Details

<p>LIST OF FIGURES ix</p> <p>LIST OF TABLES xv</p> <p>PREFACE xvii</p> <p>INTRODUCTION xxi</p> <p><b>CHAPTER 1. STATE OF THE ART: DISCRETE ELEMENT MODELING 1</b></p> <p>1.1. Introduction 1</p> <p>1.2. Classification of discrete methods 3</p> <p>1.2.1. Quantum mechanical methods 4</p> <p>1.2.2. Atomistic methods 5</p> <p>1.2.3. Mesoscopic discrete methods 8</p> <p>1.3. Discrete element method for continuous materials 16</p> <p>1.4. Discrete-continuum transition: macroscopic variables 17</p> <p>1.4.1. Stress tensor for discrete systems 18</p> <p>1.4.2. Strain tensor for discrete systems 21</p> <p>1.5. Conclusion 31</p> <p><b>CHAPTER 2. DISCRETE ELEMENT MODELING OF MECHANICAL BEHAVIOR OF CONTINUOUS MATERIALS 33</b></p> <p>2.1. Introduction 33</p> <p>2.2. Explicit dynamic algorithm 35</p> <p>2.3. Construction of the discrete domain 37</p> <p>2.3.1. The cooker compaction algorithm 39</p> <p>2.3.2. Geometrical characterization of the discrete domain 44</p> <p>2.4. Mechanical behavior modeling 56</p> <p>2.4.1. Cohesive beam model 58</p> <p>2.4.2. Calibration of the cohesive beam static parameters 64</p> <p>2.4.3. Calibration of the cohesive beam dynamic parameters 79</p> <p>2.5. Conclusion 87</p> <p><b>CHAPTER 3. DISCRETE ELEMENT MODELING OF THERMAL BEHAVIOR OF CONTINUOUS MATERIALS    93</b></p> <p>3.1. Introduction 93</p> <p>3.2. General description of the method 95</p> <p>3.2.1. Characterization of field variable variation in discrete domain 95</p> <p>3.2.2. Application to heat conduction 96</p> <p>3.3. Thermal conduction in 3D ordered discrete domains 97</p> <p>3.4. Thermal conduction in 3D disordered discrete domains 100</p> <p>3.4.1. Determination of local parameters for each discrete element 102</p> <p>3.4.2. Calculation of discrete element transmission surface 103</p> <p>3.4.3. Calculation of local volume fraction 104</p> <p>3.4.4. Interactions between each discrete element and its neighbors 105</p> <p>3.5. Validation 106</p> <p>3.5.1. Cylindrical beam in contact with a hot plane 106</p> <p>3.5.2. Dynamically heated sheet 107</p> <p>3.6. Conclusion 113</p> <p><b>CHAPTER 4. DISCRETE ELEMENT MODELING OF BRITTLE FRACTURE 115</b></p> <p>4.1. Introduction 115</p> <p>4.2. Fracture model based on the cohesive beam bonds 118</p> <p>4.2.1. Fracture criterion 118</p> <p>4.2.2. Calibration 120</p> <p>4.2.3. Convergence study 123</p> <p>4.2.4. Validation 125</p> <p>4.3. Fracture model based on the virial stress 132</p> <p>4.3.1. Fracture criterion 132</p> <p>4.3.2. Calibration 134</p> <p>4.3.3. Convergence study 134</p> <p>4.3.4. Validation 136</p> <p>4.4. Conclusion 137</p> <p>CONCLUSION 141</p> <p>BIBLIOGRAPHY 145</p> <p>INDEX 161</p>

<p><strong>Mohamed Jebahi</strong>, Université de Laval, Canada. <p><strong>Damien Andre</strong>, Arts et Métiers ParisTech, I2M, France. <p><strong>Inigo Terreros</strong>, Arts?et Métiers ParisTech, France. <p><strong>Ivan Iordanoff</strong>, Professor at Arts et Métiers ParisTech, Research at I2M laboratory, France.

US