2007-02-10 05:40:32 +08:00
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<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>
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<HR>
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<H3>compute stress/atom command
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</H3>
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<P><B>Syntax:</B>
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</P>
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2007-12-01 07:16:45 +08:00
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<PRE>compute ID group-ID stress/atom keyword ...
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2007-02-10 05:40:32 +08:00
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</PRE>
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2007-12-01 07:16:45 +08:00
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<UL><LI>ID, group-ID are documented in <A HREF = "compute.html">compute</A> command
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<LI>stress/atom = style name of this compute command
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<LI>zero or more keywords may be appended
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2008-01-10 05:57:06 +08:00
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<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>
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2007-02-10 05:40:32 +08:00
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</UL>
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<P><B>Examples:</B>
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</P>
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2008-02-07 23:17:25 +08:00
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<PRE>compute 1 mobile stress/atom
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compute 1 all stress/atom pair bond
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2007-07-03 03:59:42 +08:00
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</PRE>
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2007-02-10 05:40:32 +08:00
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<P><B>Description:</B>
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</P>
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2007-12-01 07:16:45 +08:00
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<P>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: xx, yy, zz, xy, xz, yz. See the <A HREF = "compute_pressure.html">compute
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pressure</A> command if you want the stress tensor
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(pressure) of the entire system. The 6 components can be accessed by
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2008-01-04 08:56:10 +08:00
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indices 1-6 by any command that uses per-atom computes as input,
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e.g. the <A HREF = "dump.html">dump custom</A> command or <A HREF = "fix_ave_spatial.html">fix
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ave/spatial</A> command or <A HREF = "fix_ave_atom.html">fix
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ave/atom</A> command. See <A HREF = "Section_howto.html#4_15">this
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2007-12-01 07:16:45 +08:00
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section</A> for an overview.
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2007-02-10 05:40:32 +08:00
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</P>
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2007-12-01 07:36:27 +08:00
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<P>The stress tensor for atom <I>I</I> is given by the following formula,
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where <I>a</I> and <I>b</I> take on values x,y,z to generate the 6 components of
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the symmetric tensor:
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2007-02-10 05:40:32 +08:00
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</P>
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<CENTER><IMG SRC = "Eqs/stress_tensor.jpg">
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</CENTER>
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2007-07-03 03:59:42 +08:00
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<P>The first term is a kinetic energy contribution for atom <I>I</I>. The
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2007-12-01 07:36:27 +08:00
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second term is a pairwise energy contribution where <I>n</I> loops over the
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2007-12-01 07:16:45 +08:00
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<I>Np</I> neighbors of atom <I>I</I>, <I>r1</I> and <I>r2</I> are the positions of the 2
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2007-12-01 07:36:27 +08:00
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atoms in the pairwise interaction, and <I>F1</I> and <I>F2</I> 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 <I>Nb</I> bonds which atom
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2008-01-10 05:57:06 +08:00
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<I>I</I> is part of. There are similar terms for the <I>Na</I> angle, <I>Nd</I>
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2007-12-01 07:36:27 +08:00
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dihedral, and <I>Ni</I> improper interactions atom <I>I</I> is part of.
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2008-01-10 05:57:06 +08:00
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Finally, there is a term for the <I>Nf</I> <A HREF = "fix.html">fixes</A> that apply
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internal constraint forces to atom <I>I</I>. Currently, only the <A HREF = "fix_shake.html">fix
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shake</A> and <A HREF = "fix_rigid.html">fix rigid</A> commands
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contribute to this term.
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2007-12-01 07:16:45 +08:00
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</P>
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2007-12-01 07:36:27 +08:00
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<P>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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2008-01-10 05:57:06 +08:00
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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 <A HREF = "fix_shake.html">fix shake</A>
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command.
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2007-12-01 07:16:45 +08:00
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</P>
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<P>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.
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</P>
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<P>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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</P>
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<P>The <A HREF = "dihedral_charmm.html">dihedral_style charmm</A> 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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</P>
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<P>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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2008-02-07 23:17:25 +08:00
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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 easy to compute in a deformed solid or a liquid. Thus, if the
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diagonal components of the per-atom stress tensor are summed for all
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atoms in the system and the sum is divided by 3V, where V is the
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volume of the system, the result should be -P, where P is the total
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pressure of the system.
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2007-12-01 07:16:45 +08:00
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</P>
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2008-01-10 05:57:06 +08:00
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<P>These lines in an input script should yield that result. I.e. the
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2008-01-04 03:03:15 +08:00
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last 2 columns of thermo output will be the same:
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2007-12-01 07:16:45 +08:00
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</P>
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2008-01-04 03:03:15 +08:00
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<PRE>compute peratom all stress/atom
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2008-06-18 21:47:22 +08:00
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compute p all reduce sum c_peratom[1] c_peratom[2] c_peratom[3]
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2008-01-17 03:17:20 +08:00
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variable press equal -(c_p[1]+c_p[2]+c_p[3])/(3*vol)
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2008-01-04 03:03:15 +08:00
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thermo_style custom step temp etotal press v_press
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2007-12-01 07:16:45 +08:00
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</PRE>
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<P>IMPORTANT NOTE: The per-atom stress does NOT include contributions due
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2008-01-10 05:57:06 +08:00
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to long-range Coulombic interactions (via the
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2008-01-10 05:59:42 +08:00
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<A HREF = "kspace_style.html">kspace_style</A> command). It's not clear this
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2008-02-07 23:17:25 +08:00
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contribution can easily be computed.
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2007-07-03 03:59:42 +08:00
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</P>
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2008-01-04 08:56:10 +08:00
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<P><B>Output info:</B>
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</P>
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<P>This compute calculates a vector of length 6 for each atom, which can
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be accessed by indices 1-6 by any command that uses per-atom computes
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as input. See <A HREF = "Section_howto.html#4_15">this section</A> for an overview
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of LAMMPS output options. The 6 components of the vector are ordered
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xx, yy, zz, xy, xz, yz.
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</P>
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2008-02-07 23:17:25 +08:00
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<P><B>Restrictions:</B> none
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2007-02-10 05:40:32 +08:00
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</P>
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2007-12-01 07:16:45 +08:00
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<P><B>Related commands:</B>
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2007-02-10 05:40:32 +08:00
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</P>
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2007-12-01 07:16:45 +08:00
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<P><A HREF = "compute_pe.html">compute pe</A>, <A HREF = "compute_stress_atom.html">compute
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stress/atom</A>
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2007-07-03 03:59:42 +08:00
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</P>
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2007-12-01 07:16:45 +08:00
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<P><B>Default:</B> none
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2007-02-10 05:40:32 +08:00
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</P>
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</HTML>
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