| Granular materials are complex systems composed of a large number of solid particles,which are widely present in nature and industrial productions.The discrete element method(DEM)is an important tool for simulating the macroscopic and microscopic characteristics of granular materials,and spherical particles are originally used to represent solid particles.However,irregular granular materials are widely found in nature and industrial productions.Compared with spherical particles,irregular particles have lower fluidity and stronger interlocking properties.The particle shape significantly affects the contact mode between the particles,thereby changing the flow state of granular materials.More importantly,the conclusions drawn from spherical granular materials cannot simply applied to irregular granular materials.In addition,parallel algorithms based on the graphics processing unit(GPU)have been used in DEM simulations of spherical particles,which have higher computational efficiency and can meet large-scale engineering applications.Since irregular particles have a more complex contact theory than spherical particles,they have lower computational efficiency and smaller calculation scales in DEM simulations.Meanwhile,it is difficult to perform numerical calculations of large-scale irregular particles.Therefore,the development of irregular construction methods,contact theories,and GPU high-performance parallel algorithms are important issues in DEM simulations.In this work,the superquadric model,the multi-superquadric model,the poly-superquadric model,and the spherical harmonic function model based on the level set contact theory are developed and used to construct irregular particles with different aspect ratios,surface sharpness,and concave-convex characteristics;the GPU high-performance parallel algorithm is developed for DEM models;the effects of particle shapes and boundary conditions on the flow,mixing,and segregation characteristics of granular materials are analyzed in detail.The specific work can be divided into the following points:(1)Superquadric DEM model based on continue function representationsThe superquadric equation is used to construct ellipsoids,cylinders,and cubic particles with different aspect ratios and surface sharpness.The Newton-Raphson iterative method is used to calculate the overlap and normal direction between superquadric elements,and the radius of the average curvature at the local contact points is brought into the contact force model to calculate the force between irregular particles;the contact problem of superquadric elements and complex structures is transformed into the contact detection of superquadric elements and triangular elements,and three theories of face contact,edge contact,and vertex contact are developed;the numerical results calculated by the superquadric DEM model are compared with the experimental results to verify this model.(2)Multi-superquadric and poly-superquadric models based on superquadric equationsSince the superquadric elements have the characteristics of central symmetry and strictly convex shapes,several superquadric elements are combined with a certain overlap to represent a multi-superquadric model.This model can be used to construct geometric asymmetry and concave shaped particles.Another method is to splice together eight one-eighth superquadric elements to represent a poly-superquadric model,and this model can be used to construct convex particles with asymmetric geometric shapes and smooth surfaces.In two DEM models,the contact detection between the elements is transformed into the contact detection between the superquadric elements.Meanwhile,the local coordinate system and the corresponding transformation matrix are used to update the rotation and position information of the particles.The numerical results calculated by these models are compared with the theoretical results to verify these models.(3)Spherical harmonic function model based on the level set contact theoryDue to the concave geometry characteristics and multiple contact points of the spherical harmonic function elements,a contact theory based on the level set method is developed.The spherical harmonic function element is discretized into a zero level set function and a spatial level set function composed of a series of points,and the contact detection between the spherical harmonic function elements is transformed into a solution between two level set functions.The value and gradient of the level set function calculated by using the trilinear interpolation method are the overlap and the normal direction between elements,respectively.All contact forces are accumulated to realize the calculation of multiple contact forces between spherical harmonic function elements.This model is used to simulate the elastic collision process of particles to verify the conservation of energy,and the inelastic collision process of particles is simulated to verify the numerical stability.Moreover,the influence of particle shapes on the packing characteristics of granular materials is further analyzed.(4)Parallel algorithms for irregular DEM models based on the CUDA-GPU architectureThe irregular particles are constructed using the superquadric model,and the parallel algorithm based on the CUDA-GPU architecture is developed.The cell linked method is used to create the neighbor list,and the bounding box and Newton interation methods are used to create the bounding box list and the contact point list,respectively.These two lists can improve the parallel efficiency of DEM simulations.Meanwhile,the index of the contact pair is stored in the reference list,so that the contact forces and moments between particles are directly accumulated on the GPU device.This avoids the data exchange between the CPU device and the GPU device.The GPU parallel algorithm is used to generate millions of irregular granular materials,and the numerical results of the flow process of granular materials are compared with the experimental results to verify this model.Based on the GPU parallel algorithm,the influences of the particle number and shapes on the computational time and the speedup ratio between CPU and GPU are further analyzed.(5)Study on the flow pattern transition,mixing,and segregation characteristics of irregular granular materials in the flow processThe flow states of irregular granular materials in silos and rotating drums are complicated,and the study of their dynamic characteristics has important reference value for the application of irregular granular materials in the industrial production and design.Hence,the superquadric DEM model is used to simulate the flow behaviors of irregular granular materials in silos and rotating drums,and the influences of particle shapes and boundary conditions on the flow pattern transition,mixing,and segregation characteristics are analyzed.In a gravity-driven granular flow,spherical particles are in a mass flow at the upper part of the silo and in a funnel flow at the lower part of the silo,and cylindrical particles are basically in a funnel flow.The critical transition height between the two flow states decreases as the hopper angle and external pressure increase.In addition,the granular materials with the same particle size in a horizontal drum are mixed,and the gaussian-dispersed mixture are segregated,that is,the particles with the smallest and largest particle sizes are located in the center and the periphery of the granular bed,respectively.Irregular particles have a tighter contact mode and stronger interlocking than spherical particles,which limit the sliding and relative rotation of the particles and cause the unevenness of the velocity distribution and the flow pattern transition.Furthermore,the collision force between particles is the main factor driving the mixing and dispersion of the particles.The penetration behaviors between particles are limited by the close contact mode and local cluster structures,which is conducive to the mixing of particles. |
