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<li class="toctree-l3 current"><a class="current reference internal" href="#">8.5.3. Body particles</a></li>
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<li class="breadcrumb-item active"><span class="section-number">8.5.3. </span>Body particles</li>
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<p><span class="math notranslate nohighlight">\(\renewcommand{\AA}{\text{Å}}\)</span></p>
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<section id="body-particles">
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<h1><span class="section-number">8.5.3. </span>Body particles<a class="headerlink" href="#body-particles" title="Link to this heading"></a></h1>
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<p><strong>Overview:</strong></p>
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<p>In LAMMPS, body particles are generalized finite-size particles.
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Individual body particles can represent complex entities, such as
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surface meshes of discrete points, collections of sub-particles,
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deformable objects, etc. Note that other kinds of finite-size
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spherical and aspherical particles are also supported by LAMMPS, such
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as spheres, ellipsoids, line segments, and triangles, but they are
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simpler entities than body particles. See the <a class="reference internal" href="Howto_spherical.html"><span class="doc">Howto spherical</span></a> page for a general overview of all these
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particle types.</p>
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<p>Body particles are used via the <a class="reference internal" href="atom_style.html"><span class="doc">atom_style body</span></a>
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command. It takes a body style as an argument. The current body
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styles supported by LAMMPS are as follows. The name in the first
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column is used as the <em>bstyle</em> argument for the <a class="reference internal" href="atom_style.html"><span class="doc">atom_style body</span></a> command.</p>
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<table class="docutils align-default">
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<tbody>
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<tr class="row-odd"><td><p><em>nparticle</em></p></td>
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<td><p>rigid body with N sub-particles</p></td>
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</tr>
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<tr class="row-even"><td><p><em>rounded/polygon</em></p></td>
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<td><p>2d polygons with N vertices</p></td>
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</tr>
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<tr class="row-odd"><td><p><em>rounded/polyhedron</em></p></td>
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<td><p>3d polyhedra with N vertices, E edges and F faces</p></td>
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</tr>
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</tbody>
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</table>
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<p>The body style determines what attributes are stored for each body and
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thus how they can be used to compute pairwise body/body or
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bond/non-body (point particle) interactions. More details of each
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style are described below.</p>
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<p>More styles may be added in the future. See the
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<a class="reference internal" href="Modify_body.html"><span class="doc">page on creating new body styles</span></a> for details on
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how to add a new body style to the code.</p>
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<hr class="docutils" />
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<p><strong>When to use body particles:</strong></p>
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<p>You should not use body particles to model a rigid body made of
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simpler particles (e.g. point, sphere, ellipsoid, line segment,
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triangular particles), if the interaction between pairs of rigid
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bodies is just the summation of pairwise interactions between the
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simpler particles. LAMMPS already supports this kind of model via the
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<a class="reference internal" href="fix_rigid.html"><span class="doc">fix rigid</span></a> command. Any of the numerous pair styles
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that compute interactions between simpler particles can be used. The
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<a class="reference internal" href="fix_rigid.html"><span class="doc">fix rigid</span></a> command time integrates the motion of the
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rigid bodies. All of the standard LAMMPS commands for thermostatting,
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adding constraints, performing output, etc will operate as expected on
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the simple particles.</p>
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<p>By contrast, when body particles are used, LAMMPS treats an entire
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body as a single particle for purposes of computing pairwise
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interactions, building neighbor lists, migrating particles between
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processors, output of particles to a dump file, etc. This means that
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interactions between pairs of bodies or between a body and non-body
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(point) particle need to be encoded in an appropriate pair style. If
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such a pair style were to mimic the <a class="reference internal" href="fix_rigid.html"><span class="doc">fix rigid</span></a>
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model, it would need to loop over the entire collection of
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interactions between pairs of simple particles within the two bodies,
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each time a single body/body interaction was computed.</p>
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<p>Thus it only makes sense to use body particles and develop such a pair
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style, when particle/particle interactions are more complex than what
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the <a class="reference internal" href="fix_rigid.html"><span class="doc">fix rigid</span></a> command can already calculate. For
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example, consider particles with one or more of the following
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attributes:</p>
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<ul class="simple">
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<li><p>represented by a surface mesh</p></li>
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<li><p>represented by a collection of geometric entities (e.g. planes + spheres)</p></li>
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<li><p>deformable</p></li>
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<li><p>internal stress that induces fragmentation</p></li>
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</ul>
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<p>For these models, the interaction between pairs of particles is likely
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to be more complex than the summation of simple pairwise interactions.
