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Equivalent normal stiffness of the ball in granular dynamics simulations

机译：颗粒动力学模拟中球的等效法向刚度

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摘要

In the paper a concept of an equivalent normal ball stiffness based on averaging the work done by the nonlinear Hertz force during the impact is introduced and a numerical assessment is made on its efficiency in simulating collinear collisions. The systems of balls investigated, ranging from 2 to 30, are considered to be coupled and conservative. The energy and momentum conservation principles are used to assess the accuracy of simulation results. The effect of the time step for both linear and nonlinear models is investigated and it is shown that the linear model allows an increased time step compared to a nonlinear one while meeting energy and momentum conservation requirements with the same accuracy. In the paper also the pattern of break up for both models and different number of balls is investigated. It is found that for both models the pattern is the same: the balls are disconnected one at the time with constant rate and this rate does not depend on the number of balls.
机译：在本文中，提出了一个等效法线刚度的概念，该概念基于对冲击过程中非线性赫兹力完成的功进行平均的方式，并对其在模拟共线碰撞中的效率进行了数值评估。所研究的球系统范围从2到30，被认为是耦合和保守的。能量和动量守恒原理用于评估仿真结果的准确性。研究了线性和非线性模型的时间步长的影响，结果表明，与非线性模型相比，线性模型允许增加时间步长，同时以相同的精度满足能量和动量守恒的要求。在本文中，还研究了两种模型和不同数量球的破裂模式。发现对于这两个模型，模式是相同的：球以恒定的速率同时断开一个，并且该速率不取决于球的数量。

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