Discrete Element Method to Model 3D Continuous Materials [Hardcover]

Complex behavior models (plasticity, cracks, visco elascticity) face some theoretical difficulties for the determination of the behavior law at the continuous scale. When homogenization fails to give the right behavior law, a solution is to simulate the material at a meso scale in order to simulate directly a set of discrete properties that are responsible of the macroscopic behavior.  The discrete element model has been developed for granular material. The proposed set shows how this method is capable to solve the problem of complex behavior that are linked to discrete meso scale effects.

LIST OF FIGURES ix

LIST OF TABLES xv

PREFACE xvii

INTRODUCTION xxi

CHAPTER 1. STATE OF THE ART: DISCRETE ELEMENT MODELING 1

1.1. Introduction 1

1.2. Classification of discrete methods 3

1.2.1. Quantum mechanical methods 4

1.2.2. Atomistic methods 5

1.2.3. Mesoscopic discrete methods 8

1.3. Discrete element method for continuous materials 16

1.4. Discrete-continuum transition: macroscopic variables 17

1.4.1. Stress tensor for discrete systems 18

1.4.2. Strain tensor for discrete systems 21

1.5. Conclusion 31

CHAPTER 2. DISCRETE ELEMENT MODELING OF MECHANICAL BEHAVIOR OF CONTINUOUS MATERIALS 33

2.1. Introduction 33

2.2. Explicit dynamic algorithm 35

2.3. Construction of the discrete domain 37

2.3.1. The cooker compaction algorithm 39

2.3.2. Geometrical characterization of the discrete domain 44

2.4. Mechanical behavior modeling 56