Acceleration of DEM algorithm for quasistatic processes

• Published in: International journal for numerical methods in engineering Vol. 86; no. 7; pp. 816 - 828
• Main Authors: Padbidri, Jagan M., Mesarovic, Sinisa Dj
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 20.05.2011; Wiley
• Subjects: Acceleration; Algorithms; Computation; Cross-disciplinary physics: materials science; rheology; Dimensional analysis; Discrete element method; Exact sciences and technology; Granular solids; inertial manifold; Material form; Mathematical analysis; Mathematical models; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); numerical algorithm; Numerical analysis. Scientific computation; particle dynamics; Physics; Rheology; Sciences and techniques of general use; size dependence; Translations; Performance evaluation; size dependence; Numerical integration; numerical algorithm; Optimal algorithm; Particle motion; Molecular dynamics; Quasi static theory; Discrete element method; particle dynamics; Transverse load; Modeling; Arrangement; Gear; Plate; Particle; Particle method; Manifold; Granular material; Multiscale method; Dimensional analysis; Size effect; inertial manifold; Time integration
• ISSN: 0029-5981; 1097-0207; 1097-0207
• DOI: 10.1002/nme.3076

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.