An energy consistent frictional dissipating algorithm for particle contact problems

Abstract

An energy frictional dissipating algorithm (EFDA) for time integration of Coulomb frictional impact-contact problems is presented. With the use of the penalty method, and in the context of a conserving framework, linear and angular momenta are conserved, and energy is consistently dissipated. Previously published formulations were stable, forcing the energy dissipation to be monotonic to prevent unstable energy growth. The shortcoming of many was that they were not able to reproduce the real kinematics and dissipation of physical processes, provided by analytical formulations and experiments. EFDA formulates a conserving framework on the basis of a physical energy dissipation estimator. This framework uses an enhanced penalty contact model based on a spring and a dashpot, enforcing physical frictional energy dissipation, controlling gap vibrations, and modifying the velocities and contact forces during each time step. The result is that the dissipated energy, kinematics, and contact forces are consistent with the expected physical behavior. Energy frictional dissipating algorithm has been applied to four rigid-body frictional problems using the discrete element method. The first problem is the analysis of a disk moving on a flat rough surface; the second problem analyzes the kinematics and energy dissipation of elliptical particle impacts. Numerical solutions are compared with analytical ones in both problems. The motion and impact of two disks moving on a semicircular surface are studied in the third problem. Finally, the fourth problem simulates the collapse of a two-dimensional granular column, which is compared with the experimental results.