8.6.3. Body particles
Overview:
In LAMMPS, body particles are generalized finite-size particles. Individual body particles can represent complex entities, such as surface meshes of discrete points, collections of sub-particles, deformable objects, etc. Note that other kinds of finite-size spherical and aspherical particles are also supported by LAMMPS, such as spheres, ellipsoids, line segments, and triangles, but they are simpler entities that body particles. See the Howto spherical doc page for a general overview of all these particle types.
Body particles are used via the atom_style body command. It takes a body style as an argument. The current body styles supported by LAMMPS are as follows. The name in the first column is used as the bstyle argument for the atom_style body command.
nparticle |
rigid body with N sub-particles |
rounded/polygon |
2d polygons with N vertices |
rounded/polyhedron |
3d polyhedra with N vertices, E edges and F faces |
The body style determines what attributes are stored for each body and thus how they can be used to compute pairwise body/body or bond/non-body (point particle) interactions. More details of each style are described below.
More styles may be added in the future. See the Modify body doc page for details on how to add a new body style to the code.
When to use body particles:
You should not use body particles to model a rigid body made of simpler particles (e.g. point, sphere, ellipsoid, line segment, triangular particles), if the interaction between pairs of rigid bodies is just the summation of pairwise interactions between the simpler particles. LAMMPS already supports this kind of model via the fix rigid command. Any of the numerous pair styles that compute interactions between simpler particles can be used. The fix rigid command time integrates the motion of the rigid bodies. All of the standard LAMMPS commands for thermostatting, adding constraints, performing output, etc will operate as expected on the simple particles.
By contrast, when body particles are used, LAMMPS treats an entire body as a single particle for purposes of computing pairwise interactions, building neighbor lists, migrating particles between processors, output of particles to a dump file, etc. This means that interactions between pairs of bodies or between a body and non-body (point) particle need to be encoded in an appropriate pair style. If such a pair style were to mimic the fix rigid model, it would need to loop over the entire collection of interactions between pairs of simple particles within the two bodies, each time a single body/body interaction was computed.
Thus it only makes sense to use body particles and develop such a pair style, when particle/particle interactions are more complex than what the fix rigid command can already calculate. For example, consider particles with one or more of the following attributes:
represented by a surface mesh
represented by a collection of geometric entities (e.g. planes + spheres)
deformable
internal stress that induces fragmentation
For these models, the interaction between pairs of particles is likely to be more complex than the summation of simple pairwise interactions. An example is contact or frictional forces between particles with planar surfaces that inter-penetrate. Likewise, the body particle may store internal state, such as a stress tensor used to compute a fracture criterion.
These are additional LAMMPS commands that can be used with body particles of different styles
integrate motion of a body particle in NVE ensemble |
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ditto for NVT ensemble |
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ditto for NPT ensemble |
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ditto for NPH ensemble |
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store sub-particle attributes of a body particle |
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compute temperature of body particles |
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output sub-particle attributes of a body particle |
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output body particle attributes as an image |
The pair styles defined for use with specific body styles are listed in the sections below.
Specifics of body style nparticle:
The nparticle body style represents body particles as a rigid body with a variable number N of sub-particles. It is provided as a vanilla, prototypical example of a body particle, although as mentioned above, the fix rigid command already duplicates its functionality.
The atom_style body command for this body style takes two additional arguments:
atom_style body nparticle Nmin Nmax
Nmin = minimum # of sub-particles in any body in the system
Nmax = maximum # of sub-particles in any body in the system
The Nmin and Nmax arguments are used to bound the size of data structures used internally by each particle.
When the read_data command reads a data file for this body style, the following information must be provided for each entry in the Bodies section of the data file:
atom-ID 1 M
N
ixx iyy izz ixy ixz iyz
x1 y1 z1
...
xN yN zN
where M = 6 + 3*N, and N is the number of sub-particles in the body particle.
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 sub-particles (x1 to zN) as 3N values. These values can be listed on as many lines as you wish; see the read_data command for more details.
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. The coordinates of each sub-particle 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 Atoms section of the data file, as is the total mass of the body particle.
The pair_style body/nparticle command can be used with this body style to compute body/body and body/non-body interactions.
