Hans-Georg Matuttis: Understanding the Discrete Element Method, Gebunden

Beschreibung

Gives readers a more thorough understanding of DEM and equips researchers for independent work and an ability to judge methods related to simulation of polygonal particles
Introduces DEM from the fundamental concepts (theoretical mechanics and solidstate physics), with 2D and 3D simulation methods for polygonal particles
Provides the fundamentals of coding discrete element method (DEM) requiring little advance knowledge of granular matter or numerical simulation
Highlights the numerical tricks and pitfalls that are usually only realized after years of experience, with relevant simple experiments as applications
Presents a logical approach starting withthe mechanical and physical bases, followed by a description of the techniques and finally their applications
Written by a key author presenting ideas on how to model the dynamics of angular particles using polygons and polyhedral
Accompanying website includes MATLAB-Programs providing the simulation code for two-dimensional polygons
Recommended for researchers and graduate students who deal with particle models in areas such as fluid dynamics, multi-body engineering, finite-element methods, the geosciences, and multi-scale physics.

Inhaltsangabe

About the Authors xv

Preface xvii

Acknowledgements xix

List of Abbreviations xxi

1 Mechanics 1

1.1 Degrees of freedom 1

1.2 Dynamics of rectilinear degrees of freedom 5

1.3 Dynamics of angular degrees of freedom 6

1.4 The phase space 29

1.5 Nonlinearities 39

1.6 From higher harmonics to chaos 47

1.7 Stability and conservation laws 53

1.8 Further reading 61

2 Numerical Integration of Ordinary Differential Equations 65

2.1 Fundamentals of numerical analysis 65

2.2 Numerical analysis for ordinary differential equations 75

2.3 Runge-Kutta methods 79

2.4 Symplectic methods 82

2.5 Stiff problems 92

2.6 Backward difference formulae 94

2.7 Other methods 98

2.8 Differential algebraic equations 103

2.9 Selecting an integrator 109

2.10 Further reading 111

3 Friction 129

3.1 Sliding Coulomb friction 129

3.2 Other contact geometries of Coulomb friction 136

3.3 Exact implementation of friction 144

3.4 Modeling and regularizations 153

3.5 Unfortunate treatment of Coulomb friction in the literature 155

3.6 Further reading 158

4 Phenomenology of Granular Materials 161

4.1 Phenomenology of grains 161

4.2 General phenomenology of granular agglomerates 164

4.3 History effects in granular materials 168

4.4 Further reading 173

5 Condensed Matter and Solid State Physics 175

5.1 Structure and properties of matter 176

5.2 From wave numbers to the Fourier transform 186

5.3 Waves and dispersion 194

5.4 Further reading 206

6 Modeling and Simulation 213

6.1 Experiments, theory and simulation 213

6.2 Computability, observables and auxiliary quantities 214

6.3 Experiments, theories and the discrete element method 215

6.4 The discrete element method and other particle simulation methods 217

6.5 Other simulation methods for granular materials 218

7 The Discrete Element Method in Two Dimensions 223

7.1 The discrete element method with soft particles 223

7.2 Modeling of polygonal particles 229

7.3 Interaction 237

7.4 Initial and boundary conditions 250

7.5 Neighborhood algorithms 257

7.6 Time integration 271

7.7 Program issues 272

7.8 Computing observables 280

7.9 Further reading 285

8 The Discrete Element Method in Three Dimensions 289

8.1 Generalization of the force law to three dimensions 289

8.2 Initialization of particles and their properties 292

8.3 Overlap computation 301

8.4 Optimization for vertex computation 322

8.5 The neighborhood algorithm for polyhedra 325

8.6 Programming strategy for the polyhedral simulation 329

8.7 The effect of dimensionality and the choice of boundaries 332

8.8 Further reading 333

9 Alternative Modeling Approaches 335

9.1 Rigidly connected spheres 335

9.2 Elliptical shapes 336

9.3 Composites of curves 345

9.4 Rigid particles 347

9.5 Discontinuous deformation analysis 349

9.6 Further reading 349

10 Running, Debugging and Optimizing Programs 353

10.1 Programming style 353

10.2 Hardware, memory and parallelism 362

10.3 Program writing 369

10.4 Measuring load, time and profiles 378

10.5 Speeding up programs 383

10.6 Further reading 391

11 Beyond the Scope of This Book 395

11.1 Non-convex particles 395

11.2 Contact dynamics and friction 395

11.3 Impact mechanics 396

11.4 Fragmentation and fracturing 396

11.5 Coupling codes for particles and elastic continua 396

11.6 Coupling of particles and fluid 398

11.7 The finite element method for contact problems 402

11.8 Long-range interactions 403

A MATLAB R as Programming Language 407

A. 1 Getting started with MATLAB R 407

A. 2 Data types and names 408

A. 3 Matrix functions and linear algebra 409

A. 4 Syntax and control structures 413

A. 5 Self-written functions 415

A. 6 Function overwriting and overloading 416

A. 7 Graphics 417

A. 8 Solving ordinary differential equations 418

A. 9 Pitfalls of using MATLAB R

Klappentext

The aim of this book is to advance the field of granular and multi-body studies while giving readers a more thorough understanding of the discrete element method (DEM). By working through this volume, researchers will be better equipped for independent work and will develop an ability to judge methods related to the simulation of polygonal particles.

When materials are not handled as fluids, they are dealt with mostly in granular form (e. g. cement, sand, grains, powders). Granular materials are characterized by abrupt transitions from loose to dense, from flowing to static states, and vice versa. Many problems in natural disasters (earthquakes, landslides, etc.) are also of a "granular" nature. Continuum methods have been applied in these fields, but lack any intrinsic mechanism to account for the transitions, behavior that is inherently discontinuous. The "natural" approach is to use particle simulation methods, often called the "discrete element method", where bodies in the physical system and the simulation match one to one. The field of discrete element simulation has changed little since the early 1990s, when simulations predominantly used spherical particles. The aim of this book is to show the practicability and usefulness of non-spherical discrete element simulations. Phenomena from related fields (mechanics, solid state physics, etc.) are discussed, which as test cases are sometimes not applicable due to intriguing reasons. Understanding both the pitfalls and applications will help one to predict the outcome of simulations and use the predictions for the design of future experiments.

• Introduces the discrete element method (DEM) starting from the fundamental concepts (theoretical mechanics and solid state physics), with 2D and 3D simulation methods for polygonal and polyhedral particles
• Explains the basics of coding DEM, requiring little previous knowledge of granular matter or numerical simulation
• Highlights numerical tricks and pitfalls that are usually only recognized after years of experience, using relevant simple experiments to illustrate applications
• Presents a logical approach starting with the mechanical and physical bases, followed by a description of the techniques and their applications
• Written by key authors presenting ideas on how to model the dynamics of angular particles using polygons and polyhedrals
• Accompanying website includes MATLAB programs providing the simulation code for two-dimensional
  convex polygons

This book is ideal for researchers and graduate students who deal with particle models in areas such as fluid dynamics, multi-body engineering, finite element methods, virtual reality, the geosciences, and multi-scale physics. Computer scientists involved with solid modeling and game programming will also find this book a useful reference for the design of physics engines.