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An example is contact or frictional forces between particles with
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planar surfaces that inter-penetrate. Likewise, the body particle may
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store internal state, such as a stress tensor used to compute a
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fracture criterion.</p>
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<p>These are additional LAMMPS commands that can be used with body
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particles of different styles</p>
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<table class="docutils align-default">
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<tbody>
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<tr class="row-odd"><td><p><a class="reference internal" href="fix_nve_body.html"><span class="doc">fix nve/body</span></a></p></td>
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<td><p>integrate motion of a body particle in NVE ensemble</p></td>
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</tr>
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<tr class="row-even"><td><p><a class="reference internal" href="fix_nvt_body.html"><span class="doc">fix nvt/body</span></a></p></td>
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<td><p>ditto for NVT ensemble</p></td>
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</tr>
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<tr class="row-odd"><td><p><a class="reference internal" href="fix_npt_body.html"><span class="doc">fix npt/body</span></a></p></td>
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<td><p>ditto for NPT ensemble</p></td>
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</tr>
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<tr class="row-even"><td><p><a class="reference internal" href="fix_nph_body.html"><span class="doc">fix nph/body</span></a></p></td>
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<td><p>ditto for NPH ensemble</p></td>
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</tr>
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<tr class="row-odd"><td><p><a class="reference internal" href="compute_body_local.html"><span class="doc">compute body/local</span></a></p></td>
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<td><p>store sub-particle attributes of a body particle</p></td>
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</tr>
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<tr class="row-even"><td><p><a class="reference internal" href="compute_temp_body.html"><span class="doc">compute temp/body</span></a></p></td>
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<td><p>compute temperature of body particles</p></td>
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</tr>
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<tr class="row-odd"><td><p><a class="reference internal" href="dump.html"><span class="doc">dump local</span></a></p></td>
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<td><p>output sub-particle attributes of a body particle</p></td>
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</tr>
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<tr class="row-even"><td><p><a class="reference internal" href="dump_image.html"><span class="doc">dump image</span></a></p></td>
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<td><p>output body particle attributes as an image</p></td>
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</tr>
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</tbody>
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</table>
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<p>The pair styles currently defined for use with specific body styles
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are listed in the sections below.</p>
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<p>Note that for all the body styles, if the data file defines a general
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triclinic box, then the orientation of the body particle and its
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corresponding 6 moments of inertia and other orientation-dependent
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values should reflect the fact the body is defined withing a general
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triclinic box with edge vectors <strong>A</strong>,**B**,**C**. LAMMPS will rotate
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the box to convert it to a restricted triclinic box. This operation
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will also rotate the orientation of the body particles. See the
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<a class="reference internal" href="Howto_triclinic.html"><span class="doc">Howto triclinic</span></a> doc page for more details.
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The sections below highlight the orientation-dependent values specific
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to each body style.</p>
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<hr class="docutils" />
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<p><strong>Specifics of body style nparticle:</strong></p>
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<p>The <em>nparticle</em> body style represents body particles as a rigid body
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with a variable number N of sub-particles. It is provided as a
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vanilla, prototypical example of a body particle, although as
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||
mentioned above, the <a class="reference internal" href="fix_rigid.html"><span class="doc">fix rigid</span></a> command already
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||
duplicates its functionality.</p>
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<p>The atom_style body command for this body style takes two additional
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arguments:</p>
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<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>atom_style body nparticle Nmin Nmax
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Nmin = minimum # of sub-particles in any body in the system
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Nmax = maximum # of sub-particles in any body in the system
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</pre></div>
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</div>
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<p>The Nmin and Nmax arguments are used to bound the size of data
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structures used internally by each particle.</p>
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<p>When the <a class="reference internal" href="read_data.html"><span class="doc">read_data</span></a> command reads a data file for this
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body style, the following information must be provided for each entry
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in the <em>Bodies</em> section of the data file:</p>
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<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>atom-ID 1 M
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N
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ixx iyy izz ixy ixz iyz
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x1 y1 z1
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...
