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16
doc/Eqs/stress_tensor.tex
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@ -2,10 +2,16 @@
\begin{document}
$$
S_{ab} = - \left[ m v_a v_b +
\frac{1}{2} \sum_{j = 1}^{N_p} (a_i - a_j) F_{p_{ij}} +
\frac{1}{2} \sum_{j = 1}^{N_b} (a_i - a_j) F_{b_{ij}} \right]
$$
\begin{eqnarray*}
S_{ab} & = & - \left[ m v_a v_b +
\frac{1}{2} \sum_{n = 1}^{N_p} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b}) +
\frac{1}{2} \sum_{n = 1}^{N_b} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b}) +
\frac{1}{3} \sum_{n = 1}^{N_a} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b} +
r_{3_a} F_{3_b}) + \\
&& \frac{1}{4} \sum_{n = 1}^{N_d} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b} +
r_{3_a} F_{3_b} + r_{4_a} F_{4_b}) +
\frac{1}{4} \sum_{n = 1}^{N_i} (r_{1_a} F_{1_b} + r_{2_a} F_{2_b} +
r_{3_a} F_{3_b} + r_{4_a} F_{4_b}) \right]
\end{eqnarray*}
\end{document}

20
doc/Section_commands.html
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@ -318,12 +318,12 @@ of each style or click on the style itself for a full description:
</P>
<DIV ALIGN=center><TABLE BORDER=1 >
<TR ALIGN="center"><TD ><A HREF = "fix_addforce.html">addforce</A></TD><TD ><A HREF = "fix_aveforce.html">aveforce</A></TD><TD ><A HREF = "fix_ave_atom.html">ave/atom</A></TD><TD ><A HREF = "fix_ave_spatial.html">ave/spatial</A></TD><TD ><A HREF = "fix_ave_time.html">ave/time</A></TD><TD ><A HREF = "fix_com.html">com</A></TD><TD ><A HREF = "fix_deform.html">deform</A></TD><TD ><A HREF = "fix_deposit.html">deposit</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "fix_drag.html">drag</A></TD><TD ><A HREF = "fix_dt_reset.html">dt/reset</A></TD><TD ><A HREF = "fix_efield.html">efield</A></TD><TD ><A HREF = "fix_enforce2d.html">enforce2d</A></TD><TD ><A HREF = "fix_freeze.html">freeze</A></TD><TD ><A HREF = "fix_gran_diag.html">gran/diag</A></TD><TD ><A HREF = "fix_gravity.html">gravity</A></TD><TD ><A HREF = "fix_gyration.html">gyration</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "fix_heat.html">heat</A></TD><TD ><A HREF = "fix_indent.html">indent</A></TD><TD ><A HREF = "fix_langevin.html">langevin</A></TD><TD ><A HREF = "fix_lineforce.html">lineforce</A></TD><TD ><A HREF = "fix_msd.html">msd</A></TD><TD ><A HREF = "fix_momentum.html">momentum</A></TD><TD ><A HREF = "fix_nph.html">nph</A></TD><TD ><A HREF = "fix_npt.html">npt</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "fix_npt_asphere.html">npt/asphere</A></TD><TD ><A HREF = "fix_nve.html">nve</A></TD><TD ><A HREF = "fix_nve_asphere.html">nve/asphere</A></TD><TD ><A HREF = "fix_nve_dipole.html">nve/dipole</A></TD><TD ><A HREF = "fix_nve_gran.html">nve/gran</A></TD><TD ><A HREF = "fix_nve_limit.html">nve/limit</A></TD><TD ><A HREF = "fix_nve_noforce.html">nve/noforce</A></TD><TD ><A HREF = "fix_nvt.html">nvt</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "fix_nvt_asphere.html">nvt/asphere</A></TD><TD ><A HREF = "fix_nvt_sllod.html">nvt/sllod</A></TD><TD ><A HREF = "fix_orient_fcc.html">orient/fcc</A></TD><TD ><A HREF = "fix_planeforce.html">planeforce</A></TD><TD ><A HREF = "fix_poems.html">poems</A></TD><TD ><A HREF = "fix_pour.html">pour</A></TD><TD ><A HREF = "fix_print.html">print</A></TD><TD ><A HREF = "fix_rdf.html">rdf</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "fix_recenter.html">recenter</A></TD><TD ><A HREF = "fix_rigid.html">rigid</A></TD><TD ><A HREF = "fix_setforce.html">setforce</A></TD><TD ><A HREF = "fix_shake.html">shake</A></TD><TD ><A HREF = "fix_spring.html">spring</A></TD><TD ><A HREF = "fix_spring_rg.html">spring/rg</A></TD><TD ><A HREF = "fix_spring_self.html">spring/self</A></TD><TD ><A HREF = "fix_temp_rescale.html">temp/rescale</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "fix_tmd.html">tmd</A></TD><TD ><A HREF = "fix_viscosity.html">viscosity</A></TD><TD ><A HREF = "fix_viscous.html">viscous</A></TD><TD ><A HREF = "fix_wall_gran.html">wall/gran</A></TD><TD ><A HREF = "fix_wall_lj126.html">wall/lj126</A></TD><TD ><A HREF = "fix_wall_lj93.html">wall/lj93</A></TD><TD ><A HREF = "fix_wall_reflect.html">wall/reflect</A></TD><TD ><A HREF = "fix_wiggle.html">wiggle</A>
<TR ALIGN="center"><TD ><A HREF = "fix_drag.html">drag</A></TD><TD ><A HREF = "fix_dt_reset.html">dt/reset</A></TD><TD ><A HREF = "fix_efield.html">efield</A></TD><TD ><A HREF = "fix_enforce2d.html">enforce2d</A></TD><TD ><A HREF = "fix_freeze.html">freeze</A></TD><TD ><A HREF = "fix_gravity.html">gravity</A></TD><TD ><A HREF = "fix_gyration.html">gyration</A></TD><TD ><A HREF = "fix_heat.html">heat</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "fix_indent.html">indent</A></TD><TD ><A HREF = "fix_langevin.html">langevin</A></TD><TD ><A HREF = "fix_lineforce.html">lineforce</A></TD><TD ><A HREF = "fix_msd.html">msd</A></TD><TD ><A HREF = "fix_momentum.html">momentum</A></TD><TD ><A HREF = "fix_nph.html">nph</A></TD><TD ><A HREF = "fix_npt.html">npt</A></TD><TD ><A HREF = "fix_npt_asphere.html">npt/asphere</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "fix_nve.html">nve</A></TD><TD ><A HREF = "fix_nve_asphere.html">nve/asphere</A></TD><TD ><A HREF = "fix_nve_dipole.html">nve/dipole</A></TD><TD ><A HREF = "fix_nve_gran.html">nve/gran</A></TD><TD ><A HREF = "fix_nve_limit.html">nve/limit</A></TD><TD ><A HREF = "fix_nve_noforce.html">nve/noforce</A></TD><TD ><A HREF = "fix_nvt.html">nvt</A></TD><TD ><A HREF = "fix_nvt_asphere.html">nvt/asphere</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "fix_nvt_sllod.html">nvt/sllod</A></TD><TD ><A HREF = "fix_orient_fcc.html">orient/fcc</A></TD><TD ><A HREF = "fix_planeforce.html">planeforce</A></TD><TD ><A HREF = "fix_poems.html">poems</A></TD><TD ><A HREF = "fix_pour.html">pour</A></TD><TD ><A HREF = "fix_print.html">print</A></TD><TD ><A HREF = "fix_rdf.html">rdf</A></TD><TD ><A HREF = "fix_recenter.html">recenter</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "fix_rigid.html">rigid</A></TD><TD ><A HREF = "fix_setforce.html">setforce</A></TD><TD ><A HREF = "fix_shake.html">shake</A></TD><TD ><A HREF = "fix_spring.html">spring</A></TD><TD ><A HREF = "fix_spring_rg.html">spring/rg</A></TD><TD ><A HREF = "fix_spring_self.html">spring/self</A></TD><TD ><A HREF = "fix_temp_rescale.html">temp/rescale</A></TD><TD ><A HREF = "fix_tmd.html">tmd</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "fix_viscosity.html">viscosity</A></TD><TD ><A HREF = "fix_viscous.html">viscous</A></TD><TD ><A HREF = "fix_wall_gran.html">wall/gran</A></TD><TD ><A HREF = "fix_wall_lj126.html">wall/lj126</A></TD><TD ><A HREF = "fix_wall_lj93.html">wall/lj93</A></TD><TD ><A HREF = "fix_wall_reflect.html">wall/reflect</A></TD><TD ><A HREF = "fix_wiggle.html">wiggle</A>
