Micromechanics of Granular Materials (eBook)

Bernard Cambou is the editor of Micromechanics of Granular Materials, published by Wiley. Michel Jean is the editor of Micromechanics of Granular Materials, published by Wiley. Farhang Radjaï, Directeur de Recherche (research director) at the CNRS (French National Center for Scientific Research).

Introduction xiii

Chapter 1. Experimental and Numerical Analysis of Local
Variables in Granular Materials 1

Farhang RADJAÏ and Jack LANIER

1.1. Introduction 1

1.2. Description of granular texture 3

1.3. Granular kinematics 20

1.4. Force transmission 31

1.5. Conclusion 44

1.6. Bibliography 45

Chapter 2. The Stress Tensor in Granular Media and in other
Mechanical Collections 51

Jean-Jacques MOREAU

2.1. Introduction 51

2.2. Efforts and virtual power 59

2.3. Equilibrium 65

2.4. Comparison with the pair-by-pair approach 76

2.5. Directions of cut 83

2.6. Coarse graining the equation of Statics 90

2.7. One step into Dynamics 91

2.8. Bibliography 97

Chapter 3. Multiscale Techniques for Granular Materials
101

Bernard CAMBOU, Alexandre DANESCU

3.1. Introduction 101

3.2. Scale change andfabric tensors 102

3.3. Change of scale for static variables . 112

3.4. Change of scale for kinematic variables in granular
materials 115

3.5. Statistical homogenization in granular materials 131

3.6. Bibliography 145

Chapter 4. Numerical Simulation of Granular Materials
149

Michel JEAN

4.1. Introduction 149

4.2. The actors of a contact problem 152

4.3. Kinematic relations 167

4.4. The dynamical equation 174

4.5. Frictional contact laws 179

4.6. The equations governing a collection of contacting bodies
196

4.7. Preparing numerical samples 198

4.8. Smooth DEM numerical methods 206

4.9. Non-smooth DEM numerical methods 216

4.10. Some illustrating examples 227

4.11. Quasi-static evolutions, equilibrium dedicated methods
234

4.12. Accuracy criteria 241

4.13. Indetermination in granular materials 246

4.14. Stability 265

4.15. Numerical integration schemes 275

4.16. More non-smooth DEM methods 284

4.17. Signorini mu-Coulomb derived laws 292

4.18. Conclusion 301

4.19. Appendix: basic convex analysis 303

4.20. Bibliography 307

Chapter 5. Frictionless Unilateral Multibody Dynamics
317

Patrick BALLARD

5.1. Introduction 317

5.2. The dynamics of rigid body systems 318

5.3. The dynamics of rigid body systems with perfect bilateral
constraints 322

5.4. The dynamics of rigid body systems with perfect unilateral
constraints 326

5.5. Bibliography 340

List of Authors 343

Index 345

"The book will be useful for students and specialists working in
this scientific area." (Zentralblatt MATH, 2011)