A novel random generation method of two-dimensional particles based on the complex Fourier series

A systematic method is proposed to randomly generate nonstar-like particles satisfying target shape descriptors. Considering the problem of the reentrance angle, the complex function is selected to describe the particle profile. Correlation analysis is used to determine the total harmonic number of the Fourier series, and a new expression of the phase angle that can be fitted by normal distribution is proposed. Additionally, the “Knot” phenomenon, which occurs when the complex Fourier method is utilized to form particles, is described and the criterion for its occurrence is proposed. Inspired by the particle formation process, a novel method of particle generation is proposed. Through efficiency and error tests, the method is proved to be efficient and stable to generate virtual particles. Ball-shaped, ellipse-shaped, calcareous sands and standard sands are compared in a direct shear test by using discrete element method (DEM). The samples composed of irregular particles show a significant increase in shear modulus, dilatancy and peak stress. Therefore, the particle stochastic generation method in this study is suggested for generating irregular particle with quantified shape parameters.