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xN yN zN
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</pre></div>
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</div>
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<p>where M = 6 + 3*N, and N is the number of sub-particles in the body
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particle.</p>
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<p>The integer line has a single value N. The floating point line(s)
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list 6 moments of inertia followed by the coordinates of the N
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sub-particles (x1 to zN) as 3N values. These values can be listed on
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as many lines as you wish; see the <a class="reference internal" href="read_data.html"><span class="doc">read_data</span></a> command
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||
for more details.</p>
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<p>The 6 moments of inertia (ixx,iyy,izz,ixy,ixz,iyz) should be the
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values consistent with the current orientation of the rigid body
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around its center of mass. The values are with respect to the
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simulation box XYZ axes, not with respect to the principal axes of the
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rigid body itself. LAMMPS performs the latter calculation internally.</p>
|
||
<p>The coordinates of each sub-particle are specified as its x,y,z
|
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displacement from the center-of-mass of the body particle. The
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||
center-of-mass position of the particle is specified by the x,y,z
|
||
values in the <em>Atoms</em> section of the data file, as is the total mass
|
||
of the body particle.</p>
|
||
<p>Note that if the data file defines a general triclinic simulation box,
|
||
these sub-particle displacements are orientation-dependent and, as
|
||
mentioned above, should reflect the body particle’s orientation within
|
||
the general triclinic box.</p>
|
||
<p>The <a class="reference internal" href="pair_body_nparticle.html"><span class="doc">pair_style body/nparticle</span></a> command can be used
|
||
with this body style to compute body/body and body/non-body interactions.</p>
|
||
<hr class="docutils" />
|
||
<p><strong>Specifics of body style rounded/polygon:</strong></p>
|
||
<p>The <em>rounded/polygon</em> body style represents body particles as a 2d
|
||
polygon with a variable number of N vertices. This style can only be
|
||
used for 2d models; see the <a class="reference internal" href="boundary.html"><span class="doc">boundary</span></a> command. See the
|
||
<a class="reference internal" href="pair_body_rounded_polygon.html"><span class="doc">pair_style body/rounded/polygon</span></a> page for
|
||
a diagram of two squares with rounded circles at the vertices. Special cases
|
||
for N = 1 (circle) and N = 2 (rod with rounded ends) can also be specified.</p>
|
||
<p>One use of this body style is for 2d discrete element models, as
|
||
described in <a class="reference internal" href="#body-fraige"><span class="std std-ref">Fraige</span></a>.</p>
|
||
<p>Similar to body style <em>nparticle</em>, the atom_style body command for
|
||
this body style takes two additional arguments:</p>
|
||
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>atom_style body rounded/polygon Nmin Nmax
|
||
Nmin = minimum # of vertices in any body in the system
|
||
Nmax = maximum # of vertices in any body in the system
|
||
</pre></div>
|
||
</div>
|
||
<p>The Nmin and Nmax arguments are used to bound the size of data
|
||
structures used internally by each particle.</p>
|
||
<p>When the <a class="reference internal" href="read_data.html"><span class="doc">read_data</span></a> command reads a data file for this
|
||
body style, the following information must be provided for each body
|
||
in the <em>Bodies</em> section of the data file:</p>
|
||
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>atom-ID 1 M
|
||
N
|
||
ixx iyy izz ixy ixz iyz
|
||
x1 y1 z1
|
||
...
|
||
xN yN zN
|
||
diameter
|
||
</pre></div>
|
||
</div>
|
||
<p>where M = 6 + 3*N + 1, and N is the number of vertices in the body
|
||
particle.</p>
|
||
<p>The integer line has a single value N. The floating point line(s)
|
||
list 6 moments of inertia, followed by the coordinates of the N
|
||
vertices (x1 to zN) as 3N values (with z = 0.0 for each), followed by
|
||
a diameter value = the rounded diameter of the circle that surrounds
|
||
each vertex. The diameter value can be different for each body
|
||
particle. These floating-point values can be listed on as many lines
|
||
as you wish; see the <a class="reference internal" href="read_data.html"><span class="doc">read_data</span></a> command for more
|
||
details.</p>
|
||
<div class="admonition note">
|
||
<p class="admonition-title">Note</p>
|
||
<p>It is important that the vertices for each polygonal body particle be
|
||
listed in order around its perimeter, so that edges can be inferred.
