Mechanical Engineering Department, California State University, Los Angeles, Los Angeles, California 90032, USA.
College of Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA.
Phys Rev E. 2017 Oct;96(4-1):042905. doi: 10.1103/PhysRevE.96.042905. Epub 2017 Oct 13.
We summarize and numerically compare two approaches for modeling and simulating the dynamics of dry granular matter. The first one, the discrete-element method via penalty (DEM-P), is commonly used in the soft matter physics and geomechanics communities; it can be traced back to the work of Cundall and Strack [P. Cundall, Proc. Symp. ISRM, Nancy, France 1, 129 (1971); P. Cundall and O. Strack, Geotechnique 29, 47 (1979)GTNQA80016-850510.1680/geot.1979.29.1.47]. The second approach, the discrete-element method via complementarity (DEM-C), considers the grains perfectly rigid and enforces nonpenetration via complementarity conditions; it is commonly used in robotics and computer graphics applications and had two strong promoters in Moreau and Jean [J. J. Moreau, in Nonsmooth Mechanics and Applications, edited by J. J. Moreau and P. D. Panagiotopoulos (Springer, Berlin, 1988), pp. 1-82; J. J. Moreau and M. Jean, Proceedings of the Third Biennial Joint Conference on Engineering Systems and Analysis, Montpellier, France, 1996, pp. 201-208]. The DEM-P and DEM-C are manifestly unlike each other: They use different (i) approaches to model the frictional contact problem, (ii) sets of model parameters to capture the physics of interest, and (iii) classes of numerical methods to solve the differential equations that govern the dynamics of the granular material. Herein, we report numerical results for five experiments: shock wave propagation, cone penetration, direct shear, triaxial loading, and hopper flow, which we use to compare the DEM-P and DEM-C solutions. This exercise helps us reach two conclusions. First, both the DEM-P and DEM-C are predictive, i.e., they predict well the macroscale emergent behavior by capturing the dynamics at the microscale. Second, there are classes of problems for which one of the methods has an advantage. Unlike the DEM-P, the DEM-C cannot capture shock-wave propagation through granular media. However, the DEM-C is proficient at handling arbitrary grain geometries and solves, at large integration step sizes, smaller problems, i.e., containing thousands of elements, very effectively. The DEM-P vs DEM-C comparison is carried out using a public-domain, open-source software package; the models used are available online.
我们总结并数值比较了两种用于模拟干颗粒物质动力学的方法。第一种方法是通过罚函数的离散元法（DEM-P），常用于软物质物理和地质力学领域；它可以追溯到 Cundall 和 Strack 的工作[P. Cundall，Proc. Symp. ISRM，Nancy，France 1，129（1971）；P. Cundall 和 O. Strack，Geotechnique 29，47（1979）]。第二种方法是通过互补性的离散元法（DEM-C），它认为颗粒是完全刚性的，并通过互补条件来强制不穿透；它常用于机器人和计算机图形学应用领域，在 Moreau 和 Jean 中有两个强有力的推动者[J. J. Moreau，in Nonsmooth Mechanics and Applications，edited by J. J. Moreau and P. D. Panagiotopoulos（Springer，Berlin，1988），pp. 1-82；J. J. Moreau and M. Jean，Proceedings of the Third Biennial Joint Conference on Engineering Systems and Analysis，Montpellier，France，1996，pp. 201-208]。DEM-P 和 DEM-C 明显不同：它们使用不同的(i)方法来模拟摩擦接触问题，(ii)组模型参数来捕捉感兴趣的物理现象，以及(iii)类数值方法来求解控制颗粒物质动力学的微分方程。在这里，我们报告了五个实验的数值结果：冲击波传播、圆锥贯入、直剪、三轴加载和料斗流动，我们用这些结果来比较 DEM-P 和 DEM-C 的解。这项工作帮助我们得出两个结论。首先，DEM-P 和 DEM-C 都是可预测的，即通过捕捉微观尺度上的动力学来很好地预测宏观尺度上的涌现行为。其次，存在一类问题，其中一种方法具有优势。与 DEM-P 不同，DEM-C 无法捕捉通过颗粒介质的冲击波传播。然而，DEM-C 擅长处理任意的颗粒几何形状，并在较大的积分步长下，非常有效地解决包含数千个元素的较小问题。DEM-P 与 DEM-C 的比较是使用一个公共的、开源的软件包进行的；所使用的模型可在线获得。
