A geometric algorithm based on the advancing front approach for sequential sphere packing

The arrangement of calculation samples with a high initial solid fraction and lower computation times are the primary concern of discrete element simulations. When generating thousands of particles, the advancing front algorithm, as one of the effective constructive packing methods, provides a time-saving and non-overlapping packing methodology compared to dynamic approaches, which are extremely time consuming in these situations. This paper proposes a sequential packing algorithm based on the advancing front approach. New particles with random sizes are sequentially inserted into a predefined void space to make contact with at least three existing neighboring particles by analytically solving the trilateration equations. The algorithm allows for an arrangement of particles with random sizes to obtain a low-porosity particle assembly. To increase the algorithm efficiency, a feasible measure of the spatial gridding is proposed to simplify the detection of the advancing fronts. The generated packings can be isotropic, and the number of contacts per particle is sufficiently high to reach a stable state. When the generated packing structures are filled with particles, the physical properties, including the average coordination number, solid fraction, second-order fabric tensor, contact orientation and particle size distribution, are analyzed with different size ratios. Examples of practical geometric models for real industrial applications to railway ballast and a gear are presented.