Computational Mechanics of Arbitrarily Shaped Granular Materials (Springer Tracts in Mechanical Engineering)

Preface
Contents
1 Introduction
	1.1 Discrete Element Methods for Arbitrarily Shaped Particles
		1.1.1 Arbitrarily Shaped DEM Model Based on Functional Representations
		1.1.2 Arbitrarily Shaped DEM Model Based on Geometric Topology
		1.1.3 Arbitrarily Shaped DEM Model Based on Combined Particle Approach
		1.1.4 Novel Discrete Element Methods for Arbitrarily Shaped Particles
	1.2 High Performance Computation of Discrete Element Methods
		1.2.1 GPU Parallel Algorithm for Spherical Particles
		1.2.2 GPU Parallel Algorithm for Non-spherical Particles
	1.3 DEM Analysis of the Flow Characteristics of Granular Materials
		1.3.1 Flow Properties of Granular Materials in Silos
		1.3.2 Mixing and Segregation Properties of Granular Materials in Rotating Drums
	1.4 Summary
	References
2 Superquadric DEM Model Based on Functional Representations
	2.1 Construction of Superquadric Elements
		2.1.1 Superquadric Elements Based on Continuous Function Representation
		2.1.2 Calculation of Mass and Moment of Inertia
	2.2 Contact Algorithm and Contact Force Model
		2.2.1 Contact Detection Between Particles
		2.2.2 Contact Detection Between Particles and Structures
		2.2.3 Nonlinear Contact Force Model Considering Equivalent Curvature
	2.3 Numerical Validation and Applications
		2.3.1 Collision of Two Ellipsoidal Particles
		2.3.2 Experimental Validation of Hopper Discharge
		2.3.3 Analysis of the Flow Process of Granular Materials in a Silo
	2.4 Summary
	References
3 Multi-superquadric and Poly-superquadric DEM Models
	3.1 Discrete Element Method for Multi-superquadric Elements
		3.1.1 Functional Representation of Multi-superquadric Elements
		3.1.2 Calculation of Mass and Moment of Inertia
		3.1.3 Contact Detection Between Multi-superquadric Elements
		3.1.4 Position and Information Update of Elements
	3.2 Discrete Element Method for Poly-superquadric Elements
		3.2.1 Functional Representation of Poly-superquadric Elements
		3.2.2 Calculation of Mass and Moment of Inertia
		3.2.3 Contact Detection Between Poly-superquadric Elements
		3.2.4 Position and Information Update of Elements
	3.3 Numerical Validation and Applications
		3.3.1 Theoretical Verification of a Single Particle Impacting a Plane
		3.3.2 DEM Simulation of Flow Processes of Multi-superquadric Elements
		3.3.3 DEM Simulation of Flow Processes of Poly-superquadric Elements
	3.4 Summary
	References
4 Smoothed Polyhedral DEM Model Based on Minkowski Sum Algorithm
	4.1 Dilated DEM Models of Arbitrarily Shaped Particles
		4.1.1 Polyhedral Model Based on Geometric Topology
		4.1.2 Dilated DEM Models Based on Fibonacci and Minkowski Sum Algorithms
		4.1.3 Automatic Mesh Simplification Method for Dilated DEM Models
	4.2 A Novel Minkowski Sum Contact Algorithm Between Particles
		4.2.1 Contact Detection Between a Dilated Triangular Element and a Sphere
		4.2.2 Contact Detection Between a Dilated Triangular Element and a Cylinder
		4.2.3 Contact Detection Between Two Dilated Triangular Faces
		4.2.4 Contact Force Model Between Particles
	4.3 Numerical Validation and Applications
		4.3.1 Elastic Collision Between Two Particles
		4.3.2 Inelastic Collision Between Two Particles
		4.3.3 Packing Process of Multiple Particles
		4.3.4 Engineering Applications of Mixed Granular Materials
	4.4 Summary
	References
5 Arbitrarily Shaped DEM Model Based on Level Set Method
	5.1 Modeling Methodology of Arbitrarily Shaped Elements
		5.1.1 Superquadric Equation
		5.1.2 Spherical Harmonic Function
		5.1.3 Polyhedron Method
	5.2 Contact Algorithm Between Arbitrarily Shaped Particles
		5.2.1 Creation of the Zero Level Set Function
		5.2.2 Creation of the Spatial Level Set Function
		5.2.3 Calculation of Contact Points
		5.2.4 Calculation of Contact Forces
	5.3 Contact Algorithm Between Particles and Structures
		5.3.1 Particle-Plane Contact Detection
		5.3.2 Particle-Edge Contact Detection
		5.3.3 Particle-Vertex Contact Detection
	5.4 Numerical Verification and Application
		5.4.1 Collision Between a Single Particle and a Wall
		5.4.2 Packing Process of Multiple Particles
		5.4.3 Engineering Applications of Mixed Granular Materials
	5.5 Summary
	References
6 High Performance Computation and DEM Software Development
	6.1 Modeling Methodology of Arbitrarily Shaped Elements
		6.1.1 Non-spherical Particles Represented by Superquadric Equations
		6.1.2 Motion Equation of Superquadric Particles
	6.2 GPU Parallel Computing Based on CUDA Architecture
		6.2.1 Spatial Grid Partitioning and Neighbor List Generation
		6.2.2 Bounding Box and Newton Iterative List Generation
		6.2.3 Contact Force Calculation and Element Information Updating
	6.3 Domestic and Foreign DEM Software Development
		6.3.1 Development of Foreign DEM Software
		6.3.2 Development of Domestic DEM Software
	6.4 Computational Analysis Software SDEM
		6.4.1 Introduction to the Software SDEM
		6.4.2 Million-Scale Granular Materials
		6.4.3 Flow Process of Large-Scale Granular Materials
		6.4.4 Comparison of GPU and CPU Computational Speed
		6.4.5 Mixing Process of Large-Scale Granular Materials
	6.5 Summary
	References
7 DEM Analysis of Flow Characteristics of Non-spherical Particles
	7.1 Analysis of Buffering Performance of Irregular Granular Materials
		7.1.1 Experimental Verification of the Impact Process of Granular Materials
		7.1.2 Effect of Granular Layer Thickness on the Buffering Performance
		7.1.3 Effect of Particle Shapes on the Impact Force
	7.2 Flow Characterization of Irregular Particles Driven by Gravity
		7.2.1 Influence of Particle Shape on Granular Flow Rate
		7.2.2 Transition of Granular Flow Pattern
		7.2.3 Analysis of Initial Stacking Characteristics and Normal Contact Forces
	7.3 Mixing Characteristics of Granular Materials in a Horizontal Rotating Drum
		7.3.1 Effect of Rotation Speeds on the Mixing Process of Granular Materials
		7.3.2 Effect of Particle Shapes on the Mixing Process of Granular Materials
		7.3.3 Analysis of Translational and Rotational Kinetic Energies of Particles
	7.4 Radial Segregation Characteristics of Particles in a Horizontal Rotating Drum
		7.4.1 Effect of Particle Shapes on the Segregation Process of Particles
		7.4.2 Effect of Standard Deviation on the Segregation Process of Particles
		7.4.3 Effect of Rotation Speeds on the Segregation Process of Particles
	7.5 Summary
	References