DEM verification of the damping effect in a freely falling particle motion for quasi- and non-quasi-static conditions
- 30 Downloads
The discrete element method (DEM) has been widely used in numerical evaluations in geotechnical engineering; however, simple analysis and verification are still needed to obtain the interaction mechanism between a single particle and a wall under a damping effect. A single freely falling particle model is proposed, and the analytical solutions for the stages of particle freefall, fixed wall contact, and rebound are obtained for different damping types and values. Timestepping in quasi-static and non-quasi-static conditions is considered for better understanding of the DEM hypothesis. The numerical results are quite consistent with the analytical solution. The linear and exponential relationships between the restitution coefficient and the local and viscous damping, respectively, are obtained and formulized. Kinetic energy dissipation is larger with the viscous damping effect than for the local damping when comparing the particle rebound height. Verification of the analytical and numerical solutions has been conducted with the previous studies which shows good agreement. The timestep is no longer constant when the particle velocity exceeds approximately 1.55 m/s, which means the DEM system is no longer quasi-static.
KeywordsDiscrete element method Analytical solution Damping coefficient Timestepping Quasi-static condition
The project was financially supported by the sub-topic “Study on calculation method of design flood for disaster causing in mountain basin” of the National Key R&D Program of China (no. 2017YFC1502503), “the Fundamental Research Funds for the Central Universities” (2017-YB-014; 2017-ZY-013), and the National Natural Science Foundation of China (no. 51408450).
- Crowe C, Sommerfeld M, Tsuji Y (1997) Multiphase flows with droplets and particles. CRC Press, Boca RatonGoogle Scholar
- Cundall PA (1987) Distinct element models of rock and soil structure. Analytical and computational methods in engineering rock mechanics. E.T. Brown, ed., George Allen and Unwin, London, 129-163Google Scholar
- Cundall PA (1971) A computer model for simulating progressive large scale movements in blocky rock systems. in Proceedings of the Symposium of the International Society of Rock Mechanics (Nancy, France, 1971), Vol. 1, Paper No. II-8Google Scholar
- Itasca Consulting Group: Inc. PFC3D, Version 4.0. Minneapolis: Itasca (2004)Google Scholar
- Navarro HA, Braun MPDS (2013) Linear and nonlinear hertzian contact models for materials in multibody dynamics. 22nd International Congress of Mechanical EngineeringGoogle Scholar
- Pöschel T, Schwager T (2005) Computational granular dynamics: models and algorithms. Springer-Verlag, BerlinGoogle Scholar
- Thornton C, Ning Z, Wu CY, Nasrullah M, Li LY (2001) Contact mechanics and coefficients of restitution. In: Poschel T, Luding S (eds) Granular Gases. Springer, Berlin, pp 55–66Google Scholar