</TD></TR></TABLE></DIV>
<HR>
@ -333,10 +333,10 @@ descriptions of each style or click on the style itself for a full
description:
</P>
<DIV ALIGN=center><TABLE BORDER=1 >
<TR ALIGN="center"><TD ><A HREF = "compute_attribute_atom.html">attribute/atom</A></TD><TD ><A HREF = "compute_centro_atom.html">centro/atom</A></TD><TD ><A HREF = "compute_coord_atom.html">coord/atom</A></TD><TD ><A HREF = "compute_ebond_atom.html">ebond/atom</A></TD><TD ><A HREF = "compute_epair_atom.html">epair/atom</A></TD><TD ><A HREF = "compute_ke_atom.html">ke/atom</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "compute_pe.html">pe</A></TD><TD ><A HREF = "compute_pressure.html">pressure</A></TD><TD ><A HREF = "compute_rotate_dipole.html">rotate/dipole</A></TD><TD ><A HREF = "compute_rotate_gran.html">rotate/gran</A></TD><TD ><A HREF = "compute_stress_atom.html">stress/atom</A></TD><TD ><A HREF = "compute_sum.html">sum</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "compute_sum_atom.html">sum/atom</A></TD><TD ><A HREF = "compute_temp.html">temp</A></TD><TD ><A HREF = "compute_temp_asphere.html">temp/asphere</A></TD><TD ><A HREF = "compute_temp_deform.html">temp/deform</A></TD><TD ><A HREF = "compute_temp_dipole.html">temp/dipole</A></TD><TD ><A HREF = "compute_temp_partial.html">temp/partial</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "compute_temp_ramp.html">temp/ramp</A></TD><TD ><A HREF = "compute_temp_region.html">temp/region</A></TD><TD ><A HREF = "compute_variable.html">variable</A></TD><TD ><A HREF = "compute_variable_atom.html">variable/atom</A>
<TR ALIGN="center"><TD ><A HREF = "compute_attribute_atom.html">attribute/atom</A></TD><TD ><A HREF = "compute_centro_atom.html">centro/atom</A></TD><TD ><A HREF = "compute_coord_atom.html">coord/atom</A></TD><TD ><A HREF = "compute_ke_atom.html">ke/atom</A></TD><TD ><A HREF = "compute_pe.html">pe</A></TD><TD ><A HREF = "compute_pe_atom.html">pe/atom</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "compute_pressure.html">pressure</A></TD><TD ><A HREF = "compute_rotate_dipole.html">rotate/dipole</A></TD><TD ><A HREF = "compute_rotate_gran.html">rotate/gran</A></TD><TD ><A HREF = "compute_stress_atom.html">stress/atom</A></TD><TD ><A HREF = "compute_sum.html">sum</A></TD><TD ><A HREF = "compute_sum_atom.html">sum/atom</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "compute_temp.html">temp</A></TD><TD ><A HREF = "compute_temp_asphere.html">temp/asphere</A></TD><TD ><A HREF = "compute_temp_deform.html">temp/deform</A></TD><TD ><A HREF = "compute_temp_dipole.html">temp/dipole</A></TD><TD ><A HREF = "compute_temp_partial.html">temp/partial</A></TD><TD ><A HREF = "compute_temp_ramp.html">temp/ramp</A></TD></TR>
<TR ALIGN="center"><TD ><A HREF = "compute_temp_region.html">temp/region</A></TD><TD ><A HREF = "compute_variable.html">variable</A></TD><TD ><A HREF = "compute_variable_atom.html">variable/atom</A>
</TD></TR></TABLE></DIV>
<P>These are compute styles contributed by users, which can be used if

3
doc/compute.html
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@ -93,10 +93,9 @@ defined in LAMMPS:
