Acceleration of DEM algorithm for quasistatic processes

The discrete element method (particle dynamics) is an invaluable tool for studying the complex behavior of granular matter. Its main shortcoming is its computational intensity, arising from the vast difference between the integration time scale and the observation time scale (similar to molecular dynamics). This problem is particularly acute for macroscopically quasistatic deformation processes. We first provide the proper definition of macroscopically quasistatic processes, on the basis of dimensional analysis, which reveals that the quasistatic nature of a process is size‐dependent. This result sets bounds for application of commonly used method for computational acceleration, based on superficially increased mass of particles. Next, the dimensional analysis of the governing equations motivates the separation of time scales for the numerical integration of rotations and translations. We take advantage of the existence of fast and slow variables (rotations and translations) to develop a two‐timescales algorithm based on the concept of inertial manifolds suggested by Gear and Kevrekidis. The algorithm is tested on a 2D problem with axial strain imposed by rigid plates and pressure on lateral boundaries. The benchmarking against the accurate short‐time step results confirms the accuracy of the new algorithm for the optimal arrangement of short‐ and long‐time steps. The algorithm provides moderate computational acceleration. Copyright © 2010 John Wiley & Sons, Ltd.