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Computational Mechanics of Discontinua

ISBN: 978-0-470-97080-5
284 pages
November 2011, ©2011
Computational Mechanics of Discontinua (0470970804) cover image
Mechanics of Discontinua is the first book to comprehensively tackle both the theory ofthis rapidly developing topic and the applications that span a broad field of scientific and engineering disciplines, from traditional engineering to physics of particulates, nano-technology and micro-flows. Authored by a leading researcher who has been at the cutting edge of discontinua simulation developments over the last 15 years, the book is organized into four parts: introductory knowledge, solvers, methods and applications. In the first chapter a short revision of Continuum Mechanics together with tensorial calculus is introduced. Also, a short introduction to the finite element method is given. The second part of the book introduces key aspects of the subject. These include a diverse field of applications, together with fundamental theoretical and algorithmic aspects common to all methods of Mechanics of Discontinua. The third part of the book proceeds with the most important computational and simulation methods including Discrete Element Methods, the Combined Finite-Discrete Element Method, Molecular Dynamics Methods, Fracture and Fragmentation solvers and Fluid Coupling. After these the reader is introduced to applications stretching from traditional engineering and industry (such as mining, oil industry, powders) to nanotechnology, medical and science.
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Series Preface xi

Preface xiii

Acknowledgements xv

1 Introduction to Mechanics of Discontinua 1

1.1 The Concept of Discontinua 1

1.2 The Paradigm Shift 3

1.3 Some Problems of Mechanics of Discontinua 7

1.3.1 Packing 7

1.3.2 Fracture and Fragmentation 8

1.3.3 Demolition and Structures in Distress, Progressive Collapse 11

1.3.4 Nanotechnology 12

1.3.5 Block Caving 15

1.3.6 Mineral Processing 16

1.3.7 Discrete Populations in General 16

References 18

Further Reading 18

2 Methods of Mechanics of Discontinua 21

2.1 Introduction 21

2.2 Discrete Element Methods 21

2.2.1 Spherical Particles 22

2.2.2 Blocky Particles 23

2.2.3 Oblique and Super-Quadric Particles 23

2.2.4 Rigid Potential Field Particles 25

2.2.5 3D Real Shape Particles 25

2.2.6 Computer Games and Special Effects 26

2.3 The Combined Finite-Discrete Element Method 27

2.4 Molecular Dynamics 28

2.4.1 Common Potentials 29

2.5 Smooth Particle Hydrodynamics 31

2.6 Discrete Populations Approach 33

2.7 Algorithms and Solutions 35

References 36

Further Reading 37

3 Disc to Edge Contact Interaction in 2D 39

3.1 Problem Description 39

3.2 Integration of Normal Contact Force 39

3.3 Tangential Force 44

3.4 Equivalent Nodal Forces 45

Further Reading 46

4 Triangle to Edge Contact Interaction in 2D 47

4.1 Problem Description 47

4.2 Integration of Normal Contact Force 47

4.3 Tangential Force 54

4.4 Equivalent Nodal Forces 55

Further Reading 56

5 Ball to Surface Contact Interaction in 3D 59

5.1 Problem Description 59

5.2 Integration of Normal Contact Force 59

5.3 Tangential Force 73

5.4 Equivalent Nodal Forces 74

Further Reading 75

6 Tetrahedron to Points Contact Interaction in 3D 77

6.1 Problem Description 77

6.2 Integration of Normal Contact Force 79

6.3 Tangential Force 84

6.4 Equivalent Nodal Forces 86

Further Reading 86

7 Tetrahedron to Triangle Contact Interaction in 3D 89

7.1 Problem Description 89

7.2 Integration of Normal Contact Force 89

7.3 Tangential Force 99

7.4 Equivalent Nodal Forces 101

Further Reading 102

8 Rock Joints 103

8.1 Introduction 103

8.2 Interaction between Mesh Entities in 2D 104

8.2.1 Interaction between a 2D Disk and a Straight Edge 105

8.2.2 Numerical Integration of the Roller-Edge Interaction 111

8.3 Joint Dilation 113

8.4 Shear Resistance of a 2D Rock Joint 116

8.5 Numerical Examples 120

References 124

Further Reading 124

9 MR Contact Detection Algorithm for Bodies of Similar Size 125

9.1 The Challenge 125

9.2 Constraints of MR Contact Detection Algorithm 125

9.3 Space Decomposition 127