|
||
LAMMPS does not check that this is the case.</p>
|
||
</div>
|
||
<p>The 6 moments of inertia (ixx,iyy,izz,ixy,ixz,iyz) should be the
|
||
values consistent with the current orientation of the rigid body
|
||
around its center of mass. The values are with respect to the
|
||
simulation box XYZ axes, not with respect to the principal axes of the
|
||
rigid body itself. LAMMPS performs the latter calculation internally.</p>
|
||
<p>The coordinates of each vertex are specified as its x,y,z displacement
|
||
from the center-of-mass of the body particle. The center-of-mass
|
||
position of the particle is specified by the x,y,z values in the
|
||
<em>Atoms</em> section of the data file.</p>
|
||
<p>For example, the following information would specify a square particle
|
||
whose edge length is sqrt(2) and rounded diameter is 1.0. The
|
||
orientation of the square is aligned with the xy coordinate axes which
|
||
is consistent with the 6 moments of inertia: ixx iyy izz ixy ixz iyz =
|
||
1 1 4 0 0 0. Note that only Izz matters in 2D simulations.</p>
|
||
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>3 1 19
|
||
4
|
||
1 1 4 0 0 0
|
||
-0.7071 -0.7071 0
|
||
-0.7071 0.7071 0
|
||
0.7071 0.7071 0
|
||
0.7071 -0.7071 0
|
||
1.0
|
||
</pre></div>
|
||
</div>
|
||
<p>A rod in 2D, whose length is 4.0, mass 1.0, rounded at two ends
|
||
by circles of diameter 0.5, is specified as follows:</p>
|
||
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>1 1 13
|
||
2
|
||
1 1 1.33333 0 0 0
|
||
-2 0 0
|
||
2 0 0
|
||
0.5
|
||
</pre></div>
|
||
</div>
|
||
<p>A disk, whose diameter is 3.0, mass 1.0, is specified as follows:</p>
|
||
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>1 1 10
|
||
1
|
||
1 1 4.5 0 0 0
|
||
0 0 0
|
||
3.0
|
||
</pre></div>
|
||
</div>
|
||
<p>Note that if the data file defines a general triclinic simulation box,
|
||
these polygon vertex displacements are orientation-dependent and, as
|
||
mentioned above, should reflect the body particle’s orientation within
|
||
the general triclinic box.</p>
|
||
<p>The <a class="reference internal" href="pair_body_rounded_polygon.html"><span class="doc">pair_style body/rounded/polygon</span></a>
|
||
command can be used with this body style to compute body/body
|
||
interactions. The <a class="reference internal" href="fix_wall_body_polygon.html"><span class="doc">fix wall/body/polygon</span></a>
|
||
command can be used with this body style to compute the interaction of
|
||
body particles with a wall.</p>
|
||
<hr class="docutils" />
|
||
<p><strong>Specifics of body style rounded/polyhedron:</strong></p>
|
||
<p>The <em>rounded/polyhedron</em> body style represents body particles as a 3d
|
||
polyhedron with a variable number of N vertices, E edges and F faces.
|
||
This style can only be used for 3d models; see the
|
||
<a class="reference internal" href="boundary.html"><span class="doc">boundary</span></a> command. See the “pair_style
|
||
body/rounded/polygon” page for a diagram of a two 2d squares with
|
||
rounded circles at the vertices. A 3d cube with rounded spheres at
|
||
the 8 vertices and 12 rounded edges would be similar. Special cases
|
||
for N = 1 (sphere) and N = 2 (rod with rounded ends) can also be
|
||
specified.</p>
|
||
<p>This body style is for 3d discrete element models, as described in
|
||
<a class="reference internal" href="#body-wang"><span class="std std-ref">Wang</span></a>.</p>
|
||
<p>Similar to body style <em>rounded/polygon</em>, the atom_style body command
|
||
for this body style takes two additional arguments:</p>
|
||
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>atom_style body rounded/polyhedron Nmin Nmax
|
||
Nmin = minimum # of vertices in any body in the system
|
||
Nmax = maximum # of vertices in any body in the system
|
||
</pre></div>
|
||
</div>
|
||
<p>The Nmin and Nmax arguments are used to bound the size of data
|
||
structures used internally by each particle.</p>
|
||
<p>When the <a class="reference internal" href="read_data.html"><span class="doc">read_data</span></a> command reads a data file for this
|
||
body style, the following information must be provided for each entry
|
||
in the <em>Bodies</em> section of the data file:</p>
|
||
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>atom-ID 3 M
|
||
N E F
|
||
ixx iyy izz ixy ixz iyz
|
||
x1 y1 z1
|
||
...
|
||
xN yN zN
|
||
0 1
|
||
1 2
|
||
2 3
|
||
...
|
||
0 1 2 -1
|
||
0 2 3 -1
|
||
...
