PFC Contact Models

As balls, clumps, rigid blocks, and walls (i.e., pieces) are rigid in PFC, all deformation between surfaces of adjacent pieces occurs at contacts. Specific contact models (i.e., particle-interaction laws) can be inserted to represent different physical situations using a soft contact representation where the pieces do not deform but and piece overlaps are allowed. Forces and moments are computed based on the degree of overlap. Contact models can use the piece properties to determine the resulting interactions. Contacts are created and deleted automatically during model cycling. PFC uses the null model contact model by default and therefore the user is required to explicitly specify which contact model(s) should be used in each PFC model. Each contact is assigned a single contact model manually or via the Contact Model Assignment Table (CMAT).

Contact Model Assignment Table

The Contact Model Assignment Table (CMAT) brings flexibility, using the range logic, to assigning contact models without complex FISH functions. Upon contact creation, the CMAT provides the contact model and its properties (which may be derived from the properties of two contacting surfaces). As a result, complex models involving heterogeneous material properties can be synthesized in a straightforward manner.

The Contact Model Assignment Table (CMAT) controls the assignment of contact models and their associated properties to newly created contacts and also provides the detection distances used by the contact-creation procedure.

Built-in Contact Models

The contact models provided with PFC are listed in the table below, together with their typical usage. The linear, rolling resistance linear, linear contact bond, and linear parallel bond contact models share many characteristics, and thus, are referred to as linear-based models. The linear contact bond, linear parallel bond, smooth joint, and flat joint contact models utilize the bonding concept wherein shear and/or tensile forces may develop as a consequence of relative motion. These models may be used to model Bonded-Particle Materials (BPMs).

Contact model name Description
Null The null contact model is the default contact model with no mechanical interaction. No force or moment is generated.
Linear The linear model reproduces the mechanical behavior of an infinitesimal, linear elastic and frictional interface that carries a point force. The interface does not resist relative rotation and optional viscous dashpots may be activated.
Linear Contact Bond The linear contact bond model provides the behavior of an infinitesimal, linear elastic, and either frictional or bonded interface that carries a point force and does not resist relative rotation.
Linear Parallel Bond The linear parallel bond model provides the force-displacement behavior of a finite-sized piece of cementitious material deposited between two pieces in the vicinity of the contact location, acting in parallel with a linear model.
Soft-Bond Similar to the linear parallel bond with the addition that a softening parameter can be specified to modify the stiffness in the post tensile failure regime, allowing for a degradation of the tensile stiffness as a function of increasing bond elongation.
Rolling Resistance Linear

Based on the linear model but incorporates a torque acting on the contacting pieces to resisting rolling motion for granular applications.

Adhesive Rolling Resistance Linear Based on the rolling resistance linear model to which an adhesive component is added. The cohesion arises from a short-range attraction, which is a linear approximation of the van der Waals force law.
Flat Joint A flatjoint contact simulates the behavior of an interface between two notional surfaces, each of which is connected rigidly to a ball or pebble. The notional surfaces are called faces, which are lines (PFC2D) or disks (PFC3D).
Smooth Joint The smoothjoint model simulates the behavior of an interface regardless of the local particle contact orientations along the interface. The behavior of a frictional or bonded joint can be modeled by assigning smooth-joint models to all contacts between particles that lie on opposite sides of the joint.
Hertz The Hertz contact model in PFC consists in a non-linear formulation based on an approximation of the theory of Mindlin and Deresiewicz.
Hysteretic The Hysteretic contact model in PFC consists in a combination of the elastic portion of the Hertz model as described in the Hertz Contact Model document, combined an alternate dashpot group consisting in a nonlinear visco-elastic element in the normal direction.
Burger's Simulates creep mechanisms by using a Kelvin model and a Maxwell model connected in series in both the normal and shear directions.
Linear-Based Models

The linear, rolling resistance linear, linear contact bond, and linear parallel bond contact models share many characteristics, and thus, are called linear-based models. The linear-based models were also available in PFC 4.0. The distinct-element modeling framework within which they are embedded has been generalized and expanded in PFC 5.0 and PFC 6.0 so that their implementation differs from that in PFC 4.0; however, the contact mechanics embodied in these models remains the same so that their behavior in PFC 4.0 can be reproduced in PFC 5.0 and PFC 6.0.

The linear-based models provide two standard bonding behaviors embodied in the contact bonds and parallel bonds. These bonds can be installed at both ball-ball and ball-facet contacts. Both bonds can be envisioned as a kind of glue joining the contacting pieces. The contact-bond glue is of a vanishingly small size that acts only at the contact point, while the parallel-bond glue is of a finite size that acts over a 2D rectangular or 3D circular cross-section lying between the contacting pieces. The contact bond can transmit only a force, while the parallel bond can transmit both a force and a moment. By default, pieces are not bonded. Bonds are created by invoking the bond method. Bonds are removed when their strength is exceeded or by invoking the unbond method.

Bonded-Particle Materials (BPM) and Interfaces

The bonded-particle modeling methodology defines materials and interfaces based on the contact models that are employed. The following materials and interfaces are defined. A contact-bonded material is a granular assembly with all contacts using the linear contact bond model. A parallel-bonded material is a granular assembly with all contacts using the linear parallel bond model. A flat-jointed material is a granular assembly with all contacts using the flat-joint model. A smooth-jointed interface can be inserted into the contact-bonded, parallel-bonded and flat-jointed materials by identifying the contacts near the interface and replacing their contact models with the smooth-joint model.

A BPM material is created by bonding selected contacts of a packed particle assembly. Contacts are bonded by invoking the bond method of the contact model. One can ensure the existence of contacts between all pieces with a contact gap less than a specified bonding gap (gb) by specifying gb as the proximity in the Contact Model Assignment Table (CMAT).

C++ Contact Models

Enables users to add new contact models in PFC. A contact model describes the force-displacement response at a contact. During each cycle, the PFC program calls each contact model (passing in relevant information about the two contacting entities) and the contact model updates the force and moment acting in an equal and opposite sense on the two contacting entities. User-defined contact models are written in C++ and compiled as DLL (dynamic link library) files to be loaded whenever needed in a PFC simulation. The Visual Studio 2010 C++ compiler is used to compile the DLL files. Source files for all PFC contact models are provided to users. This component provides the flexibility to incorporate the physics relevant to particular problems into the distinct-element framework.

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