Discrete Element Method to Model 3D Continuous Materials

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
2. 4. 1. Cohesive beam model  58
2. 4. 2. Calibration of the cohesive beam static parameters 64
2. 4. 3. Calibration of the cohesive beam dynamic parameters 79
2. 5. Conclusion 87
CHAPTER 3. DISCRETE ELEMENT MODELING OF THERMAL BEHAVIOR OF CONTINUOUS MATERIALS      93
3. 1. Introduction 93
3. 2. General description of the method 95
3. 2. 1. Characterization of field variable variation in discrete domain  95
3. 2. 2. Application to heat conduction 96
3. 3. Thermal conduction in 3D ordered discrete domains 97
3. 4. Thermal conduction in 3D disordered discrete domains 100
3. 4. 1. Determination of local parameters for each discrete element  102
3. 4. 2. Calculation of discrete element transmission surface  103
3. 4. 3. Calculation of local volume fraction  104
3. 4. 4. Interactions between each discrete element and its neighbors  105
3. 5. Validation 106
3. 5. 1. Cylindrical beam in contact with a hot plane  106
3. 5. 2. Dynamically heated sheet  107
3. 6. Conclusion 113
CHAPTER 4. DISCRETE ELEMENT MODELING OF BRITTLE FRACTURE  115
4. 1. Introduction 115
4. 2. Fracture model based on the cohesive beam bonds  118
4. 2. 1. Fracture criterion  118
4. 2. 2. Calibration 120
4. 2. 3. Convergence study  123
4. 2. 4. Validation 125
4. 3. Fracture model based on the virial stress 132
4. 3. 1. Fracture criterion 132
4. 3. 2. Calibration 134
4. 3. 3. Convergence study  134
4. 3. 4. Validation 136
4. 4. Conclusion 137
CONCLUSION  141
BIBLIOGRAPHY 145
INDEX 161