4.1. Spherical Particle

In this section, we will describe the various information used to build simulations with sphererical particles. Note that exaDEM::Interaction and Shape are described in the section: Polyhedron.

4.1.1. Spheres - Interaction / Contact

The exaDEM::Interaction class in ExaDEM is used to model various types of interactions between spheres themselves and between spheres and drivers. This class serves as a crucial component for identifying two elements within the data grid and characterizing the type of interaction between them. Note that, for the sake of consistency between the sphere and sphere sections, we use the same interaction structure, and that the type field that qualifies the nature of the interaction has the same values as for polyhedra.

Interaction Class Attributes:

• \(id_i\) and \(id_j\): Id of both spheres.

• \(cell_i\) and \(cell_j\): Indices of the cells containing the interacting spheres.

• \(p_i\) and \(p_j\): Positions of the spheres within their respective cells.

• \(sub_i\) and \(sub_j\): Indices of the vertex, edge, or face of the sphere involved in the interaction.

• type: Type of interaction (integer). See Interaction Glossary.

• friction and moment: Storage used for temporary computations.

Note

When the interaction involves a sphere and a driver, particle j is used to locate the driver. In this scenario, cell_j represents the index of the driver. If the driver utilizes a shape, such as with RShapeDriver, sub_j is also utilized to store the index of the vertex, edge, or face.

Glossary of Interaction types for Spheres

Value	Type	Description
0:	Sphere - Sphere	Contact between two vertices of two different spheres
4	Sphere - Cylinder	Contact between a vertex of a sphere and a cylinder
5	Sphere - Surface	Contact between a vertex of a sphere and a rigid surface or wall
6	Sphere - Ball	Contact between a vertex of a sphere and a ball / sphere
7	Sphere - Vertex (Driver)	Contact between a vertex of a sphere and a vertex of a RShape Driver
8	Sphere - Edge (Driver)	Contact between a vertex of a sphere and an edge of a RShape Driver
9	Sphere - Face (Driver)	Contact between a vertex of a sphere and a face of a RShape Driver

Interaction Class Usage With Spheres:

To retrieve data associated with a specific interaction between two spheres, the attributes of the exaDEM::Interaction class are used to identify cells, positions, and interaction types. These informations are then utilized within simulation computations to accurately model interactions between spheres, considering the interaction type.

These interactions are utilized as a level of granularity for intra-node parallelization, applicable to both CPU and upcoming GPU implementations. The interactions are populated within the nbh_sphere operator and subsequently processed in the contact_sphere operator.

In summary, the exaDEM::Interaction class provides a crucial data structure for managing interactions between spheres and drivers within DEM simulations. By storing information such as cell numbers, positions, and interaction types, it enables precise modeling of physical interactions between simulated objects.

4.1.2. Operators

4.1.2.1. randomize_radius

The randomize_radius operator randomly modifies the radius of spherical particles and updates their physical properties accordingly.

For each particle, a new radius is sampled from a Gaussian distribution centered on the current radius. The width of the distribution is controlled by the relative_deviation parameter. After the new radius is computed, the particle mass and inertia tensor are updated consistently assuming that the particle density remains constant.

The radius variation is bounded in order to avoid unrealistic values.

Parameters

• relative_deviation (double, required)

  Relative deviation applied to the particle radius. For example, 0.2 corresponds to a variation of approximately \(\pm 20\%\) around the current radius.

• allow_exceed (bool, optional, default = true)

  Controls whether the new radius is allowed to exceed the original radius.

  • true: the radius may increase or decrease within the allowed range.

  • false: the radius cannot become larger than the initial radius.

• region (optional)

  A ParticleRegionCSG definition used to restrict the operation to particles belonging to a specific region.

• particle_regions (optional)

  Collection of particle regions used to evaluate the region expression.

Example

Basic usage:

- randomize_radius:
    relative_deviation: 0.2

Allowing the radius to increase beyond its initial value:

- randomize_radius:
    relative_deviation: 0.2
    allow_exceed: true

Applying the operator only to a specific particle region:

- randomize_radius:
    relative_deviation: 0.15
    allow_exceed: true
    region: my_region