Understanding the Discrete Element Method - Simulation of Non Spherical Particles for Granular Multi Body

Informationen zum Autor Hans-Georg Matuttis , The University of Electro-Communications, Japan Jian Chen , RIKEN Advanced Institute for Computational Science, Japan Klappentext 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 polygonsRecommended 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. Zusammenfassung 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. This title introduces DEM from the fundamental concepts (theoretical mechanics and solidstate physics), with 2D and 3D simulation methods for polygonal particles. Inhaltsverzeichnis About the Authors xv Preface xvii Acknowledgements xix List of Abbreviations xxi 1 Mechanics 1 1.1 Degrees of freedom 1 1.1.1 Particle mechanics and constraints 1 1.1.2 From point particles to rigid bodies 3 1.1.3 More context and terminology 4 1.2 Dynamics of rectilinear degrees of freedom 5 1.3 Dynamics of angular degrees of freedom 6 1.3.1 Rotation in two dimensions 6 1.3.2 Moment of inertia 7 1.3.3 From two to three dimensions 9 1.3.4 Rotation matrix in three dimensions 12 1.3.5 Three-dimensional moments of inertia 13 1.3.6 Space-fixed and body-fixed coordinate systems and equations of motion 16 1.3.7 Problems with Euler angles 19 1.3.8 Rotations represented using complex numbers 20 1.3.9 Quaternions 21 1.3.10 Derivation of quaternion dynamics 27 1.4 The phase space 29 1.4.1 Qualitative discussion of the time dependence of linear oscillations 31 1.4.2 Resonance 34 1.4.3 The flow in phase space 35 1.5 Nonlinearities 39 1.5.1 Harmonic balance 40 1.5.2 Resonance in nonlinear systems 42 1.5.3 Higher harmonics and frequency mixing 44 1.5.4 The van der Pol oscillator 45 1.6 From higher harmonics to chaos 47 1.6.1 The bifurcation cascade 47 1.6.2 The nonlinear frictional oscillator and Poincaré maps 47 1.6.3 The route to chaos 51 1.6.4 Boundary conditions and many-particle systems 52 1.7 Stability and conservation laws 53 1.7.1 Stability in statics 54 1.7.2 Stability in dynamics 55 1.7.3 Stable axes of rotation around the principal axis 56 1.7.4 Noether's theorem and conservation laws 58 1.8 Further reading 61 Exercises 61 References 63 2 Numerical Integration of Ordinary Differential Equations 65 2.1 Fundamentals of numerical analysis 65 2.1.1 Floating point numbers 65 2.1.2 Big-O notation 67 2.1.3 Relative and absolute error 69 2.1.4 Truncation error 69 2.1.5 Local and g...

List of contents

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 Furthe

Product details

• Authors: Jian Chen, Chen Jian, Hans-Geor Matuttis, Hans-Georg Matuttis, Hans-Georg (The University of Electro-Co Matuttis, Hans-Georg Chen Matuttis, Hg Matuttis, Matuttis Hans-Georg
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 24.06.2014
• EAN: 9781118567203
• ISBN: 978-1-118-56720-3
• No. of pages: 448
• Subjects: Natural sciences, medicine, IT, technology > Physics, astronomy > Mechanics, acoustics; Physik, Mathematik, Maschinenbau, Mathematische Physik, Mathematics, Physics, Mechanical Engineering, Computational / Numerical Methods, Rechnergestützte / Numerische Verfahren im Maschinenbau, Applied Mathematics in Science, Mathematik in den Naturwissenschaften, Mathematical & Computational Physics, Diskrete-Elemente-Methode