Fourier series-based discrete element method for two-dimensional concave irregular particles

This paper aims to develop a discrete element method (DEM) framework applicable to two-dimensional star-shape particles with concave features. Particle contours are represented by the Fourier series expansion of radii to take advantage of its limited number of coefficients. The essential ingredients of DEM, i.e., contact detection and contact resolution, are tailored to consider the possible concave feature of star-shape particles and the overlapping area of particles. A multilevel method is adopted to identify possible multiple contacts between two particles or between a particle and a boundary. The approaches for determining the contact geometric features of both convex-shape and concave-shape overlapping areas are presented. The methods to calculate the contact forces and to determine the overlapping area-based normal contact stiffness are provided. With the developed DEM program-SSP2D, three series of numerical tests are conducted to demonstrate its capability and efficiency in modeling dynamic and pseudo-static behaviors of concave particles.