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. This first book solves the local problem, the second one presents a coupling approach to link the structural effects to the local ones, the third book presents the software workbench that includes all the theoretical developments.
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ix | |
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xv | |
| Preface |
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xvii | |
| Introduction |
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xxi | |
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Chapter 1 State of the Art: Discrete Element Modeling |
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1 | (32) |
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1 | (2) |
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1.2 Classification of discrete methods |
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3 | (13) |
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1.2.1 Quantum mechanical methods |
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4 | (1) |
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5 | (3) |
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1.2.3 Mesoscopic discrete methods |
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8 | (8) |
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1.3 Discrete element method for continuous materials |
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16 | (1) |
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1.4 Discrete-continuum transition: macroscopic variables |
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17 | (14) |
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1.4.1 Stress tensor for discrete systems |
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18 | (3) |
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1.4.2 Strain tensor for discrete systems |
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21 | (10) |
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31 | (2) |
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Chapter 2 Discrete Element Modeling of Mechanical Behavior of Continuous Materials |
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33 | (60) |
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33 | (2) |
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2.2 Explicit dynamic algorithm |
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35 | (2) |
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2.3 Construction of the discrete domain |
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37 | (19) |
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2.3.1 The cooker compaction algorithm |
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39 | (5) |
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2.3.2 Geometrical characterization of the discrete domain |
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44 | (12) |
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2.4 Mechanical behavior modeling |
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56 | (31) |
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2.4.1 Cohesive beam model |
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58 | (6) |
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2.4.2 Calibration of the cohesive beam static parameters |
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64 | (15) |
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2.4.3 Calibration of the cohesive beam dynamic parameters |
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79 | (8) |
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87 | (6) |
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Chapter 3 Discrete Element Modeling of Thermal Behavior of Continuous Materials |
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93 | (22) |
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93 | (2) |
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3.2 General description of the method |
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95 | (2) |
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3.2.1 Characterization of field variable variation in discrete domain |
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95 | (1) |
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3.2.2 Application to heat conduction |
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96 | (1) |
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3.3 Thermal conduction in 3D ordered discrete domains |
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97 | (3) |
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3.4 Thermal conduction in 3D disordered discrete domains |
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100 | (6) |
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3.4.1 Determination of local parameters for each discrete element |
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102 | (1) |
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3.4.2 Calculation of discrete element transmission surface |
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103 | (1) |
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3.4.3 Calculation of local volume fraction |
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104 | (1) |
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3.4.4 Interactions between each discrete element and its neighbors |
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105 | (1) |
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106 | (7) |
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3.5.1 Cylindrical beam in contact with a hot plane |
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106 | (1) |
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3.5.2 Dynamically heated sheet |
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107 | (6) |
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113 | (2) |
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Chapter 4 Discrete Element Modeling of Brittle Fracture |
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115 | (26) |
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115 | (3) |
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4.2 Fracture model based on the cohesive beam bonds |
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118 | (14) |
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118 | (2) |
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120 | (3) |
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123 | (2) |
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125 | (7) |
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4.3 Fracture model based on the virial stress |
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132 | (5) |
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132 | (2) |
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134 | (1) |
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134 | (2) |
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136 | (1) |
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137 | (4) |
| Conclusion |
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141 | (4) |
| Bibliography |
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145 | (16) |
| Index |
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161 | |
Mohamed Jebahi, Université de Laval, Canada.
Damien Andre, Arts et Métiers ParisTech, I2M, France.
Inigo Terreros, Arts?et Métiers ParisTech, France.
Ivan Iordanoff, Professor at Arts et Métiers ParisTech, Research at I2M laboratory, France.
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