lammps/doc/compute_stress_atom.txt

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compute stress/atom command :h3

[Syntax:]

compute ID group-ID stress/atom keyword ... :pre

ID, group-ID are documented in "compute"_compute.html command
stress/atom = style name of this compute command
zero or more keywords may be appended
keyword = {ke} or {pair} or {bond} or {angle} or {dihedral} or {improper} or {kspace} or {fix} or {virial} :ul

[Examples:]

compute 1 mobile stress/atom
compute 1 all stress/atom pair bond :pre

[Description:]

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 and is stored as a 6-element vector in the following order:
xx, yy, zz, xy, xz, yz.  See the "compute
pressure"_compute_pressure.html command if you want the stress tensor
(pressure) of the entire system.

The stress tensor for atom {I} is given by the following formula,
where {a} and {b} take on values x,y,z to generate the 6 components of
the symmetric tensor:

:c,image(Eqs/stress_tensor.jpg)

The first term is a kinetic energy contribution for atom {I}.  The
second term is a pairwise energy contribution where {n} loops over the
{Np} neighbors of atom {I}, {r1} and {r2} are the positions of the 2
atoms in the pairwise interaction, and {F1} and {F2} are the forces on
the 2 atoms resulting from the pairwise interaction.  The third term
is a bond contribution of similar form for the {Nb} bonds which atom
{I} is part of.  There are similar terms for the {Na} angle, {Nd}
dihedral, and {Ni} improper interactions atom {I} is part of.  There
is also a term for the KSpace contribution from long-range Coulombic
interactions, if defined.  Finally, there is a term for the {Nf}
"fixes"_fix.html that apply internal constraint forces to atom {I}.
Currently, only the "fix shake"_fix_shake.html and "fix
rigid"_fix_rigid.html commands contribute to this term.

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, or 1/3 of the fix virial due to SHAKE constraints applied
to atoms in a a water molecule via the "fix shake"_fix_shake.html
command.

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.  The
{virial} keyword means include all terms except the kinetic energy
{ke}.

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.

The "dihedral_style charmm"_dihedral_charmm.html style calculates
pairwise interactions between 1-4 atoms.  The virial contribution of
these terms is included in the pair virial, not the dihedral virial.

The KSpace contribution is calculated using the method in
"(Heyes)"_#Heyes for the Ewald method and by the methodology described
in "(Sirk)"_#Sirk for PPPM.  The choice of KSpace solver is specified
by the "kspace_style pppm"_kspace_style.html command.  Note that for
PPPM, the calcluation requires 6 extra FFTs each timestep that
per-atom stress is calculated.  Thus it can significantly increase the
cost of the PPPM calculation if it is needed on a large fraction of
the simulation timesteps.

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, meaning the computed quantity is in units of
pressure*volume.  It would need to be divided by a per-atom volume to
have units of stress (pressure), but an individual atom's volume is
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.

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:

compute		peratom all stress/atom
compute		p all reduce sum c_peratom\[1\] c_peratom\[2\] c_peratom\[3\]
variable	press equal -(c_p\[1\]+c_p\[2\]+c_p\[3\])/(3*vol)
thermo_style	custom step temp etotal press v_press :pre

[Output info:]

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 "Section_howto
15"_Section_howto.html#howto_15 for an overview of LAMMPS output
options.

The per-atom array values will be in pressure*volume
"units"_units.html as discussed above.

[Restrictions:] none

[Related commands:]

"compute pe"_compute_pe.html, "compute pressure"_compute_pressure.html

[Default:] none

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:link(Heyes)
[(Heyes)] Heyes, Phys Rev B 49, 755 (1994),

:link(Sirk)
[(Sirk)] Sirk, Moore, Brown, J Chem Phys, 138, 064505 (2013).