A discrete element method with spherical harmonics for irregular granular materials based on the level set contact algorithm

Abstract

<p indent=0mm>To calculate the mechanical properties of irregular granular materials in natural or industrial fields, a discrete element model based on spherical harmonics that can describe arbitrarily shaped particles is developed. Considering the uneven surfaces and multiple contact points of the spherical harmonic elements, a contact model of arbitrary shapes based on the level set algorithm is developed to calculate the contact direction and overlap between the elements. In this model, spherical harmonic elements with different shapes are discretized into a zero level set function and a discrete spatial-level set function composed of a series of points. In addition, the contact detection between elements is transformed into a solution of two level set functions. All zero level set points are brought into the spatial-level set function of the neighboring element, and the multiple contact points and forces between the two neighboring elements are determined via trilinear interpolation. The elastic collision of a single particle with a wall, the free fall of a particle, and the packing process of multiple particles are simulated using the discrete element method, and the evolution of the translational and rotational kinetic energy of particles over time is studied to validate the discrete element model of the spherical harmonic function based on the level set method. The results show that the discrete element model of spherical harmonic functions based on the level set method can be used to calculate the contact forces between elements. Meanwhile, the energy of the granular system remains constant during the elastic collision, and the system energy decays during the inelastic collision until the kinetic energy approaches zero. Based on the aforementioned method, the influence of uneven surfaces on the packing fraction and average coordination number of granular materials is analyzed, and an effective discrete element model is provided for the numerical simulation of irregular granular materials.