A novel Minkowski sum contact algorithm for arbitrarily shaped particles constructed by multiple dilated DEM models

Abstract

Nonspherical granular materials are widely used in various industrial fields. Because the simulation of mixed granular flows consisting of arbitrarily shaped particles with smooth surfaces modeled by multiple discrete element models remains difficult for practical applications, a novel Minkowski sum contact algorithm in the CUDA-GPU architecture was proposed. In this algorithm, super-ellipsoidal equations, spherical harmonic functions, and polyhedrons were used to model differently shaped particles with smooth surfaces using the Fibonacci and Minkowski sum algorithms. Subsequently, single or multiple contact points between arbitrarily shaped particles were determined using the Minkowski sum contact algorithm. The automatic mesh simplification and GPU parallel computing methods were employed to improve the calculation efficiency of the discrete element method. The conservation, accuracy, and robustness of the proposed algorithm were verified by four sets of numerical examples: elastic collisions between particles, inelastic collisions between particles, accumulation of multiple particles, and dynamic granular flows. The relative DEM results show good agreement with the analytical solution, which indicates that the proposed Minkowski sum contact algorithm can accurately reflect the dynamic properties of arbitrarily shaped granular materials containing differently dilated DEM models.