|
||
1 2 3 4
|
||
diameter
|
||
</pre></div>
|
||
</div>
|
||
<p>where M = 6 + 3*N + 2*E + 4*F + 1, and N is the number of vertices
|
||
in the body particle, E = number of edges, F = number of faces. For N
|
||
= 1 or 2, the format is simpler. E and F are ignored and no edges or
|
||
faces are listed, so that M = 6 + 3*N + 1.</p>
|
||
<p>The integer line has three values: number of vertices (N), number of
|
||
edges (E) and number of faces (F). The floating point line(s) list 6
|
||
moments of inertia followed by the coordinates of the N vertices (x1
|
||
to zN) as 3N values, followed by 2E vertex indices corresponding to
|
||
the end points of the E edges, then 4*F vertex indices defining F
|
||
faces. The last value is the diameter value = the rounded diameter of
|
||
the sphere that surrounds each vertex. The diameter value can be
|
||
different for each body particle. These floating-point values can be
|
||
listed on as many lines as you wish; see the <a class="reference internal" href="read_data.html"><span class="doc">read_data</span></a> command for more details.</p>
|
||
<p>Note that vertices are numbered from 0 to N-1 inclusive. The order of
|
||
the 2 vertices in each edge does not matter. Faces can be triangles
|
||
or quadrilaterals. In both cases 4 vertices must be specified. For a
|
||
triangle the 4th vertex is -1. The 4 vertices within each triangle or
|
||
quadrilateral face should be ordered by the right-hand rule so that
|
||
the normal vector of the face points outwards from the center of mass.
|
||
For polyhedron with faces with more than 4 vertices, you should split
|
||
the complex face into multiple simple faces, each of which is a
|
||
triangle or quadrilateral.</p>
|
||
<div class="admonition note">
|
||
<p class="admonition-title">Note</p>
|
||
<p>If a face is a quadrilateral then its 4 vertices must be co-planar.
|
||
LAMMPS does not check that this is the case. If you have a quad-face
|
||
of a polyhedron that is not planar (e.g. a cube whose vertices have
|
||
been randomly displaced), then you should represent the single quad
|
||
face as two triangle faces instead.</p>
|
||
</div>
|
||
<p>The 6 moments of inertia (ixx,iyy,izz,ixy,ixz,iyz) should be the
|
||
values consistent with the current orientation of the rigid body
|
||
around its center of mass. The values are with respect to the
|
||
simulation box XYZ axes, not with respect to the principal axes of the
|
||
rigid body itself. LAMMPS performs the latter calculation internally.</p>
|
||
<p>The coordinates of each vertex are specified as its x,y,z displacement
|
||
from the center-of-mass of the body particle. The center-of-mass
|
||
position of the particle is specified by the x,y,z values in the
|
||
<em>Atoms</em> section of the data file.</p>
|
||
<p>For example, the following information would specify a cubic particle
|
||
whose edge length is 2.0 and rounded diameter is 0.5.
|
||
The orientation of the cube is aligned with the xyz coordinate axes
|
||
which is consistent with the 6 moments of inertia: ixx iyy izz ixy ixz
|
||
iyz = 0.667 0.667 0.667 0 0 0.</p>
|
||
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>1 3 79
|
||
8 12 6
|
||
0.667 0.667 0.667 0 0 0
|
||
1 1 1
|
||
1 -1 1
|
||
-1 -1 1
|
||
-1 1 1
|
||
1 1 -1
|
||
1 -1 -1
|
||
-1 -1 -1
|
||
-1 1 -1
|
||
0 1
|
||
1 2
|
||
2 3
|
||
3 0
|
||
4 5
|
||
5 6
|
||
6 7
|
||
7 4
|
||
0 4
|
||
1 5
|
||
2 6
|
||
3 7
|
||
0 1 2 3
|
||
4 5 6 7
|
||
0 1 5 4
|
||
1 2 6 5
|
||
2 3 7 6
|
||
3 0 4 7
|
||
0.5
|
||
</pre></div>
|
||
</div>
|
||
<p>A rod in 3D, whose length is 4.0, mass 1.0 and rounded at two ends
|
||
by circles of diameter 0.5, is specified as follows:</p>
|
||
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>1 3 13
|
||
2 1 1
|
||
0 1.33333 1.33333 0 0 0
|
||
-2 0 0
|
||
2 0 0
|
||
0.5
|
||
</pre></div>
|
||
</div>
|
||
<p>A sphere whose diameter is 3.0 and mass 1.0, is specified as follows:</p>
|
||
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>1 3 10
|
||
1 1 1
|
||
0.9 0.9 0.9 0 0 0
|
||
0 0 0
|
||
3.0
|
||
</pre></div>
|
||
</div>
|
||
<p>The number of edges and faces for a rod or sphere must be listed,
|
||
but is ignored.</p>
|
||
