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Abstract
The discrete element method, developed by Cundall and Strack, typically uses some variation of the central difference numerical integration scheme. However, like all explicit schemes, the scheme is only conditionally stable, with the stability determined by the size of the timestep. The current methods for estimating appropriate DEM timesteps are based on many assumptions; therefore large factors of safety are usually applied to the timestep to ensure stability which substantially increases the computational cost of a simulation. This work introduces a general framework for estimating critical timesteps for any planar rigid body subject to linear damping and forcing. A numerical investigation of how system damping, coupled with noncollinear impact, affects the critical timestep is also presented. It is shown that the critical timestep is proportional to $\sqrt{\frac{m}{k}}$ if a linear contact model is adopted, where $m$ and $k$ represent mass and stiffness, respectively. The term which multiplies this factor is a function of known physical parameters of the system. The stability of a system is independent of the initial conditions.
Original language  English 

Pages (fromto)  186200 
Number of pages  15 
Journal  International Journal for Numerical Methods in Engineering 
Volume  110 
Issue number  2 
Early online date  22 Sep 2016 
DOIs  
Publication status  Published  2016 
Fingerprint Dive into the research topics of 'Establishing stable timesteps for DEM simulations of noncollinear planar collisions with linear contact laws'. Together they form a unique fingerprint.
Projects
 1 Finished

Improving estimates of critical timesteps for discrete element simulations
7/12/15 → 6/05/17
Project: Research