<p>on each atom where <em>K</em> is the specified force constant, <em>r</em> is the
distance from the atom to the center of the indenter, and <em>R</em> is the
radius of the indenter. The force is repulsive and F(r) = 0 for <em>r</em>>
<em>R</em>.</p>
<p>A cylindrical indenter exerts the same force, except that <em>r</em> is the
distance from the atom to the center axis of the cylinder. The
cylinder extends infinitely along its axis.</p>
<p>Spherical and cylindrical indenters account for periodic boundaries in
two ways. First, the center point of a spherical indenter (x,y,z) or
axis of a cylindrical indenter (c1,c2) is remapped back into the
simulation box, if the box is periodic in a particular dimension.
This occurs every timestep if the indenter geometry is specified with
a variable (see below), e.g. it is moving over time. Second, the
calculation of distance to the indenter center or axis accounts for
periodic boundaries. Both of these mean that an indenter can
effectively move through and straddle one or more periodic boundaries.</p>
<p>A planar indenter is really an axis-aligned infinite-extent wall
exerting the same force on atoms in the system, where <em>R</em> is the
position of the plane and <em>r-R</em> is the distance from the plane. If
the <em>side</em> parameter of the plane is specified as <em>lo</em> then it will
indent from the lo end of the simulation box, meaning that atoms with
a coordinate less than the plane’s current position will be pushed
towards the hi end of the box and atoms with a coordinate higher than
the plane’s current position will feel no force. Vice versa if <em>side</em>
is specified as <em>hi</em>.</p>
<p>Any of the 4 quantities defining a spherical indenter’s geometry can
be specified as an equal-style <aclass="reference internal"href="variable.html"><em>variable</em></a>, namely <em>x</em>,
<em>y</em>, <em>z</em>, or <em>R</em>. Similarly, for a cylindrical indenter, any of <em>c1</em>,
<em>c2</em>, or <em>R</em>, can be a variable. For a planar indenter, <em>pos</em> can be
a variable. If the value is a variable, it should be specified as
v_name, where name is the variable name. In this case, the variable
will be evaluated each timestep, and its value used to define the
indenter geometry.</p>
<p>Note that equal-style variables can specify formulas with various
mathematical functions, and include <aclass="reference internal"href="thermo_style.html"><em>thermo_style</em></a>
command keywords for the simulation box parameters and timestep and
elapsed time. Thus it is easy to specify indenter properties that
change as a function of time or span consecutive runs in a continuous
fashion. For the latter, see the <em>start</em> and <em>stop</em> keywords of the
<aclass="reference internal"href="run.html"><em>run</em></a> command and the <em>elaplong</em> keyword of <aclass="reference internal"href="thermo_style.html"><em>thermo_style custom</em></a> for details.</p>
<p>For example, if a spherical indenter’s x-position is specfied as v_x,
then this variable definition will keep it’s center at a relative
position in the simulation box, 1/4 of the way from the left edge to
the right edge, even if the box size changes:</p>
<divclass="highlight-python"><divclass="highlight"><pre>variable x equal "xlo + 0.25*lx"
</pre></div>
</div>
<p>Similarly, either of these variable definitions will move the indenter
from an initial position at 2.5 at a constant velocity of 5:</p>
<divclass="highlight-python"><divclass="highlight"><pre>variable x equal "2.5 + 5*elaplong*dt"
variable x equal vdisplace(2.5,5)
</pre></div>
</div>
<p>If a spherical indenter’s radius is specified as v_r, then these
variable definitions will grow the size of the indenter at a specfied
<h2>Restart, fix_modify, output, run start/stop, minimize info<aclass="headerlink"href="#restart-fix-modify-output-run-start-stop-minimize-info"title="Permalink to this headline">¶</a></h2>
<p>No information about this fix is written to <aclass="reference internal"href="restart.html"><em>binary restart files</em></a>.</p>
<p>The <aclass="reference internal"href="fix_modify.html"><em>fix_modify</em></a><em>energy</em> option is supported by this
fix to add the energy of interaction between atoms and the indenter to
the system’s potential energy as part of <aclass="reference internal"href="thermo_style.html"><em>thermodynamic output</em></a>. The energy of each particle interacting
with the indenter is K/3 (r - R)^3.</p>
<p>This fix computes a global scalar energy and a global 3-vector of
forces (on the indenter), which can be accessed by various <aclass="reference internal"href="Section_howto.html#howto-15"><span>output commands</span></a>. The scalar and vector values
calculated by this fix are “extensive”.</p>
<p>The forces due to this fix are imposed during an energy minimization,
invoked by the <aclass="reference internal"href="minimize.html"><em>minimize</em></a> command. Note that if you
define the indenter geometry with a variable using a time-dependent
formula, LAMMPS uses the iteration count in the minimizer as the
timestep. But it is almost certainly a bad idea to have the indenter
change its position or size during a minimization. LAMMPS does not
check if you have done this.</p>
<divclass="admonition note">
<pclass="first admonition-title">Note</p>
<pclass="last">If you want the atom/indenter interaction energy to be included
in the total potential energy of the system (the quantity being
minimized), you must enable the <aclass="reference internal"href="fix_modify.html"><em>fix_modify</em></a><em>energy</em>
option for this fix.</p>
</div>
</div>
<divclass="section"id="restrictions">
<h2>Restrictions<aclass="headerlink"href="#restrictions"title="Permalink to this headline">¶</a></h2>
<blockquote>
<div>none</div></blockquote>
<p><strong>Related commands:</strong> none</p>
</div>
<divclass="section"id="default">
<h2>Default<aclass="headerlink"href="#default"title="Permalink to this headline">¶</a></h2>
<p>The option defaults are side = out and units = lattice.</p>
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