Characterization and regeneration of 2D general-shape particles by a Fourier series-based approach

The macroscopic mechanical behaviors of granular construction materials are fundamentally linked to the morphology of the particles. Characterization of real particles is important for exploring the linkage through physical investigation, while regeneration of virtual particles is a key step for reliable numerical investigation. This paper proposes a Fourier series-based approach to represent and characterize two-dimensional (2D) general-shape particles, which is more versatile than the traditional complex Fourier analysis for characterizing 2D nonstar-like particles. Additionally, a numerical algorithm that combines the concepts of principal component analysis and empirical cumulative distribution functions is proposed to generate 2D general-shape particles that bears the morphological features of real particles. The approach can consider both the intrinsic relationships among the Fourier coefficients for the x and y coordinates at the first degree of harmonics. The empirical correlation among the Fourier coefficients at different degrees of harmonics can also be taken into account. Precise controlling the elongation property of virtual particles is also readily achievable in this approach. A comprehensive study with two types of construction material particles reveals that the proposed approach is promising.