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Establishing stable time‐steps for DEM simulations of non‐collinear planar collisions with linear contact laws
Author(s) -
Burns Shane J.,
Hanley Kevin J.
Publication year - 2016
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5361
Subject(s) - stability (learning theory) , work (physics) , stiffness , planar , discrete time and continuous time , control theory (sociology) , function (biology) , numerical analysis , forcing (mathematics) , numerical integration , mathematics , computer science , mathematical analysis , engineering , structural engineering , mechanical engineering , statistics , computer graphics (images) , control (management) , machine learning , artificial intelligence , evolutionary biology , biology
Summary The discrete element method, developed by Cundall and Strack, typically uses some variations 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 time‐step. The current methods for estimating appropriate discrete element method time‐steps are based on many assumptions; therefore, large factors of safety are usually applied to the time‐step to ensure stability, which substantially increases the computational cost of a simulation. This work introduces a general framework for estimating critical time‐steps for any planar rigid body subject to linear damping and forcing. A numerical investigation of how system damping, coupled with non‐collinear impact, affects the critical time‐step is also presented. It is shown that the critical time‐step is proportional tom kif 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. © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd.