ITASCA PFC3D 7.0.146

The PFC programs (PFC2D and PFC3D) provide a general purpose, distinct-element modeling framework that includes both a computational engine and a graphical user interface. A particular instance of the distinct-element model is referred to as a PFC *model*. The term PFC *model* refers to both the 2D and 3D models. The PFC model simulates the movement and interaction of many finite-sized particles The particles are rigid bodies with finite mass that move independently of one another and can both translate and rotate. Particles interact at pair-wise contacts by means of an internal force and moment. Contact mechanics is embodied in particle-interaction laws that update the internal forces and moments. The time evolution of this system is computed via the distinct-element method, which provides an explicit dynamic solution to Newton’s laws of motion. The PFC model provides a synthetic material consisting of an assembly of rigid grains that interact at contacts and includes both granular and bonded materials.

Thanks to its general design, PFC can be easily customized and applied to a very broad range of numerical investigations where the discrete nature of the systems is of interest. Since the release of the first version in 1994, PFC has been successfully used by many academic institutions and private companies around the world for problems ranging from fundamental research on soil and rock behavior at the laboratory scale to slope stability and rockfall hazard mitigation, hydraulic fracturing, rock-tool interactions, bulk flow, mixing, conveying and compaction of aggregates and powders, blast furnace modeling, etc. A large panel of references can be found in the proceedings of the past PFC and *FLAC/DEM* symposia periodically organized by Itasca.

## The PFC Model

A general particle-flow model simulates the mechanical behavior of a system made up of a collection of arbitrarily shaped particles. (Note that the term *particle*, as used here, differs from its more common definition in the field of mechanics, where it is taken as a body whose dimensions are negligible and therefore occupies only a single point in space. In the present context, the term *particle* denotes a body that occupies a finite amount of space.) The model is composed of distinct particles that displace independent of one another and interact at pair-wise contacts. If the particles are assumed to be rigid, then the mechanical behavior of such a system is described in terms of the movement of each particle and the inter-particle forces acting at each contact point. Newton’s laws of motion provide the fundamental relationship between particle motion and the forces causing that motion. The force system may be in static equilibrium (in which case, there is no motion), or it may be such as to cause the particles to flow. If the particle-interaction law models a physical contact between particles, the behavior of the contacts is characterized using a soft contact approach, in which a finite normal stiffness is taken to represent the measurable stiffness that exists at a contact, and the rigid particles are allowed to overlap in the vicinity of the contact point. More complex behavior can be modeled by allowing the particles to be bonded together at their contact points such that, when the inter-particle forces acting at any bond exceed the bond strength, that bond is broken. This allows tensile forces to develop between particles. One can then model the interaction of these bonded “blocks,” including the formation of cracks that may cause blocks to fragment into smaller blocks. The particle-interaction law can also be derived from potential energy functions and model long range interactions.

PFC provides a particle-flow model containing the following assumptions:

- The particles are treated as rigid bodies.

- The fundamental particle shape is a {disk with unit thickness in 2D; sphere in 3D}, denoted
ball.

- The clump logic supports the creation of rigidly attached {disks with unit thickness in 2D; spheres in 3D}, denoted
pebbles. Each clump consists of a set of overlapping pebbles that acts as a rigid body with a deformable boundary. Clumps may be of arbitrary shape.

- Particles interact at pair-wise contacts by means of an internal force and moment. Contact mechanics is embodied in particle-interaction laws that update the internal forces and moments.

- Behavior at physical contacts uses a soft-contact approach where the rigid particles are allowed to overlap one another at contact points. The contacts occur over a vanishingly small area (i.e., at a point), and the magnitude of the overlap and/or the relative displacement at the contact point are related to the contact force via the force-displacement law.

- Bonds can exist at contacts between particles.

- Long range interactions can also be derived from energy potential functions.
Product:ITASCA PFC3D 7.0.146

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