +08:00
|
|
|
listed, only those terms are summed to compute the tensor. The
|
|
|
|
|
<I>virial</I> keyword means include all terms except the kinetic energy
|
|
|
|
|
<I>ke</I>.
|
2007-12-01 07:16:45 +08:00
|
|
|
</P>
|
|
|
|
|
<P>Note that the stress for each atom is due to its interaction with all
|
|
|
|
|
other atoms in the simulation, not just with other atoms in the group.
|
|
|
|
|
</P>
|
|
|
|
|
<P>The <A HREF = "dihedral_charmm.html">dihedral_style charmm</A> style calculates
|
|
|
|
|
pairwise interactions between 1-4 atoms. The virial contribution of
|
|
|
|
|
these terms is included in the pair virial, not the dihedral virial.
|
|
|
|
|
</P>
|
|
|
|
|
<P>Note that as defined in the formula, per-atom stress is the negative
|
2010-01-24 08:08:59 +08:00
|
|
|
of the per-atom pressure tensor. It is also really a stress*volume
|
2008-02-07 23:17:25 +08:00
|
|
|
formulation, meaning the computed quantity is in units of
|
2010-01-24 08:08:59 +08:00
|
|
|
pressure*volume. It would need to be divided by a per-atom volume to
|
2008-02-07 23:17:25 +08:00
|
|
|
have units of stress (pressure), but an individual atom's volume is
|
2010-01-24 07:33:43 +08:00
|
|
|
not well defined or easy to compute in a deformed solid or a liquid.
|
|
|
|
|
Thus, if the diagonal components of the per-atom stress tensor are
|
|
|
|
|
summed for all atoms in the system and the sum is divided by dV, where
|
|
|
|
|
d = dimension and V is the volume of the system, the result should be
|
|
|
|
|
-P, where P is the total pressure of the system.
|
2007-12-01 07:16:45 +08:00
|
|
|
</P>
|
2009-03-04 01:19:44 +08:00
|
|
|
<P>These lines in an input script for a 3d system should yield that
|
|
|
|
|
result. I.e. the last 2 columns of thermo output will be the same:
|
2007-12-01 07:16:45 +08:00
|
|
|
</P>
|
2008-01-04 03:03:15 +08:00
|
|
|
<PRE>compute peratom all stress/atom
|
2008-06-18 21:47:22 +08:00
|
|
|
compute p all reduce sum c_peratom[1] c_peratom[2] c_peratom[3]
|
2008-01-17 03:17:20 +08:00
|
|
|
variable press equal -(c_p[1]+c_p[2]+c_p[3])/(3*vol)
|
2008-01-04 03:03:15 +08:00
|
|
|
thermo_style custom step temp etotal press v_press
|
2007-12-01 07:16:45 +08:00
|
|
|
</PRE>
|
|
|
|
|
<P>IMPORTANT NOTE: The per-atom stress does NOT include contributions due
|
2008-01-10 05:57:06 +08:00
|
|
|
to long-range Coulombic interactions (via the
|
2008-01-10 05:59:42 +08:00
|
|
|
<A HREF = "kspace_style.html">kspace_style</A> command). It's not clear this
|
2008-02-07 23:17:25 +08:00
|
|
|
contribution can easily be computed.
|
2007-07-03 03:59:42 +08:00
|
|
|
</P>
|
2008-01-04 08:56:10 +08:00
|
|
|
<P><B>Output info:</B>
|
|
|
|
|
</P>
|
2009-12-05 05:04:00 +08:00
|
|
|
<P>This compute calculates a per-atom array with 6 columns, which can be
|
|
|
|
|
accessed by indices 1-6 by any command that uses per-atom values from
|
|
|
|
|
a compute as input. See <A HREF = "Section_howto.html#4_15">this section</A> for an
|
|
|
|
|
overview of LAMMPS output options.
|
2008-01-04 08:56:10 +08:00
|
|
|
</P>
|
2010-01-24 07:33:43 +08:00
|
|
|
<P>The per-atom array values will be in pressure*volume
|
|
|
|
|
<A HREF = "units.html">units</A> as discussed above.
|
2010-01-24 07:20:05 +08:00
|
|
|
</P>
|
2008-02-07 23:17:25 +08:00
|
|
|
<P><B>Restrictions:</B> none
|
2007-02-10 05:40:32 +08:00
|
|
|
</P>
|
2007-12-01 07:16:45 +08:00
|
|
|
<P><B>Related commands:</B>
|
2007-02-10 05:40:32 +08:00
|
|
|
</P>
|
2009-03-04 01:03:38 +08:00
|
|
|
<P><A HREF = "compute_pe.html">compute pe</A>, <A HREF = "compute_pressure.html">compute pressure</A>
|
2007-07-03 03:59:42 +08:00
|
|
|
</P>
|
2007-12-01 07:16:45 +08:00
|
|
|
<P><B>Default:</B> none
|
2007-02-10 05:40:32 +08:00
|
|
|
</P>
|
|
|
|
|
</HTML>
|
