Critical time step for DEM simulations of dynamic systems using a Hertzian contact model

被引:72
作者
Burns, Shane J. [1 ]
Piiroinen, Petri T. [2 ]
Hanley, Kevin J. [1 ]
机构
[1] Univ Edinburgh, Inst Infrastruct & Environm, Sch Engn, Edinburgh EH9 3FB, Midlothian, Scotland
[2] Natl Univ Ireland Galway, Sch Math Stat & Appl Math, Galway, Ireland
基金
英国工程与自然科学研究理事会;
关键词
damping; DEM; Hertzian contact; stability; time step; DISCRETE ELEMENT SIMULATIONS; PART II; CRITERIA;
D O I
10.1002/nme.6056
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
The discrete element method (DEM) typically uses an explicit numerical integration scheme to solve the equations of motion. However, like all explicit schemes, the scheme is only conditionally stable, with the stability determined by the size of the time step. Currently, there are no comprehensive techniques for estimating appropriate DEM time steps when a nonlinear contact interaction is used. It is common practice to apply a large factor of safety to these estimates to ensure stability, which unnecessarily increases the computational cost of these simulations. This work introduces an alternative framework for selecting a stable time step for nonlinear contact laws, specifically for the Hertz-Mindlin contact law. This approach uses the fact that the discretised equations of motion take the form of a nonlinear map and can be analysed as such. Using this framework, we analyse the effects of both system damping and the initial relative velocity of collision on the critical time step for a Hertz-Mindlin contact event between spherical particles.
引用
收藏
页码:432 / 451
页数:20
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