Random generation of 2D geometry-controlled particles via the epicycle series

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: [Figure not available: see fulltext.]