Discrete-continuum Coupling Method to Simulate Highly Dynamic Multi-scale Problems Simulation of Laser-induced Damage in Silica Glass, Volume 2

Complex behavior models (plasticity, crack, visco-elascticity) are facing several theoretical difficulties in determining the behavior law at the continuous (macroscopic) scale. When homogenization fails to give the right behavior law, a solution is to simulate the material at a mesoscale using the discrete element model (DEM) in order to directly simulate a set of discrete properties that are responsible for the macroscopic behavior. Originally, the discrete element model was developed for granular material.

This book, the second in the Discrete Element Model and Simulation of Continuous Materials Behavior set of books, shows how to choose the adequate coupling parameters to avoid spurious wave reflection and to allow the passage of all the dynamic information both from the fine to the coarse model and vice versa. The authors demonstrate the coupling method to simulate a highly nonlinear dynamical problem: the laser shock processing of silica glass.

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 α  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

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