forked from lijiext/lammps
129 lines
5.1 KiB
Plaintext
129 lines
5.1 KiB
Plaintext
"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
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:link(lws,http://lammps.sandia.gov)
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:link(ld,Manual.html)
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:link(lc,Section_commands.html#comm)
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:line
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compute stress/atom command :h3
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[Syntax:]
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compute ID group-ID stress/atom keyword ... :pre
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ID, group-ID are documented in "compute"_compute.html command
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stress/atom = style name of this compute command
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zero or more keywords may be appended
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keyword = {ke} or {pair} or {bond} or {angle} or {dihedral} or {improper} or {kspace} or {fix} or {virial} :ul
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[Examples:]
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compute 1 mobile stress/atom
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compute 1 all stress/atom pair bond :pre
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[Description:]
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Define a computation that computes the symmetric per-atom stress
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tensor for each atom in a group. The tensor for each atom has 6
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components and is stored as a 6-element vector in the following order:
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xx, yy, zz, xy, xz, yz. See the "compute
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pressure"_compute_pressure.html command if you want the stress tensor
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(pressure) of the entire system.
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The stress tensor for atom {I} is given by the following formula,
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where {a} and {b} take on values x,y,z to generate the 6 components of
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the symmetric tensor:
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:c,image(Eqs/stress_tensor.jpg)
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The first term is a kinetic energy contribution for atom {I}. The
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second term is a pairwise energy contribution where {n} loops over the
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{Np} neighbors of atom {I}, {r1} and {r2} are the positions of the 2
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atoms in the pairwise interaction, and {F1} and {F2} are the forces on
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the 2 atoms resulting from the pairwise interaction. The third term
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is a bond contribution of similar form for the {Nb} bonds which atom
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{I} is part of. There are similar terms for the {Na} angle, {Nd}
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dihedral, and {Ni} improper interactions atom {I} is part of. There
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is also a term for the KSpace contribution from long-range Coulombic
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interactions, if defined. Finally, there is a term for the {Nf}
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"fixes"_fix.html that apply internal constraint forces to atom {I}.
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Currently, only the "fix shake"_fix_shake.html and "fix
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rigid"_fix_rigid.html commands contribute to this term.
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As the coefficients in the formula imply, a virial contribution
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produced by a small set of atoms (e.g. 4 atoms in a dihedral or 3
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atoms in a Tersoff 3-body interaction) is assigned in equal portions
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to each atom in the set. E.g. 1/4 of the dihedral virial to each of
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the 4 atoms, or 1/3 of the fix virial due to SHAKE constraints applied
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to atoms in a a water molecule via the "fix shake"_fix_shake.html
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command.
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If no extra keywords are listed, all of the terms in this formula are
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included in the per-atom stress tensor. If any extra keywords are
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listed, only those terms are summed to compute the tensor. The
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{virial} keyword means include all terms except the kinetic energy
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{ke}.
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Note that the stress for each atom is due to its interaction with all
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other atoms in the simulation, not just with other atoms in the group.
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The "dihedral_style charmm"_dihedral_charmm.html style calculates
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pairwise interactions between 1-4 atoms. The virial contribution of
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these terms is included in the pair virial, not the dihedral virial.
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The KSpace contribution is calculated using the method in
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"(Heyes)"_#Heyes for the Ewald method and by the methodology described
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in "(Sirk)"_#Sirk for PPPM. The choice of KSpace solver is specified
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by the "kspace_style pppm"_kspace_style.html command. Note that for
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PPPM, the calcluation requires 6 extra FFTs each timestep that
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per-atom stress is calculated. Thus it can significantly increase the
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cost of the PPPM calculation if it is needed on a large fraction of
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the simulation timesteps.
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Note that as defined in the formula, per-atom stress is the negative
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of the per-atom pressure tensor. It is also really a stress*volume
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formulation, meaning the computed quantity is in units of
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pressure*volume. It would need to be divided by a per-atom volume to
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have units of stress (pressure), but an individual atom's volume is
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not well defined or easy to compute in a deformed solid or a liquid.
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Thus, if the diagonal components of the per-atom stress tensor are
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summed for all atoms in the system and the sum is divided by dV, where
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d = dimension and V is the volume of the system, the result should be
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-P, where P is the total pressure of the system.
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These lines in an input script for a 3d system should yield that
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result. I.e. the last 2 columns of thermo output will be the same:
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compute peratom all stress/atom
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compute p all reduce sum c_peratom\[1\] c_peratom\[2\] c_peratom\[3\]
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variable press equal -(c_p\[1\]+c_p\[2\]+c_p\[3\])/(3*vol)
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thermo_style custom step temp etotal press v_press :pre
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[Output info:]
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This compute calculates a per-atom array with 6 columns, which can be
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accessed by indices 1-6 by any command that uses per-atom values from
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a compute as input. See "Section_howto
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15"_Section_howto.html#howto_15 for an overview of LAMMPS output
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options.
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The per-atom array values will be in pressure*volume
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"units"_units.html as discussed above.
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[Restrictions:] none
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[Related commands:]
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"compute pe"_compute_pe.html, "compute pressure"_compute_pressure.html
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[Default:] none
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:line
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:link(Heyes)
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[(Heyes)] Heyes, Phys Rev B 49, 755 (1994),
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:link(Sirk)
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[(Sirk)] Sirk, Moore, Brown, J Chem Phys, 138, 064505 (2013).
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