Particle Shape in PFC

There is one important distinction that should be recognized when applying PFC, as opposed to a continuum code, to a modeling situation: the fundamental element in PFC is a {disk with unit thickness in 2D; sphere in 3D}. If the physical problem is concerned with the movement and interaction of {disks in 2D; spheres in 3D}, then PFC may be applied directly [OSullivan2004]. If the particles to be modeled have complex shapes, representing these shapes accurately may be important in the numerical model. There are three ways of representing blocky shapes with PFC:

• by bonding two or more spherical particles together, forming a cluster. The spherical particles are rigid, but contacts are soft. Thus, the response of the assembly is studied by adjusting the parameters at the particle and contact levels; the constitutive behavior of the assemblage is derived automatically from the contact model and properties. In [Cheng2003], the authors use this technique to simulate the mechanical response of assemblies of such clusters, or crushable agglomerates, under isotropic compression and triaxial compression. The numerical results, compared to experimental data obtained on silica sand specimen, show that the model is capable of replicating the complex behavior of sands in relation to their strength, dilatancy, and critical states. As a limiting case, every particle may be bonded to its neighbor; the resulting assembly can be regarded as a “solid” that has elastic properties and is capable of “fracturing” when bonds break in a progressive manner. This is the essence of the Bonded-Particle Model (BPM) methodology described in [Potyondy2004f]. A comprehensive overview the the BPM methodology and applications can be found in [Potyondy2014].

• by using clumps to approximate complex shapes as collections of pebbles rigidly attached. A clump behaves as a rigid body. The inertia parameters of a clump can be automatically computed from the shape geometry or from the outer surface delineated by the pebble distribution or input by the user. Clump templates may be defined by the user and replicated at will in the PFC model. The tutorial example “Clumps in a Box” illustrates this feature. [Cho2007] compared the mechanical response of BPM specimen made of spheres and clumps, and showed that the introduction of complex particle shapes using the clump model permits predictive validation of 2D DEM models once calibrated. More recently, [Rong2013] constructed 3D BPM with clumps, which showed good agreement between experimental data of a triaxial compression test on quartz sandstone and studied the influence of the particle sphericity index on the deformability and strength of the specimen.

• by using rigid blocks to model closed, convex, and manifold shapes — polygons in 2D, and polyhedra in 3D. The facets of the rigid blocks are linear segments in 2D, triangles in 3D. As with clumps, the full inertia tensor is used to update the rotational equations of motion (see the description here). The inertial properties of each rigid block are computed as presented here. Facet connectivity information is retained to assist in contact detection and resolution. Rigid blocks exist within the model domain and can interact with balls, clumps, walls, zones (via the wall-zone coupling) and structural elements in 3D (via the wall-structure coupling and also directly). They can be created from vertices, imported from geometry objects, cut, and they also support edge/vertex rounding.