<UL><LI><A HREF = "compute_attribute_atom.html">attribute/atom</A> - attribute (x,v,f,etc) of each atom
<LI><A HREF = "compute_centro_atom.html">centro/atom</A> - centro-symmetry parameter for each atom
<LI><A HREF = "compute_coord_atom.html">coord/atom</A> - coordination number for each atom
<LI><A HREF = "compute_ebond_atom.html">ebond/atom</A> - bond energy for each atom
<LI><A HREF = "compute_epair_atom.html">epair/atom</A> - pairwise energy for each atom
<LI><A HREF = "compute_ke_atom.html">ke/atom</A> - kinetic energy for each atom
<LI><A HREF = "compute_pe.html">pe</A> - potential energy
<LI><A HREF = "compute_pe.html">pe</A> - potential energy for each atom
<LI><A HREF = "compute_pressure.html">pressure</A> - total pressure and pressure tensor
<LI><A HREF = "compute_rotate_dipole.html">rotate/dipole</A> - rotational energy of dipolar atoms
<LI><A HREF = "compute_rotate_gran.html">rotate/gran</A> - rotational energy of granular atoms

9
doc/compute_pe.html
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@ -23,14 +23,13 @@
<P><B>Examples:</B>
</P>
<PRE>compute 1 all pe
compute molPE all bond angle dihedral improper
compute molPE all pe bond angle dihedral improper
</PRE>
<P><B>Description:</B>
</P>
<P>Define a computation that calculates the potential energy of the
entire system of atoms. The specified group must be "all". See the
<A HREF = "compute_epair_atom.html">compute epair/atom</A> and <A HREF = "compute_ebond_atom.html">compute
ebond/atom</A> commands if you want per-atom
<A HREF = "compute_pe_atom.html">compute pe/atom</A> command if you want per-atom
energies. These per-atom values could be summed for a group of atoms
via the <A HREF = "compute_sum.html">compute sum</A> command.
</P>
@ -57,7 +56,9 @@ LAMMPS starts up, as if this command were in the input script:
</P>
<P><B>Restrictions:</B> none
</P>
<P><B>Related commands:</B> none
<P><B>Related commands:</B>
</P>
<P><A HREF = "compute_pe_atom.html">compute pe/atom</A>
</P>
<P><B>Default:</B> none
</P>

9
doc/compute_pe.txt
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@ -20,14 +20,13 @@ keyword = {pair} or {bond} or {angle} or {dihedral} or {improper} or {kspace} :u
[Examples:]
compute 1 all pe
compute molPE all bond angle dihedral improper :pre
compute molPE all pe bond angle dihedral improper :pre
[Description:]
Define a computation that calculates the potential energy of the
entire system of atoms. The specified group must be "all". See the
"compute epair/atom"_compute_epair_atom.html and "compute
ebond/atom"_compute_ebond_atom.html commands if you want per-atom
"compute pe/atom"_compute_pe_atom.html command if you want per-atom
energies. These per-atom values could be summed for a group of atoms
via the "compute sum"_compute_sum.html command.
@ -54,6 +53,8 @@ See the "thermo_style" command for more details.
[Restrictions:] none
[Related commands:] none
[Related commands:]
"compute pe/atom"_compute_pe_atom.html
[Default:] none

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doc/compute_pressure.html
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@ -13,15 +13,18 @@
</H3>
<P><B>Syntax:</B>
</P>
<PRE>compute ID group-ID pressure compute-ID
<PRE>compute ID group-ID pressure temp-ID keyword ...
