# Clumps

A clump is a rigid collection of \(n\) rigid spherical pebbles. The surface is defined by the pebble positions and radii (\(\{\mathbf{x}^{(i)},R^{(i)}\},i=1,2,\ldots{,n}\)). The surface properties of a clump can be specified independently for each pebble. Clumps can translate and rotate (defined by \(\{\mathbf{v},\mathbf{w}\}\), the generalized velocity and angular velocity, or spin of the clump centroid). Clump motion obeys the equations of motion. This requires that mass properties, loading conditions, and velocity conditions exist. Mass properties are mass, centroid position, and inertia tensor (\(\{m,\mathbf{x},\mathbf{I}\}\)). Mass properties are defined below. Loading conditions are defined by: the force and moment resulting from interactions with other pieces; gravity (defined by \(\mathbf{g}\), the gravitational acceleration vector); and an externally applied force and moment acting on the clump (defined by \(\mathbf{F_A}\) and \(\mathbf{M_A}\)). Velocity conditions are defined by velocity-fixities \(V_f\) with {three values in 2D; six values in 3D} of the clump.

Mass properties are defined by: (1) the reference configuration and clump density (\(\rho\)); (2) the reference configuration and \(\{m,\mathbf{x},\mathbf{I}\}\) for the reference configuration; or (3) a closed surface and associated mass properties given by the clump density. In all three cases, the reference configuration defines the clump surface used for contact detection/resolution and must be provided. The mass properties are determined for the first case by the positions and sizes of the pebbles in the reference configuration accounting for sphere overlap. The mass properties are determined for the second case by direct specification; this separates the mass and pebble distributions so that pebbles are used only for surface representation. The mass properties are determined for the third case by automatic computation (see http://number-none.com/blow/inertia/index.html) assuming that the reference configuration is consistent with the closed surface.

The preferred clump work flow is to first define a set of clump templates (see `clump template create`

) that represent the desired particles. A surface description, in the form of a closed geometry of {line segments in 2D; triangular facets in 3D} that is manifold and orientable may be used to 1) create the pebble distribution and 2) calculate the mass properties. The `clump template create bubblepack`

command is used to automatically create the pebbles to represent the surface to a desired fidelity. The surface decsriptions may be either convex or concave. Once the set of clump templates have been defined, one can insert clumps into the domain (see the `model domain`

command) in three ways: by replicating clumps one at a time (using `clump replicate`

); by generating non-overlapping sets of clumps (using `clump generate`

); or by distributing overlapping clumps to match a specified size distribution (using `clump distribute`

).

Alternatively, one can create clumps that do not refer to clump templates with the `clump create`

command. The user may either specify the mass properties directly or calculate the actual mass properties based on the sphere distribution using the `clump create calculate`

command using a voxelization approach that accounts for the sphere overlaps.

The `clump attribute`

and `clump property`

commands are used to specify clump attributes and pebble properties as discussed in “Model Components.” The entire attribute/property lists can be listed with the `clump list attribute`

and `clump list property`

commands along with the values of specific attributes/properties.

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