Discrete-continuum Coupling Method to Simulate Highly Dynamic Multi-scale Problems (eBook)

Mohamed Jebahi is a post-doctoral researcher at the Institute of Mechanics and Engineering of Bordeaux, France, and Laval University, Quebec, Canada. Frédéric Dau is Assistant Professor at Ecole Nationale Supérieure d'Arts et Métiers, ParisTech, France. Jean-Luc Charlesis Assistant Professor at Ecole Nationale Supérieure d&'Arts et Métiers, ParisTech, France. Ivan Iordanoff is Director of Research and Innovation at Ecole Nationale Supérieure d'Arts et Métiers, ParisTech, France.

List of Figures ix

List of Tables xv

Preface xvii

Introduction xix

Part 1. Discrete-Continuum Coupling Method to Model Highly Dynamic Multi-Scale Problems 1

Chapter 1. State of the Art: Concurrent Discrete-continuum Coupling 3

1.1. Introduction 3

1.2. Coupling challenges 4

1.2.1. Dissimilar variables due to different mechanical bases 4

1.2.2. Wave reflections due to different analysis scales 4

1.3. Coupling techniques 10

1.3.1. Edge-to-edge coupling methods 11

1.3.2. Bridging domain coupling methods 15

1.3.3. Bridging-scale coupling methods 19

1.3.4. Other coupling techniques 23

1.4. Conclusion 25

Chapter 2. Choice of the Continuum Method to be Coupled with the Discrete Element Method 27

2.1. Introduction 27

2.2. Classification of the continuum methods 28

2.2.1. Grid-based methods 28

2.2.2. Meshless methods 33

2.3. Choice of continuum method 38

2.4. The constrained natural element method 41

2.4.1. Natural neighbor interpolation 41

2.4.2. Visibility criterion 48

2.4.3. Constrained natural neighbor interpolation 48

2.4.4. Numerical integration 49

2.5. Conclusion 51

Chapter 3. Development of Discrete-Continuum Coupling Method Between DEM and CNEM 53

3.1. Introduction 53

3.2. Discrete-continuum coupling method: DEM-CNEM 54

3.2.1. DEM-CNEM coupling formulation 54

3.2.2. Discretization and spatial integration 59

3.2.3. Time integration 62

3.2.4. Algorithmic 63

3.2.5. Implementation 66

3.3. Parametric study of the coupling parameters 67

3.3.1. Influence of the junction parameter l 71

3.3.2. Influence of the weight function alpha 73

3.3.3. Influence of the approximated mediator spaceM~ 79

3.3.4. Influence of the width of the bridging zone LB 79

3.3.5. Dependence between LB andM~ 81

3.4. Choice of the coupling parameters in practice 83

3.5. Validation 84

3.6. Conclusion 85

Part 2. Application: Simulation of Laser Shock Processing of Silica Glass 89

Chapter 4. Some Fundamental Concepts in Laser Shock Processing 91

4.1. Introduction 91

4.2. Theory of laser-matter interaction: high pressure generation 92

4.2.1. Generation of shock wave by laser ablation 93

4.2.2. Shock wave propagation in materials 96

4.2.3. Laser-induced damage in materials 106

4.3. Mechanical response of silica glass under high pressure 109

4.3.1. Silica glass response under quasi-static hydrostatic compression 109

4.3.2. Silica glass response under shock compression 114

4.3.3. Summary of the silica glass response under high pressure 118

4.4. Conclusion 119

Chapter 5. Modeling of the Silica Glass Mechanical Behavior 121

5.1. Introduction 121

5.2. Mechanical behavior modeling 122

5.2.1. Modeling assumption 123

5.2.2. Cohesive beam model 124

5.2.3. Quasi-static calibration and validation 127

5.2.4. Dynamic calibration and validation 139

5.3. Brittle fracture modeling 147

5.4. Conclusion 149

Chapter 6. Simulation of Laser Shock Processing of Silica Glass 151

6.1. Introduction 151

6.2. LSP test 153

6.3. LSP model 155

6.4. Results 159

6.5. Conclusion 163

Conclusion 165

Bibliography 171

Index 185