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "compute.html">compute</A> command
<LI>pressure = style name of this compute command
<LI>compute-ID = ID of compute that calculates temperature
<LI>temp-ID = ID of compute that calculates temperature
<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> or <I>kspace</I> or <I>fix</I>
</UL>
<P><B>Examples:</B>
</P>
<PRE>compute 1 all pressure myTemp
compute 1 all pressure thermo_temp pair bond
</PRE>
<P><B>Description:</B>
</P>
@ -39,26 +42,35 @@ of atoms via the <A HREF = "compute_sum.html">compute sum</A> command.
below), Kb is the Boltzmann constant, T is the temperature, d is the
dimensionality of the system (2 or 3 for 2d/3d), V is the system
volume (or area in 2d), and the second term is the virial, computed
within LAMMPS for all pairwise as well as 2-body, 3-body, 4-body, and
long-range interactions. <A HREF = "fix.html">Fixes</A> that impose constraints
within LAMMPS for all pairwise as well as 2-body, 3-body, and 4-body,
and long-range interactions. <A HREF = "fix.html">Fixes</A> that impose constraints
(e.g. the <A HREF = "fix_shake.html">fix shake</A> command) also contribute to the
virial term.
</P>
<P>A 6-component pressure tensor is also calculated by this compute which
can be output by the <A HREF = "thermo_style.html">thermo_style custom</A> command.
The formula for the components of the tensor is the same as in above
formula, except that the first term uses the components of the kinetic
energy tensor (vx * vy instead of v^2 for temperature) and the second
term uses Rx * Fy for the Wxy component of the virial tensor, etc.
<P>A 6-component pressure tensor is also calculated by this compute whose
componenents can be output by the <A HREF = "thermo_style.html">thermo_style
custom</A> command or accessed by other
<A HREF = "compute.html">compute</A> and <A HREF = "fix.html">fix</A> commands. The equation for
the components of the tensor is the same as in above formula, except
that the first term uses the components of the kinetic energy tensor
(vx * vy instead of v^2 for temperature) and the second term uses Rx *
Fy for the Wxy component of the virial tensor, etc.
</P>
<P>If no extra keywords are listed, the entire equation above is
calculated which includes a temperature term (or kinetic energy
tensor) and the virial as the sum of pair, bond, angle, dihedral,
improper, kspace (long-range), and fix contributions. If any extra
keywords are listed, then only those components are summed to compute
ke and/or the virial.
</P>
<P>The temperature and kinetic energy tensor is not calculated by this
compute, but rather by the temperature compute specified as the last
argument of the command. Normally this compute should calculate the
temperature of all atoms for consistency with the virial term, but any
compute style that calculates temperature can be used, e.g. one that
excludes frozen atoms or other degrees of freedom.
compute, but rather by the temperature compute specified with the
command. Normally this compute should calculate the temperature of
all atoms for consistency with the virial term, but any compute style
that calculates temperature can be used, e.g. one that excludes frozen
atoms or other degrees of freedom.
</P>
<P>Note that the N is the above formula is really degrees-of-freedom/d
<P>Note that the N is the above formula is really degrees-of-freedom
where the DOF is specified by the temperature compute. See the
various <A HREF = "compute.html">compute temperature</A> styles for details.
</P>
@ -74,7 +86,9 @@ LAMMPS starts up, as if this command were in the input script:
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "compute_temp.html">compute temp</A>, <A HREF = "themo_style.html">thermo_style</A>
<P><A HREF = "compute_temp.html">compute temp</A>, <A HREF = "compute_stress_atom.html">compute
stress/atom</A>,
<A HREF = "themo_style.html">thermo_style</A>,
</P>
<P><B>Default:</B> none
</P>

50
doc/compute_pressure.txt
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@ -10,15 +10,18 @@ compute pressure command :h3
[Syntax:]
compute ID group-ID pressure compute-ID :pre
compute ID group-ID pressure temp-ID keyword ... :pre
ID, group-ID are documented in "compute"_compute.html command
pressure = style name of this compute command
compute-ID = ID of compute that calculates temperature :ul
temp-ID = ID of compute that calculates temperature
zero or more keywords may be appended
keyword = {ke} or {pair} or {bond} or {angle} or {dihedral} or {improper} or {kspace} or {fix} :ul
[Examples:]
compute 1 all pressure myTemp :pre
compute 1 all pressure myTemp
compute 1 all pressure thermo_temp pair bond :pre
[Description:]
@ -36,26 +39,35 @@ where N is the number of atoms in the system (see discussion of DOF
below), Kb is the Boltzmann constant, T is the temperature, d is the
dimensionality of the system (2 or 3 for 2d/3d), V is the system
volume (or area in 2d), and the second term is the virial, computed
within LAMMPS for all pairwise as well as 2-body, 3-body, 4-body, and
long-range interactions. "Fixes"_fix.html that impose constraints
within LAMMPS for all pairwise as well as 2-body, 3-body, and 4-body,
and long-range interactions. "Fixes"_fix.html that impose constraints
(e.g. the "fix shake"_fix_shake.html command) also contribute to the
virial term.
A 6-component pressure tensor is also calculated by this compute which
can be output by the "thermo_style custom"_thermo_style.html command.
The formula for the components of the tensor is the same as in above
formula, except that the first term uses the components of the kinetic
energy tensor (vx * vy instead of v^2 for temperature) and the second
term uses Rx * Fy for the Wxy component of the virial tensor, etc.
A 6-component pressure tensor is also calculated by this compute whose
componenents can be output by the "thermo_style
custom"_thermo_style.html command or accessed by other
"compute"_compute.html and "fix"_fix.html commands. The equation for
the components of the tensor is the same as in above formula, except
that the first term uses the components of the kinetic energy tensor
(vx * vy instead of v^2 for temperature) and the second term uses Rx *
Fy for the Wxy component of the virial tensor, etc.
If no extra keywords are listed, the entire equation above is
calculated which includes a temperature term (or kinetic energy
tensor) and the virial as the sum of pair, bond, angle, dihedral,
improper, kspace (long-range), and fix contributions. If any extra
keywords are listed, then only those components are summed to compute
ke and/or the virial.
The temperature and kinetic energy tensor is not calculated by this
compute, but rather by the temperature compute specified as the last
argument of the command. Normally this compute should calculate the
temperature of all atoms for consistency with the virial term, but any
compute style that calculates temperature can be used, e.g. one that
excludes frozen atoms or other degrees of freedom.
compute, but rather by the temperature compute specified with the
command. Normally this compute should calculate the temperature of
all atoms for consistency with the virial term, but any compute style
that calculates temperature can be used, e.g. one that excludes frozen
atoms or other degrees of freedom.
Note that the N is the above formula is really degrees-of-freedom/d
Note that the N is the above formula is really degrees-of-freedom
where the DOF is specified by the temperature compute. See the
various "compute temperature"_compute.html styles for details.
@ -71,6 +83,8 @@ where "thermo_temp" is the ID of a similarly defined compute of style
[Related commands:]
"compute temp"_compute_temp.html, "thermo_style"_themo_style.html
"compute temp"_compute_temp.html, "compute
stress/atom"_compute_stress_atom.html,
"thermo_style"_themo_style.html,
[Default:] none

126
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@ -13,97 +13,99 @@
</H3>
<P><B>Syntax:</B>
</P>
<PRE>compute ID group-ID stress/atom keyword value ...
<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 keyword/arg pairs may be appended
<LI>keyword = <I>ke</I> or <I>pair</I> or <I>bond</I>
<PRE> <I>ke</I> arg = <I>yes</I> or <I>no</I>
yes/no = include/exclude kinetic energy contribution to stress
<I>pair</I> arg = <I>yes</I> or <I>no</I>
yes/no = include/exclude pairwise energy contribution to stress
<I>bond</I> arg = <I>yes</I> or <I>no</I>
yes/no = include/exclude bond energy contribution to stress
</PRE>
<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 ke no
<PRE>compute 1 all stress/atom pair bond
</PRE>
<P><B>Description:</B>
</P>
<P>Define a computation that computes the per-atom stress tensor for each
atom in a group. The tensor for each atom has 6 components: xx, yy,
zz, xy, xz, yz. The resulting values can be accessed by indices 1-6
by any command that uses per-atom computes, e.g. the <A HREF = "dump.html">dump
<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.
