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rLAMMPS lammps
compute_stress_atom.html
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<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>
<PRE>
compute ID group-ID stress/atom keyword ...
</PRE>
<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
<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>
</UL>
<P><B>
Examples:
</B>
</P>
<PRE>
compute 1 mobile stress/atom
</PRE>
<PRE>
compute 1 all stress/atom pair bond
</PRE>
<P><B>
Description:
</B>
</P>
<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
components: xx, yy, zz, xy, xz, yz. See the
<A
HREF =
"compute_pressure.html"
>
compute
pressure
</A>
command if you want the stress tensor
(pressure) of the entire system. The 6 components can be accessed by
indices 1-6 by any command that uses per-atom computes, e.g. the
<A
HREF =
"dump.html"
>
dump
custom
</A>
command or
<A
HREF =
"fix_ave_spatial.html"
>
fix ave/spatial
</A>
command or
<A
HREF =
"fix_ave_atom.html"
>
fix ave/atom
</A>
command. See
<A
HREF =
"Section_howto.html#4_15"
>
this
section
</A>
for an overview.
</P>
<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:
</P>
<CENTER><IMG
SRC =
"Eqs/stress_tensor.jpg"
>
</CENTER>
<P>
The first term is a kinetic energy contribution for atom
<I>
I
</I>
. The
second term is a pairwise energy contribution where
<I>
n
</I>
loops over the
<I>
Np
</I>
neighbors of atom
<I>
I
</I>
,
<I>
r1
</I>
and
<I>
r2
</I>
are the positions of the 2
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
<I>
I
</I>
is part of. The remaining terms are for the
<I>
Na
</I>
angle,
<I>
Nd
</I>
dihedral, and
<I>
Ni
</I>
improper interactions atom
<I>
I
</I>
is part of.
</P>
<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
the 4 atoms.
</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
listed, only those terms are summed to compute the tensor.
</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
of the per-atom pressure tensor. It is also really a stress-volume
formulation. It would need to be divided by a per-atom volume to have
units of stress, but an individual atom's volume is not 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 3V, where V is the volume of the
system, the result should be -P, where P is the total pressure of the
system.
</P>
<P>
These lines in an input script should yield that result (assuming
there is no fix or long-range contribution to the stress):
</P>
<PRE>
compute global all pressure thermo_temp
compute peratom all stress/atom
compute p all sum peratom
variable p equal div(add(add(c_p
<B>
1
</B>
,c_p
<B>
2
</B>
),c_p
<B>
3
</B>
),mult(3.0,vol))
thermo_style custom step temp etotal c_global v_p
</PRE>
<P>
IMPORTANT NOTE: The per-atom stress does NOT include contributions due
to fixes (e.g.
<A
HREF =
"fix_shake.html"
>
SHAKE
</A>
) or long-range Coulombic
interactions (via the
<A
HREF =
"kspace_style.html"
>
kspace_style
</A>
command). The
former needs to be added to LAMMPS. We're not sure if the latter is
possible to compute. There are also a few pair styles for manybody
potentials that are not yet instrumented to yield per-atom stress.
See the Restrictions below.
</P>
<P><B>
Restrictions:
</B>
</P>
<P>
These pair styles do not yet work with this compute: "airebo", "meam",
and "TIP4P".
</P>
<P><B>
Related commands:
</B>
</P>
<P><A
HREF =
"compute_pe.html"
>
compute pe
</A>
,
<A
HREF =
"compute_stress_atom.html"
>
compute
stress/atom
</A>
</P>
<P><B>
Default:
</B>
none
</P>
</HTML>
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