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<li class="toctree-l1"><a class="reference internal" href="Section_intro.html">1. Introduction</a></li>
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<div class="section" id="compute-stress-atom-command">
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<span id="index-0"></span><h1>compute stress/atom command<a class="headerlink" href="#compute-stress-atom-command" title="Permalink to this headline">¶</a></h1>
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<div class="section" id="syntax">
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<h2>Syntax<a class="headerlink" href="#syntax" title="Permalink to this headline">¶</a></h2>
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<div class="highlight-python"><div class="highlight"><pre>compute ID group-ID stress/atom temp-ID keyword ...
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</pre></div>
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</div>
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<ul class="simple">
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<li>ID, group-ID are documented in <a class="reference internal" href="compute.html"><em>compute</em></a> command</li>
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<li>stress/atom = style name of this compute command</li>
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<li>temp-ID = ID of compute that calculates temperature, can be NULL if not needed</li>
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<li>zero or more keywords may be appended</li>
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<li>keyword = <em>ke</em> or <em>pair</em> or <em>bond</em> or <em>angle</em> or <em>dihedral</em> or <em>improper</em> or <em>kspace</em> or <em>fix</em> or <em>virial</em></li>
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</ul>
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</div>
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<div class="section" id="examples">
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<h2>Examples<a class="headerlink" href="#examples" title="Permalink to this headline">¶</a></h2>
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<div class="highlight-python"><div class="highlight"><pre>compute 1 mobile stress/atom NULL
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compute 1 mobile stress/atom myRamp
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compute 1 all stress/atom NULL pair bond
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</pre></div>
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</div>
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</div>
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<div class="section" id="description">
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<h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
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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 and is stored as a 6-element vector in the following order:
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xx, yy, zz, xy, xz, yz. See the <a class="reference internal" href="compute_pressure.html"><em>compute pressure</em></a> command if you want the stress tensor
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(pressure) of the entire system.</p>
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<p>The stress tensor for atom <em>I</em> is given by the following formula,
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where <em>a</em> and <em>b</em> take on values x,y,z to generate the 6 components of
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the symmetric tensor:</p>
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<img alt="_images/stress_tensor.jpg" class="align-center" src="_images/stress_tensor.jpg" />
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<p>The first term is a kinetic energy contribution for atom <em>I</em>. See
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details below on how the specified <em>temp-ID</em> can affect the velocities
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used in this calculation. The second term is a pairwise energy
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contribution where <em>n</em> loops over the <em>Np</em> neighbors of atom <em>I</em>, <em>r1</em>
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and <em>r2</em> are the positions of the 2 atoms in the pairwise interaction,
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and <em>F1</em> and <em>F2</em> are the forces on the 2 atoms resulting from the
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pairwise interaction. The third term is a bond contribution of
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similar form for the <em>Nb</em> bonds which atom <em>I</em> is part of. There are
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similar terms for the <em>Na</em> angle, <em>Nd</em> dihedral, and <em>Ni</em> improper
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interactions atom <em>I</em> is part of. There is also a term for the KSpace
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contribution from long-range Coulombic interactions, if defined.
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Finally, there is a term for the <em>Nf</em> <a class="reference internal" href="fix.html"><em>fixes</em></a> that apply
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internal constraint forces to atom <em>I</em>. Currently, only the <a class="reference internal" href="fix_shake.html"><em>fix shake</em></a> and <a class="reference internal" href="fix_rigid.html"><em>fix rigid</em></a> commands
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contribute to this term.</p>
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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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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 class="reference internal" href="fix_shake.html"><em>fix shake</em></a>
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command.</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. The
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<em>virial</em> keyword means include all terms except the kinetic energy
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<em>ke</em>.</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.</p>
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<p>Details of how LAMMPS computes the virial for individual atoms for
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either pairwise or manybody potentials, and including the effects of
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periodic boundary conditions is discussed in <a class="reference internal" href="#thompson"><span>(Thompson)</span></a>.
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The basic idea for manybody potentials is to treat each component of
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the force computation between a small cluster of atoms in the same
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manner as in the formula above for bond, angle, dihedral, etc
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interactions. Namely the quantity R dot F is summed over the atoms in
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the interaction, with the R vectors unwrapped by periodic boundaries
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so that the cluster of atoms is close together. The total
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contribution for the cluster interaction is divided evenly among those
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atoms.</p>
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<p>The <a class="reference internal" href="dihedral_charmm.html"><em>dihedral_style charmm</em></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.</p>
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<p>The KSpace contribution is calculated using the method in
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<a class="reference internal" href="#heyes"><span>(Heyes)</span></a> for the Ewald method and by the methodology described
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in <a class="reference internal" href="pair_srp.html#sirk"><span>(Sirk)</span></a> for PPPM. The choice of KSpace solver is specified
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by the <a class="reference internal" href="kspace_style.html"><em>kspace_style pppm</em></a> 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.</p>
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<p>The <em>temp-ID</em> argument can be used to affect the per-atom velocities
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used in the kinetic energy contribution to the total stress. If the
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kinetic energy is not included in the stress, than the temperature
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compute is not used and can be specified as NULL. If the kinetic
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energy is included and you wish to use atom velocities as-is, then
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<em>temp-ID</em> can also be specified as NULL. If desired, the specified
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temperature compute can be one that subtracts off a bias to leave each
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atom with only a thermal velocity to use in the formula above, e.g. by
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subtracting a background streaming velocity. See the doc pages for
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individual <a class="reference internal" href="compute.html"><em>compute commands</em></a> to determine which ones
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include a bias.</p>
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<hr class="docutils" />
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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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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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See the <a class="reference internal" href="compute_voronoi_atom.html"><em>compute voronoi/atom</em></a> command for
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one possible way to estimate a per-atom volume.</p>
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<p>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.</p>
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<p>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:</p>
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<div class="highlight-python"><div class="highlight"><pre>compute peratom all stress/atom NULL
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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
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</pre></div>
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</div>
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<p><strong>Output info:</strong></p>
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<p>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 <a class="reference internal" href="Section_howto.html#howto-15"><span>Section_howto 15</span></a> for an overview of LAMMPS output
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options.</p>
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<p>The per-atom array values will be in pressure*volume
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<a class="reference internal" href="units.html"><em>units</em></a> as discussed above.</p>
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</div>
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<div class="section" id="restrictions">
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<h2>Restrictions<a class="headerlink" href="#restrictions" title="Permalink to this headline">¶</a></h2>
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<blockquote>
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<div>none</div></blockquote>
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</div>
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<div class="section" id="related-commands">
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<h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
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<p><a class="reference internal" href="compute_pe.html"><em>compute pe</em></a>, <a class="reference internal" href="compute_pressure.html"><em>compute pressure</em></a></p>
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<p><strong>Default:</strong> none</p>
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<hr class="docutils" />
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<p id="heyes"><strong>(Heyes)</strong> Heyes, Phys Rev B 49, 755 (1994),</p>
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<p id="sirk"><strong>(Sirk)</strong> Sirk, Moore, Brown, J Chem Phys, 138, 064505 (2013).</p>
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<p id="thompson"><strong>(Thompson)</strong> Thompson, Plimpton, Mattson, J Chem Phys, 131, 154107 (2009).</p>
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