Critical time step for DEM simulations of dynamic systems using a Hertzian contact model
Critical time step for DEM simulations of dynamic systems using a Hertzian contact model
复制标题
DOI：
10.1002/nme.6056
复制
发表时间：
2019-08-03
影响因子：
2.9
通讯作者：
Hanley, Kevin J.
中科院分区：
文献类型：
--
作者：
Burns, Shane J.;Piiroinen, Petri T.;Hanley, Kevin J.
离散元法 (DEM) 通常使用显式数值积分方案来求解运动方程。然而，与所有显式方案一样，该方案只是有条件稳定，稳定性由时间步长决定。目前，当使用非线性接触相互作用时，没有全面的技术来估计适当的 DEM 时间步长。通常的做法是对这些估计应用较大的安全系数以确保稳定性，但这不必要地增加了这些模拟的计算成本。这项工作引入了一种替代框架，用于为非线性接触定律（特别是赫兹-明德林接触定律）选择稳定的时间步长。该方法利用了这样一个事实：离散运动方程采用非线性映射的形式，并且可以这样进行分析。 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.
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.