Hans-Georg Matuttis, Jian Chen

Understanding the Discrete Element Method

Simulation of Non-Spherical Particles for Granular and Multi-Body Systems

• Gebundenes Buch

Produktbeschreibung

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.

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Produktdetails

• Verlag: Wiley & Sons
• 1. Auflage
• Seitenzahl: 448
• Erscheinungstermin: 23. Juni 2014
• Englisch
• Abmessung: 260mm x 183mm x 30mm
• Gewicht: 1092g
• ISBN-13: 9781118567203
• ISBN-10: 111856720X
• Artikelnr.: 40134445

Autorenporträt

Hans-Georg Matuttis, The University of Electro-Communications, Japan Jian Chen, RIKEN Advanced Institute for Computational Science, Japan

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 420 A.10
Profiling and optimization 424 A.11 Free alternatives to MATLAB R 425 A.12
Further reading 425 Exercises 426 References 430 B Geometry and
Computational Geometry 433 B.1 Trigonometric functions 433 B.2 Points, line
segments and vectors 435 B.3 Products of vectors 436 B.4 Projections and
rejections 441 B.5 Lines and planes 442 B.6 Oriented quantities: distance,
area, volume etc. 446 B.7 Further reading 449 References 449 Index 451