The discrete element method (DEM) represents a classical and popular research approach to exploring the particle shape effects of granular materials. For many modellers, the acquisition of irregular particle outlines is a problem of considerable practical importance. To mitigate this problem, a novel method based on epicycle series is introduced in this study, and it can produce geometry-controlled particles from two major shape indexes. First, the three key steps of the proposed method are explained: (1) a series of complex numbers, namely, the epicycle series, is used to represent the discrete outline of a particle; (2) the magnitudes of the epicycle descriptors are correlated with the particle shape indexes; and (3) the particle shape is controlled by predicting and adjusting the epicycle descriptors. Then, sensitivity analysis and a case study are conducted to test the proposed method's capacity for reproducing particle shape features. The results suggest that the proposed framework can generate granular particles with accurately controlled shape indexes and realistic outlines, which can facilitate the DEM modelling of irregular particles.

Graphical Abstract

中文翻译：

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通过Epicycle系列随机生成2D几何控制的粒子

离散元素法（DEM）代表了一种探索颗粒材料颗粒形状效应的经典且流行的研究方法。对于许多建模者而言，不规则粒子轮廓的获取是相当重要的现实问题。为了缓解这个问题，本研究介绍了一种基于大环周期序列的新方法，该方法可以从两个主要形状指标生成几何控制的粒子。首先，说明了该方法的三个关键步骤：（1）一系列复数，即Epicycle系列，用于表示粒子的离散轮廓；（2）周转描述符的大小与颗粒形状指数相关；（3）通过预测和调整周转周期描述符来控制粒子形状。然后，进行了敏感性分析和案例研究，以测试所提出的方法再现颗粒形状特征的能力。结果表明，提出的框架可以生成具有精确控制的形状指数和逼真的轮廓的颗粒，这可以促进不规则颗粒的DEM建模。

图形概要