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### Body particles

Overview:

This doc page is not about a LAMMPS input script command, but about body particles, which 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 Section 6.14 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 convex polygon with N vertices

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.

NOTE: The rounded/polygon style listed in the table above and described below has not yet been relesed in LAMMPS. It will be soon.

We hope to add more styles in the future. See Section 10.12 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, outputting 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, if particles have 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

then the interaction between pairs of particles is likely to be more complex than the summation of simple sub-particle interactions. An example is contact or frictional forces between particles with planar sufaces that inter-penetrate.

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 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 vanillia, 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

N is the number of sub-particles in the body particle. M = 6 + 3*N. 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 prinicpal 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 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:

NOTE: Aug 2016 - This body style has not yet been added to LAMMPS. The info below is a placeholder.

The rounded/polygon body style represents body particles as a convex polygon with a variable number N > 2 of vertices, which can only be used for 2d models. One example 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 ...
    radius

N is the number of vertices in the body particle. M = 6 + 3*N + 2*N + 1. 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, followed by 2N vertex indices corresponding to the end points of the N edges, followed by a single radius value = the smallest circle encompassing the polygon. That last value is used to facilitate the body/body contact detection. 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 prinicpal 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 particles whose edge length is sqrt(2):

    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

The pair_style body/rounded/polygon command can be used with this body style to compute body/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 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 convex 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).