Abstract

There are two key problems in discrete element simulations of super-ellipse systems. One is the determination of contact point, and the other is the mechanical equilibrium with almost zero kinetic energy. The Newton–Raphson method or its modification used to determine the contact point is only sufficiently numerically stable for suitable deformation parameters, and the state of all particles with almost zero velocity is difficult to reach. In this paper, a novel contact detection method for all deformation parameters is used to determine the contact point, and a rolling resistance model is used to dissipate rotational kinetic energy for mechanical equilibrium. A series of tests are investigated to verify the validity of this method. For random packing under gravity, no residual kinetic energy (or almost 0) is observed, and the force that acts on the bottom is equal to the gravity, meaning that the system reaches mechanical equilibrium. After equilibrium, the process of hopper discharge, in which the kinetic energy remains stable for shape and material parameters, is also modeled. Furthermore, direct shear tests at different shear rates are simulated, and the results meet the rate independence, which is in agreement with experiments. The method is also suitable for investigation of sound propagation properties in the super-ellipse system, and the velocities of compressional and shear waves are calculated in uniaxial compression tests. In addition to super-ellipses, the method can be applied to other particle systems once the shape functions are given.

Graphical abstract

After reaching the equilibrium state, a hole is opened at the bottom, and its width is 15 times the width of the particle. Figure shows the snapshots of particle flow at different times. Then, 0.372 seconds later, after 136 particles drop through the hole, a semi-circular structure of force arch occurs, and the particle flow stops. These findings are different from the results of the previous research and show that the shape has a significant effect on the flow rate.

中文翻译：

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超级椭圆系统的离散元模拟

摘要

在超级椭圆系统的离散元素模拟中存在两个关键问题。一个是确定接触点，另一个是具有几乎为零的动能的机械平衡。用于确定接触点的Newton–Raphson方法或其修改对于合适的变形参数仅在数值上足够稳定，并且几乎无法达到速度几乎为零的所有粒子的状态。本文采用一种针对所有变形参数的新型接触检测方法来确定接触点，并使用滚动阻力模型来耗散旋转动能以实现机械平衡。研究了一系列测试以验证该方法的有效性。对于在重力作用下的随机堆积，没有观察到残余动能（或几乎为零），而作用在底部的力等于重力，这意味着系统达到了机械平衡。平衡后，还对料斗卸料过程进行了建模，在该过程中，动能对于形状和材料参数保持稳定。此外，模拟了在不同剪切速率下的直接剪切试验，结果符合速率独立性，这与实验一致。该方法还适用于研究超椭圆系统中的声音传播特性，并且在单轴压缩测试中计算了压缩波和剪切波的速度。一旦给出了椭圆函数，除了超椭圆外，该方法还可以应用于其他粒子系统。还对料斗卸料过程进行了建模，在该过程中，动能对于形状和材料参数保持稳定。此外，模拟了在不同剪切速率下的直接剪切试验，结果符合速率独立性，这与实验一致。该方法还适用于研究超椭圆系统中的声音传播特性，并且在单轴压缩测试中计算了压缩波和剪切波的速度。一旦给出了椭圆函数，除了超椭圆外，该方法还可以应用于其他粒子系统。还对料斗卸料过程进行了建模，在该过程中，动能对于形状和材料参数保持稳定。此外，模拟了在不同剪切速率下的直接剪切试验，结果符合速率独立性，这与实验一致。该方法还适用于研究超椭圆系统中的声音传播特性，并且在单轴压缩测试中计算了压缩波和剪切波的速度。一旦给出了椭圆函数，除了超椭圆形之外，该方法还可以应用于其他粒子系统。这与实验相符。该方法还适用于研究超椭圆系统中的声音传播特性，并且在单轴压缩测试中计算了压缩波和剪切波的速度。一旦给出了椭圆函数，除了超椭圆外，该方法还可以应用于其他粒子系统。这与实验相符。该方法还适用于研究超椭圆系统中的声音传播特性，并且在单轴压缩测试中计算了压缩波和剪切波的速度。一旦给出了椭圆函数，除了超椭圆外，该方法还可以应用于其他粒子系统。

图形概要

达到平衡状态后，在底部开一个孔，其宽度是粒子宽度的15倍。图中显示了不同时间的粒子流快照。然后，在0.372秒后，有136个颗粒从孔中掉落后，出现了力拱的半圆形结构，颗粒流停止了。这些发现与以前的研究结果不同，表明形状对流速有重大影响。