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 each atom is the sum of 3 terms in the following
formula. Any of the terms can be excluded by setting the <I>ke</I>,
<I>pair</I>, or <I>bond</I> keywords to <I>no</I>. The ab component of stress on
atom <I>I</I> is as follows, where <I>a</I> and <I>b</I> take on values x,y,z to
generate the 6 components of the symmetric tensor:
<P>The stress tensor for each atom is given by the following formula.
where the ab component of stress on atom <I>I</I> is as shown 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>J</I> loops over the
<I>Np</I> neighbors of atom <I>I</I>, and <I>Fp</I> is one of 3 components of force
on atom <I>I</I> due to the pairwise interaction with atom <I>J</I>. The third
term is a bond energy contribution where <I>J</I> loops over the <I>Nb</I> bonds
which atom <I>I</I> is part of, and <I>Fb</I> is one of 3 components of force on
atom <I>I</I> due to the bonded interaction with atom <I>J</I>.
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, and <I>F1</I> and <I>F2</I> are the forces on the 2 atoms. The third
term is a bond contribution for the <I>Nb</I> bonds whihc atom <I>I</I> is part
of. And similarly 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>If two atoms interact, either pairwise or in a bond, and only one of
them is in the compute group, the interaction is included in the
per-atom stress of the atom in the group.
<P>As the formula implies, 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>For force fields that include a contribution to the pairwise
interaction that is computed as part of dihedral terms (i.e. 1-4
interactions), this contribution is NOT included in the per-atom
pairwise stress.
<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>IMPORTANT NOTE: The per-atom stress does NOT include contributions due
to angles, dihedrals, impropers that the atom is part of, or a
long-range Coulombic contribution. Currently, there is no way in
LAMMPS to calculate per-atom stress from angles, dihedrals, improper,
or long-range interactions.
<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>Note that as defined above, per-atom stress is the negative of the
per-atom pressure tensor. It is also really a stress-volume
<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. Thus, if you sum the diagonal components
of the per-atom stress tensor for all atoms in the system and divide
the sum by 3V, where V is the volume of the system, you should get -P,
where P is the total pressure of the system (assuming there is no
angle, dihedral, improper, or long-range contribution to the total
pressure).
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>Computation of per-atom stress tensor components requires a loop thru
the pairwise and bond neighbor lists and inter-processor
communication, so it can be inefficient to compute/dump this quantity
too frequently or to have multiple compute/dump commands, each of a
<I>stress/atom</I> style.
<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>Some pair potentials do not allow the calculation of per-atom stress
via this command. An error will be generated if this is the case.
<P>These pair styles do not yet work with this compute: "airebo", "meam",
and "TIP4P".
</P>
<P><B>Related commands:</B> none
<P><B>Related commands:</B>
</P>
<P><B>Default:</B>
<P><A HREF = "compute_pe.html">compute pe</A>, <A HREF = "compute_stress_atom.html">compute
stress/atom</A>
</P>
<P>The option defaults are ke = yes, pair = yes, bond = yes.
<P><B>Default:</B> none
</P>
</HTML>

125
doc/compute_stress_atom.txt
View File

@ -10,89 +10,96 @@ compute stress/atom command :h3
[Syntax:]
compute ID group-ID stress/atom keyword value ... :pre
compute ID group-ID stress/atom keyword ... :pre
ID, group-ID are documented in "compute"_compute.html command :ulb,l
stress/atom = style name of this compute command :l
zero or more keyword/arg pairs may be appended :l
keyword = {ke} or {pair} or {bond} :l
{ke} arg = {yes} or {no}
yes/no = include/exclude kinetic energy contribution to stress
{pair} arg = {yes} or {no}
yes/no = include/exclude pairwise energy contribution to stress
{bond} arg = {yes} or {no}
yes/no = include/exclude bond energy contribution to stress :pre
:ule
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} :ul
[Examples:]
compute 1 mobile stress/atom :pre
compute 1 all stress/atom ke no :pre
compute 1 all stress/atom pair bond :pre
[Description:]
Define a computation that computes the per-atom stress tensor for each
atom in a group. The tensor for each atom has 6 components: xx, yy,
zz, xy, xz, yz. The resulting values can be accessed by indices 1-6
by any command that uses per-atom computes, e.g. the "dump
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 "compute
pressure"_compute_pressure.html 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 "dump
custom"_dump.html command or "fix ave/spatial"_fix_ave_spatial.html
command or "fix ave/atom"_fix_ave_atom.html command.
command or "fix ave/atom"_fix_ave_atom.html command. See "this
section"_Section_howto.html#4_15 for an overview.
