The discrete element method can effectively simulate the discontinuity, inhomogeneity, and large deformation damage of rock and soil. It is widely used in both research and industry. Based on the innovative matrix discrete element computing method, the author developed the high-performance discrete element software MatDEM from scratch, which can handle millions of elements in discrete element numerical simulations. This book introduces the basic structure, modeling methods, numerical calculation processes, post-processing, and system functions of MatDEM, which apply the basic principles and algorithm of the discrete element method. It also presents several examples of applications in geological and geotechnical engineering, including basic geotechnical engineering problems, discrete element tests, three-dimensional landslides, and dynamic and multi-field coupling functions. Teaching videos and the relevant software can be accessed on the MatDEM website (http://matdem.com).
The book will serve as a useful reference for research and engineering staffs, undergraduates, and postgraduates who work in the fields of geology, geotechnique, water conservancy, civil engineering, mining, and physics.

Doctor Chun Liu graduated from Nanjing University in 2012, and received the "Excellent Doctoral Dissertation Award of ]iangsu Province" in 2013. After postdoctoral research at Stanford University, he joined Nanjing University as an associate professor in 2014. Since 2019, he served as the vice president of the Institute of Earth Exploration and Sensing of Naniing University and the deputy director of the Youth Committee of the Chinese Society for Rock Mechanics and Engineering. He has been engaged in the research field of computational engineering geology, and has made rich achievements in the theoretical research and system development of the discrete element method, and its application in engineering. He has developed the high-performance discrete element software MatDEM (http://matdem.com), which has been widely used in geology, geotechnical engineering, energy, chemical industry, and other fields. Until 2020, he has participated in the researches of 9 projects of the National Natural Science Foundation of China. In 2017, he was selected into the "Young Elite Scientist Sponsorship Program" of the China Association for Science, and Technology, and was selected into the "Six Talent Peaks" High-Level Talent Selection and Training Funding Plan of ]iangsu Province, etc.

Foreword I
Foreword II
Preface
Chapter 1 Principles and Implementation of DEM
1.1 Application and Numerical Calculation Software of DEM
1.2 Basic Principles of DEM
1.2.1 Contact Model of Elements
1.2.2 Connection of Two Different Elements
1.2.3 Time Step Iterative Algorithm
1.3 Damping Harmonic Vibration of Elements
1.3.1 Damping Force of Elements
1.3.2 Equation of the Damping Harmonic Vibration
1.3.3 Relation Between Vibration Period and Element Radius
1.3.4 Differences of the Element Motion
1.3.5 Damping and Optimal Damping Coefficient
1.4 Energy Conversion and Energy Conservation of DEM
1.4.1 Mechanical Energy of Systems
1.4.2 Calculation of Heat
1.4.3 Energy Conservation and External Work
1.5 Calculation Scale and Engineering Application Feasibility of DEM
1.6 Understanding and Solution to the Three Major Issues in DEM
1.6.1 High-Performance Matrix Computing of the Discrete Element Method
1.6.2 Quantitative Modeling Problem of DEM
1.6.3 Multi-field Coupling Method Based on DEM
1.7 Development and Prospect of MatDEM
Chapter 2 The Basic Structure of MatDEM
2.1 The Software Foundation
2.1.1 The Operating Environment and Software Installation
2.1.2 The Windows Program for MatDEM
2.1.3 Operation and Termination of the Software
2.1.4 A Brief Introduction to the Application of the Software
2.1.5 A Brief Introduction to the Help File
2.2 The Program Structure of MatDEM
2.2.1 The Software Folders of MatDEM
2.2.2 The Hierarchical Structure of MatDEM
2.2.3 The Main Classes in MatDEM
2.3 Types of Element in MatDEM
2.3.1 Active Element， Wall Element， and Virtual Element
2.3.2 Fix the Degree of Freedom of Elements
2.3.3 The Rule of Numbering Elements
2.4 The Data Structure of MatDEM
2.4.1 The Property Arrays of Elements
2.4.2 The Neighbor Matrix and Connection Information Matrix
2.4.3 The Data Structure and Operation of Groups
2.5 The Contact Model Between Elements
2.5.1 The Linear Elastic Contact Model
2.5.2 The Hertz Contact Model
2.6 The Elastic Clump
2.6.1 The Principle of the Elastic Clump
2.6.2 Usage of the Elastic Clump
Chapter 3 Geometric Modeling and Material Setup
3.1 Building a Numerical Simulation Box
3.1.1 Building a Packing Model
3.1.2 Creating an Empty Box
3.2 The Foundation of Modular Modeling
3.2.1 Modeling with a Structure
3.2.2 Element Filtering
3.2.3 Tool_Cut and Digital Elevation Model
3.3 Modeling Based on Digital Images
3.3.1 Importing a Binary Image to Cut a Model
4.5.1 Compression of Files
4.5.2 Saving and Reading of Files
Chapter5 Post-processing and System Functions
5.1 Post-processing Window Interface
5.1.1 Main Post-processing Window
5.1.2 Saving the Post-processing Figure
5.1.3 Making GIF Window
5.2 Post-processing Drawing Functions
5.2.1 General Drawing Function d.show
5.2.2 Slice Display and Filter Display
5.2.3 Element Position and Force Display
5.3 Data Processing and Curve Drawing
5.3.1 Drawing Curves with Saved Data
5.3.2 Drawing Curves with MatDEM Automatically Recorded Data
5.3.3 Processing Data and Plotting in MATLAB
5.4 System Functions
5.4.1 GPU Computing Settings and Status Viewing
5.4.2 Definition and Operation of Functions
5.4.3 Batch Processing of Code Files
5.4.4 Random Seed and Stochastic Model
5.4.5 Timing Functions
5.5 Modeling with System Underlying Functions
5.5.1 Underlying Modeling of the Two-Ball Collision Process
5.5.2 Use Graphs to Analyze Collision Processes
Chapter 6 Basic Application of Geotechnical Engineering
6.1 Pile-soil Interaction
6.1.1 Packing Model of Particles
6.1.2 Build a Pile-Soil Interaction Model
6.1.3 Numerical Simulat