Software: PFC

Distinct Element Method

The motion and interaction of a system of disks/spheres is simulated by a time-marching scheme that integrates the equations of motion by a central, finite-difference method that ensures excellent accuracy and freedom from drift. Even quasi-static systems are solved with the same dynamic scheme, allowing physical instability and path dependence to be tracked without numerical problems.

The explicit calculation cycle (illustrated opposite) solves two sets of equations — motion and constitutive. In both sets, variables on the right-hand-side of expressions are all known, and can be regarded as fixed for the duration of the step. Thus, nonlinear contact relations (even extreme examples of softening, such as brittle bond breakage) are used without difficulty, because only local conditions are relevant during the timestep. No iterations are necessary to follow nonlinear laws, and no matrices are formed. The formulation is based on that of Cundall & Strack (1979), with several enhancements, such as bonded contacts (Potyondy & Cundall, 2004), alternative damping schemes, and more general wall logic.

In parallel with the mechanical calculations, there is continuous activity to detect new contacts between particles and delete contacts when particles separate. The algorithms are invisible to the user of PFC, and they are optimized to consume very little calculation time. For example, the detection logic is only triggered at a local level when movement sufficient to allow potential new contacts has accumulated. Overall, the searching and detection scheme executes in a time that is linearly dependent on the number of particles.

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Cundall, P. A., and O. D. L. Strack. "A Discrete Model for Granular Assemblies," Geotechnique, 29(1), 47-65 (1979).

Potyondy, D. O., and P. A. Cundall. (2004) "A Bonded-Particle Model for Rock," Int. J. Rock Mech. Min. Sci., 41, 1329-1364.