Explicit contact force model for superellipses by Fourier transform and application to superellipse packing

Abstract

This paper presents a method to establish explicit force models for identical superellipses. Currently for two superellipses in contact, the overlap parameters must be solved by using numerical iteration but cannot be explicitly calculated. Our method is firstly to numerically solve these solutions in the comprehensive range of the orientation angles with the angles varying discretely. Then using two-dimensional (2D) discrete Fourier transform (DFT), the discrete solutions as a function of two angles are transformed to the frequency domain. The transformed terms are sorted according to their magnitudes, and those below a certain value are filtered in the inverse discrete Fourier transform (IDFT). This finally results in simplified Fourier series that can approximate overlap parameters explicitly. The method was realized for a wide range of superellipse shapes and the errors between the approximate Fourier series and the original solutions were analyzed and shown to be small. In addition, the established explicit force model was applied to the simulation of the packing of superellipses. The results show that the explicit force model established by this method can be effectively used in DEM simulations. And the packing of superellipses is complicatedly dependent on the squareness, aspect ratio and friction. These findings provide a novel way to establish the explicit force models for non-spherical particles and also improve our understanding on the packing of non-spherical particles.