散体单元法DEM的核心内容是运用所谓的中心差分法,实际上使用了迭代计算,在计算中确定合理的计算时步及其法向刚度是研究问题非常重要的方面,时步的选取与被研究颗粒的刚度、质量、阻尼,以及它们之间的匹配关系密切相关。目前,确定刚度的一般做法是实测,但实测只能对特定条件进行,且需要研究人员具有较丰富的经验,才能保证计算结果接近实际。本文通过质量—弹簧系统,对DEM计算过程进行理论与数值模拟讨论,给出确定计算时步和法向刚度的选取方法,对同类计算具有一定的参考意义。
The discrete element method (DEM), with its core of using the so-called central difference method, involves actually iterative calculations. During the DEM calculations, the determinations of a reasonable computation time step and the normal stiffness are very important. The determination of the time step is closely related to the stiffness, the mass and the damping of the granule in question, and to their matching relationship. To decide the stiffness is so far through actual measurements. However, it can be done only in some special conditions and it needs a wealth of experience for the simulation results to be close to the practical results. This paper, based on the theoretical consideration and numerical simulations of a mass-spring system, proposes optional ways to determine the calculation time step and the normal stiffness.
[1] Cundall P A, Strack O D L. A discrete numerical model for granule assemblies[J]. Geotechnique, 1979, 29(1): 47-65.
[2] 王永嘉, 邢际波. 离散单元法及其在岩土力学中的应用[M]. 沈阳: 东北工学院出版社, 1991: 9-47. Wang Yongjia, Xing Jibo. Discrete element method and the application in geotechnical mechanics[M]. Shenyang: Northeastern University of Technology Press, 1991: 9-47.
[3] 魏群. 散体单元法的基本原理数值方法及程序[M]. 北京: 科学出版社, 1991: 8-13. Wei Qun. Basic principle and numerical method and program about discrete element method[M]. Beijing: Science Press, 1991: 8-13.
[4] 孙其成, 王光谦. 颗粒物质力学导论[M]. 北京: 科学出版社, 2009: 67-70. Sun Qicheng, Wang Guangqian. An introduction to the mechanics of granular materials[M]. Beijing: Science Press, 2009: 67-70.
[5] 吴清松, 胡茂彬. 颗粒流的动力学模型和实验研究进展[J]. 力学进展, 2002, 32(2): 250-258. Wu Qingsong, Hu Maobin. Advances on dynamic modeling and experimental studies for granule flow[J]. Advances in Mechanics, 2002, 32(2): 250-258.
[6] 徐泳, 孙其诚, 张凌, 等. 颗粒离散元法研究进展[J]. 力学进展, 2003, 33(2): 251-260. Xu Yong, Sun Qicheng, Zhang Ling, et al. Advances in discrete element methods for particulate materials[J]. Advances in Mechanics, 2003, 33(2): 251-260.
[7] 张楚汉. 论岩石、混凝土离散-接触-断裂分析[J]. 岩石力学与工程学报, 2008, 27(2): 217-235. Zhang Chuhan. Discrete-contact-fracture analysis of rock and concrete[J]. Chinese Journal of Rock Mechanics and Engineering, 2008, 27(2): 217-235.
[8] 闫民, 贾启芬, 陈予恕, 等. 振动磨DEM动力学分析模型[J]. 天津大学学报, 2000, 33(1): 60-62. Yan Min, Jia Qifen, Chen Yushu, et al. Dynamic analytical modeling vibration ball mills[J]. Journal of Tianjin University, 2000, 33(1): 60-62.
[9] 闫民, 陈予恕, 曹树谦. 转子系统非线性动力学DEM建模研究[J]. 力学学报, 2001, 33(3): 390-401. Yan Min, Chen Yushu, Cao Shuqian. The study of nonlinear dynamics DEM modeling of rotor systems[J]. Journal of Theoretical Applied Mechanics, 2001, 33(3): 390-401.
[10] 闫民, 尹建业, 孙保平. 沙粒群的散体动力学建模[J]. 科技导报, 2008, 26(6): 66-69. Yan Min, Yin Jianye, Sun Baoping. DEM modeling of sand group dynamics[J]. Science & Technology Review, 2008, 26(6): 66-69.
[11] Yan M, Yin J Y, Sun B P. Granule hydrodynamics method: A discrete element method on fluid motions[J]. International Journal of Computational Methods, 2012, 9(1): 8-9.
[12] Yan M, Zhang K, Chen Y. Dynamic DEM model of multi-spans rotor system[J]. Journal of Sound and Vibration, 2002, 255(5): 867-881.