9.4 Mapping of Spherical Bounding Boxes onto Cells 127

9.5 Spatial Sorting 129

9.6 Quick Sort Algorithm 130

9.7 MR-Linear Sort Algorithm 135

9.8 Implementation of the MR-Linear Sort Algorithm 136

9.9 Quick Search Algorithm 141

9.10 MR-Linear Search Algorithm 143

9.11 CPU and RAM Performance 145

9.12 CPU Performance and RAM Consumption 151

References 152

Further Reading 152

10 MR Contact Detection Algorithm for Bodies of Different Sizes 155

10.1 Introduction 155

10.2 Description of the Multi-Step-MR Algorithm (MMR) 155

10.3 Polydispersity 156

10.4 CPU Performance 157

10.5 RAM Requirements 158

10.6 Robustness 158

10.7 Applications 160

Further Reading 160

11 MR Contact Detection Algorithm for Complex Shapes in 2D 163

11.1 Introduction 163

11.2 Contactor Circle to Target Point MR Contact Detection Algorithm 163

11.2.1 Cell Size and Space Boundaries 163

11.2.2 Rendering of 2D Target Points onto Cells 166

11.2.3 Sorting of Target Cells 167

11.2.4 Interrogation Tools for Sorted Target Cells 167

11.2.5 Rendering of 2D Contactor Circles onto Cells 168

11.3 Contactor Circle to Target Edge MR Contact Detection Algorithm 176

11.3.1 Rendering 2D Target Edges onto Cells 176

11.3.2 Searching for Contacts 182

11.4 Contactor Triangle to Target Edge MR Contact Detection Algorithm 184

11.4.1 Rendering 2D Triangles onto Cells 185

11.5 Extension to Other Shapes 192

11.6 Reporting of Contacting Couples 193

Further Reading 194

12 MR Contact Detection Algorithm for Complex Shapes in 3D 197

12.1 Introduction 197

12.2 Rendering Target Simplex Shapes 198

12.2.1 Rendering 3D Points onto Cells 198

12.2.2 Rendering 3D Edges onto Cells 198

12.3 Sorting Target Cells 210

12.4 Target Cells Interrogation Tools 211

12.5 Searching for Contacts 212

12.5.1 Rendering Contactor Tetrahedron 212

12.5.2 Rendering Contactor Triangular Facet 226

12.5.3 Rendering Other Contactor Simplex Shapes 241

Further Reading 241

13 Parallelization 243

13.1 Introduction 243

13.2 Domain Decomposition Approach 247

13.2.1 Communication Engine 252

13.2.2 Broadcasting Engine 254

13.2.3 Summing Engine 254

13.2.4 Gathering Engine 256

13.2.5 Distribution of Physical Objects across Processors 257

13.2.6 Creating Proxies 258

13.2.7 Relocating Originals 259

13.3 Graphics Processing Units (GPU) 260

13.4 Structured Parallelization 262

Further Reading 263

Index 265

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Ante Munjiza, Queen Mary College, London
Ante Munjiza is professor of computational mechanics in the Department of Computational Mechanics at Queen Mary College, London. His research interests include finite element methods, discrete element methods, molecular dynamics, structures and solids, structural dynamics, software engineering, blasts, impacts, and nanomaterials. He has authored one book, The Combined Finite-Discrete Element Method (Wiley 2004), and over 110 refereed journal papers. In addition, he is on the editorial board of seven international journals. Dr Munjiza is widely recognised as a key international expert in computational mechanics of discontinua. He is also an accomplished software engineer with three research codes behind him and one commercial code all based on his technology.

Earl E. Knight & Esteban Rougier, Los Alamos National Laboratories
Earl Knight is a Team Leader in the Geodynamics Team at Los Alamos National Laboratory. His research interests include geodynamic modeling, rock mechanical modeling for deep water oil reservoirs and ground based nuclear explosion monitoring

Esteban Rougier is a Post Doctoral Research Associate at LANL. He has received his Ph.D. from Queen Mary, University of London in 2008` on Computational Mechanics of Discontinuum and its Application to the Simulation of Micro-Flows.

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“This introduction to the rapidly growing field of Mechanics of Discontinua will appeal to graduate and undergraduate students, as well as practicing engineers, and will equip the reader with a sound theoretical and practical understanding of the topic.”  (Mathematical Reviews, 1 January 2013)

 

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