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). 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.

This book:
• 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

Contents
1 Mechanics
1.1 Degrees of freedom
1.2 Dynamics of rectilinear degrees of freedom
1.3 Dynamics of angular degrees of freedom
1.4 The phase space
1.5 Nonlinearities
1.6 From higher harmonics to chaos
1.7 Stability and conservation laws
1.8 Further reading
2 Numerical Integration of Ordinary Differential Equations
2.1 Fundamentals of numerical analysis
2.2 Numerical analysis for ordinary differential equations
2.3 Runge-Kutta methods
2.4 Symplectic methods
2.5 Stiff problems
2.6 Backward difference formulae
2.7 Other methods
2.8 Differential algebraic equations
2.9 Selecting an integrator
2.10 Further reading
3.1 Sliding Coulomb friction
3.2 Other contact geometries of Coulomb friction
3.3 Exact implementation of friction
3.4 Modeling and regularizations
3.5 Unfortunate treatment of Coulomb friction in the literature
3.6 Further reading
4 Phenomenology of Granular Materials
4.1 Phenomenology of grains
4.2 General phenomenology of granular agglomerates
4.3 History effects in granular materials
4.4 Further reading
5 Condensed Matter and Solid State Physics
5.1 Structure and properties of matter
5.2 From wave numbers to the Fourier transform
5.3 Waves and dispersion
5.4 Further reading
References
6 Modeling and Simulation
6.1 Experiments, theory and simulation
6.2 Computability, observables and auxiliary quantities
6.3 Experiments, theories and the discrete element method
6.4 The discrete element method and other particle simulation methods
6.5 Other simulation methods for granular materials
7 The Discrete Element Method in Two Dimensions
7.1 The discrete element method with soft particles
7.2 Modeling of polygonal particles
7.3 Interaction
7.4 Initial and boundary conditions
7.5 Neighborhood algorithms
7.6 Time integration
7.7 Program issues
7.8 Computing observables
7.9 Further reading
8 The Discrete Element Method in Three Dimensions
8.1 Generalization of the force law to three dimensions
8.2 Initialization of particles and their properties
8.3 Overlap computation
8.4 Optimization for vertex computation
8.5 The neighborhood algorithm for polyhedra
8.6 Programming strategy for the polyhedral simulation
8.7 The effect of dimensionality and the choice of boundaries
8.8 Further reading
9 Alternative Modeling Approaches
9.1 Rigidly connected spheres
9.2 Elliptical shapes
9.3 Composites of curves
9.4 Rigid particles
9.5 Discontinuous deformation analysis
9.6 Further reading
10 Running, Debugging and Optimizing Programs
10.1 Programming style
10.2 Hardware, memory and parallelism
10.3 Program writing
10.4 Measuring load, time and profiles
10.5 Speeding up programs10.6 Further reading
11 Beyond the Scope of This Book
11.1 Non-convex particles
11.2 Contact dynamics and friction
11.3 Impact mechanics
11.4 Fragmentation and fracturing
11.5 Coupling codes for particles and elastic continua
11.6 Coupling of particles and fluid
11.7 The finite element method for contact problems
11.8 Long-range interactions
Index

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