Highlights

Funding for this work has been provided by The O'Reilly Foundation and David and Lucile Packard Foundation. Professor Ng of the University of New Mexico provided the source code for the program Ellipse3D. Two excellent reviews by anonymous reviewers significantly helped the authors to address a number of shortcomings in the first draft of this paper and the sharing of their insight and expertise is gratefully acknowledged.

Keywords Simulation, Time measurement

Abstract The distinct element method as proposed by Cundall and Strack uses the computationally efficient, explicit, central difference time integration scheme. A limitation of this scheme is that it is only conditionally stable, so small time steps must be used. Some researchers have proposed using an implicit time integration scheme to avoid the stability issues arising from the explicit time integrator typically used in these simulations. However, these schemes are computationally expensive and can require a significant number of iterations to form the stiffness matrix that is compatible with the contact state at the end of each time step. In this paper, a new, simple approach for calculating the critical time increment in explicit discrete element simulations is proposed. Using this approach, it is shown that...