The stress tensor for each atom is the sum of 3 terms in the following
formula. Any of the terms can be excluded by setting the {ke},
{pair}, or {bond} keywords to {no}. The ab component of stress on
atom {I} is as follows, where {a} and {b} take on values x,y,z to
generate the 6 components of the symmetric tensor:
The stress tensor for each atom is given by the following formula.
where the ab component of stress on atom {I} is as shown 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 {J} loops over the
{Np} neighbors of atom {I}, and {Fp} is one of 3 components of force
on atom {I} due to the pairwise interaction with atom {J}. The third
term is a bond energy contribution where {J} loops over the {Nb} bonds
which atom {I} is part of, and {Fb} is one of 3 components of force on
atom {I} due to the bonded interaction with atom {J}.
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, and {F1} and {F2} are the forces on the 2 atoms. The third
term is a bond contribution for the {Nb} bonds whihc atom {I} is part
of. And similarly for the {Na} angle, {Nd} dihedral, and {Ni}
improper interactions atom {I} is part of.
If two atoms interact, either pairwise or in a bond, and only one of
them is in the compute group, the interaction is included in the
per-atom stress of the atom in the group.
As the formula implies, 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.
For force fields that include a contribution to the pairwise
interaction that is computed as part of dihedral terms (i.e. 1-4
interactions), this contribution is NOT included in the per-atom
pairwise stress.
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.
IMPORTANT NOTE: The per-atom stress does NOT include contributions due
to angles, dihedrals, impropers that the atom is part of, or a
long-range Coulombic contribution. Currently, there is no way in
LAMMPS to calculate per-atom stress from angles, dihedrals, improper,
or long-range interactions.
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.
Note that as defined above, per-atom stress is the negative of the
per-atom pressure tensor. It is also really a stress-volume
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.
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. Thus, if you sum the diagonal components
of the per-atom stress tensor for all atoms in the system and divide
the sum by 3V, where V is the volume of the system, you should get -P,
where P is the total pressure of the system (assuming there is no
angle, dihedral, improper, or long-range contribution to the total
pressure).
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.
Computation of per-atom stress tensor components requires a loop thru
the pairwise and bond neighbor lists and inter-processor
communication, so it can be inefficient to compute/dump this quantity
too frequently or to have multiple compute/dump commands, each of a
{stress/atom} style.
These lines in an input script should yield that result (assuming
there is no fix or long-range contribution to the stress):
compute global all pressure thermo_temp
compute peratom all stress/atom
compute p all sum peratom
variable p equal div(add(add(c_p[1],c_p[2]),c_p[3]),mult(3.0,vol))
thermo_style custom step temp etotal c_global v_p :pre
IMPORTANT NOTE: The per-atom stress does NOT include contributions due
to fixes (e.g. "SHAKE"_fix_shake.html) or long-range Coulombic
interactions (via the "kspace_style"_kspace_style.html 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.
[Restrictions:]
Some pair potentials do not allow the calculation of per-atom stress
via this command. An error will be generated if this is the case.
These pair styles do not yet work with this compute: "airebo", "meam",
and "TIP4P".
[Related commands:] none
[Related commands:]
[Default:]
"compute pe"_compute_pe.html, "compute
stress/atom"_compute_stress_atom.html
The option defaults are ke = yes, pair = yes, bond = yes.
[Default:] none

1
doc/fix.html
View File

@ -94,7 +94,6 @@ for individual fixes for info on which ones can be restarted.
<LI><A HREF = "fix_efield.html">efield</A> - impose electric field on system
<LI><A HREF = "fix_enforce2d.html">enforce2d</A> - zero out z-dimension velocity and force
<LI><A HREF = "fix_freeze.html">freeze</A> - freeze atoms in a granular simulation
<LI><A HREF = "fix_gran_diag.html">gran/diag</A> - compute granular diagnostics
<LI><A HREF = "fix_gravity.html">gravity</A> - add gravity to atoms in a granular simulation
<LI><A HREF = "fix_gyration.html">gyration</A> - compute radius of gyration
<LI><A HREF = "fix_heat.html">heat</A> - add/subtract momentum-conserving heat