<p>Note that if the data file defines a general triclinic simulation box,
|
||
these polyhedron vertex displacements are orientation-dependent and,
|
||
as mentioned above, should reflect the body particle’s orientation
|
||
within the general triclinic box.</p>
|
||
<p>The <a class="reference internal" href="pair_body_rounded_polyhedron.html"><span class="doc">pair_style body/rounded/polhedron</span></a> command can be used with this body
|
||
style to compute body/body interactions. The <a class="reference internal" href="fix_wall_body_polygon.html"><span class="doc">fix
|
||
wall/body/polyhedron</span></a> command can be used with
|
||
this body style to compute the interaction of body particles with a
|
||
wall.</p>
|
||
<hr class="docutils" />
|
||
<p><strong>Output specifics for all body styles:</strong></p>
|
||
<p>For the <a class="reference internal" href="compute_body_local.html"><span class="doc">compute body/local</span></a> and <a class="reference internal" href="dump.html"><span class="doc">dump
|
||
local</span></a> commands, all 3 of the body styles described on his page
|
||
produces one datum for each of the N vertices (of sub-particles) in a
|
||
body particle. The datum has 3 values:</p>
|
||
<div class="highlight-none notranslate"><div class="highlight"><pre><span></span>1 = x position of vertex (or sub-particle)
|
||
2 = y position of vertex
|
||
3 = z position of vertex
|
||
</pre></div>
|
||
</div>
|
||
<p>These values are the current position of the vertex within the
|
||
simulation domain, not a displacement from the center-of-mass (COM) of
|
||
the body particle itself. These values are calculated using the
|
||
current COM and orientation of the body particle.</p>
|
||
<p>The <a class="reference internal" href="dump_image.html"><span class="doc">dump image</span></a> command and its <em>body</em> keyword can
|
||
be used to render body particles.</p>
|
||
<p>For the <em>nparticle</em> body style, each body is drawn as a
|
||
collection of spheres, one for each sub-particle. The size of each
|
||
sphere is determined by the <em>bflag1</em> parameter for the <em>body</em> keyword.
|
||
The <em>bflag2</em> argument is ignored.</p>
|
||
<p>For the <em>rounded/polygon</em> body style, each body is drawn as a polygon
|
||
with N line segments. For the <em>rounded/polyhedron</em> body style, each
|
||
face of each body is drawn as a polygon with N line segments. The
|
||
drawn diameter of each line segment is determined by the <em>bflag1</em>
|
||
parameter for the <em>body</em> keyword. The <em>bflag2</em> argument is ignored.</p>
|
||
<p>Note that for both the <em>rounded/polygon</em> and <em>rounded/polyhedron</em>
|
||
styles, line segments are drawn between the pairs of vertices.
|
||
Depending on the diameters of the line segments this may be slightly
|
||
different than the physical extent of the body as calculated by the
|
||
<a class="reference internal" href="pair_body_rounded_polygon.html"><span class="doc">pair_style rounded/polygon</span></a> or
|
||
<a class="reference internal" href="pair_body_rounded_polyhedron.html"><span class="doc">pair_style rounded/polyhedron</span></a>
|
||
commands. Conceptually, the pair styles define the surface of a 2d or
|
||
3d body by lines or planes that are tangent to the finite-size spheres
|
||
of specified diameter which are placed on each vertex position.</p>
|
||
<hr class="docutils" />
|
||
<p id="body-fraige"><strong>(Fraige)</strong> F. Y. Fraige, P. A. Langston, A. J. Matchett, J. Dodds,
|
||
Particuology, 6, 455 (2008).</p>
|
||
<p id="body-wang"><strong>(Wang)</strong> J. Wang, H. S. Yu, P. A. Langston, F. Y. Fraige, Granular
|
||
Matter, 13, 1 (2011).</p>
|
||
</section>
|
||
|
||
|
||
</div>
|
||
</div>
|
||
<footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
|
||
<a href="Howto_granular.html" class="btn btn-neutral float-left" title="8.5.2. Granular models" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
|
||
<a href="Howto_bpm.html" class="btn btn-neutral float-right" title="8.5.4. Bonded particle models" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a>
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||
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