For output purposes via the compute body/local and dump local commands, this body style produces one datum for each of the N sub-particles in a body particle. The datum has 3 values:
1 = x position of sub-particle
2 = y position of sub-particle
3 = z position of sub-particle
These values are the current position of the sub-particle 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.
For images created by the dump image command, if the body keyword is set, then each body particle is drawn as a collection of spheres, one for each sub-particle. The size of each sphere is determined by the bflag1 parameter for the body keyword. The bflag2 argument is ignored.
Specifics of body style rounded/polygon:
The rounded/polygon 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 boundary command. See the “pair_style body/rounded/polygon” doc 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.
One use of this body style is for 2d discrete element models, as described in Fraige.
Similar to body style nparticle, the atom_style body command for this body style takes two additional arguments:
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
The Nmin and Nmax arguments are used to bound the size of data structures used internally by each particle.
When the read_data command reads a data file for this body style, the following information must be provided for each entry in the Bodies section of the data file:
atom-ID 1 M
N
ixx iyy izz ixy ixz iyz
x1 y1 z1
...
xN yN zN
i j j k k ...
diameter
where M = 6 + 3*N + 2*N + 1, and N is the number of vertices in the body particle.
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 2N vertex indices corresponding to the end points of the N edges, followed by a single 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 read_data command for more details.
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. 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 Atoms section of the data file.
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.
3 1 27
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
0 1
1 2
2 3
3 0
1.0
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:
1 1 13
2
1 1 1.33333 0 0 0
-2 0 0
2 0 0
0.5
A disk, whose diameter is 3.0, mass 1.0, is specified as follows:
1 1 10
1
1 1 4.5 0 0 0
0 0 0
3.0
The pair_style body/rounded/polygon command can be used with this body style to compute body/body interactions. The fix wall/body/polygon command can be used with this body style to compute the interaction of body particles with a wall.
Specifics of body style rounded/polyhedron:
The rounded/polyhedron 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 boundary command. See the “pair_style body/rounded/polygon” doc 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.
This body style is for 3d discrete element models, as described in Wang.
Similar to body style rounded/polygon, the atom_style body command for this body style takes two additional arguments:
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
The Nmin and Nmax arguments are used to bound the size of data structures used internally by each particle.
When the read_data command reads a data file for this body style, the following information must be provided for each entry in the Bodies section of the data file:
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
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.
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 2N 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 read_data command for more details. Because the maximum number of vertices per face is hard-coded to be 4 (i.e. quadrilaterals), faces with more than 4 vertices need to be split into triangles or quadrilaterals. For triangular faces, the last vertex index should be set to -1.
The ordering of the 4 vertices within a face should follow the right-hand rule so that the normal vector of the face points outwards from the center of mass.
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. 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 Atoms section of the data file.
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.
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
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:
1 1 13
2
0 1.33333 1.33333 0 0 0
-2 0 0
2 0 0
0.5
A sphere whose diameter is 3.0 and mass 1.0, is specified as follows:
1 1 10
1
0.9 0.9 0.9 0 0 0
0 0 0
3.0
The pair_style body/rounded/polhedron command can be used with this body style to compute body/body interactions. The fix wall/body/polyhedron command can be used with this body style to compute the interaction of body particles with a wall.
For output purposes via the compute body/local and dump local commands, this body style produces one datum for each of the N sub-particles in a body particle. The datum has 3 values:
1 = x position of vertex
2 = y position of vertex
3 = z position of vertex
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.
For images created by the dump image command, if the body keyword is set, then each body particle is drawn as a polygon consisting of N line segments. Note that the line segments are drawn between the N vertices, which does not correspond exactly to the physical extent of the body (because the pair_style rounded/polygon defines finite-size spheres at those point and the line segments between the spheres are tangent to the spheres). The drawn diameter of each line segment is determined by the bflag1 parameter for the body keyword. The bflag2 argument is ignored.
(Fraige) F. Y. Fraige, P. A. Langston, A. J. Matchett, J. Dodds, Particuology, 6, 455 (2008).
(Wang) J. Wang, H. S. Yu, P. A. Langston, F. Y. Fraige, Granular Matter, 13, 1 (2011).