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# 10.5.3. 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 than body particles. See the Howto spherical 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 page on creating new body styles 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

fix nve/body | integrate motion of a body particle in NVE ensemble
fix nvt/body | ditto for NVT ensemble
fix npt/body | ditto for NPT ensemble
fix nph/body | ditto for NPH ensemble
compute body/local | store sub-particle attributes of a body particle
compute temp/body | compute temperature of body particles
dump local | output sub-particle attributes of a body particle
dump image | output body particle attributes as an image

The pair styles currently defined for use with specific body styles are listed in the sections below.

Note that for all the body styles, if the data file defines a general triclinic box, then the orientation of the body particle and its corresponding 6 moments of inertia and other orientation-dependent values should reflect the fact the body is defined withing a general triclinic box with edge vectors A,**B**,**C**. LAMMPS will rotate the box to convert it to a restricted triclinic box. This operation will also rotate the orientation of the body particles. See the Howto triclinic doc page for more details. The sections below highlight the orientation-dependent values specific to each body style.

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.

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.

The pair_style body/nparticle command can be used with this body style to compute body/body and body/non-body interactions.

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 dimension command. See the pair_style body/rounded/polygon 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 body 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
    diameter

where M = 6 + 3*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 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 read_data command for more details.

Note

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.

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 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

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

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.

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” 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. 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.

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 read_data command for more details.

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.

Note

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.

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 3 13
    2 1 1
    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 3 10
    1 1 1
    0.9 0.9 0.9 0 0 0
    0 0 0
    3.0

The number of edges and faces for a rod or sphere must be listed, but is ignored.

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.

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.

Output specifics for all body styles:

For the compute body/local and dump local 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:

    1 = x position of vertex (or sub-particle)
    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.

The dump image command and its body keyword can be used to render body particles.

For the nparticle 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 bflag1 parameter for the body keyword. The bflag2 argument is ignored.

For the rounded/polygon body style, each body is drawn as a polygon and for rounded/polyhedron as a polyhedron. The bflag2 argument selects how the bodies are represented: for a value of 1, only the faces are drawn; for a value of 2, only a wireframe mesh is drawn, and for a value of 3 both. The diameter of each wireframe line is determined by the bflag1 parameter for the body keyword.

Note that for both the rounded/polygon and rounded/polyhedron 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 pair_style rounded/polygon or pair_style rounded/polyhedron 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.

(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).