Computational Mechanics of Discontinua -- Contents -- Series Preface -- Preface -- Acknowledgements -- 1 Introduction to Mechanics of Discontinua -- 1.1 The Concept of Discontinua -- 1.2 The Paradigm Shift -- 1.3 Some Problems of Mechanics of Discontinua -- 1.3.1 Packing -- 1.3.2 Fracture and Fragmentation -- 1.3.3 Demolition and Structures in Distress, Progressive Collapse -- 1.3.4 Nanotechnology -- 1.3.5 Block Caving -- 1.3.6 Mineral Processing -- 1.3.7 Discrete Populations in General -- References -- Further Reading -- 2 Methods of Mechanics of Discontinua -- 2.1 Introduction -- 2.2 Discrete Element Methods -- 2.2.1 Spherical Particles -- 2.2.2 Blocky Particles -- 2.2.3 Oblique and Super-Quadric Particles -- 2.2.4 Rigid Potential Field Particles -- 2.2.5 3D Real Shape Particles -- 2.2.6 Computer Games and Special Effects -- 2.3 The Combined Finite-Discrete Element Method -- 2.4 Molecular Dynamics -- 2.4.1 Common Potentials -- 2.5 Smooth Particle Hydrodynamics -- 2.6 Discrete Populations Approach -- 2.7 Algorithms and Solutions -- References -- Further Reading -- 3 Disc to Edge Contact Interaction in 2D -- 3.1 Problem Description -- 3.2 Integration of Normal Contact Force -- 3.3 Tangential Force -- 3.4 Equivalent Nodal Forces -- Further Reading -- 4 Triangle to Edge Contact Interaction in 2D -- 4.1 Problem Description -- 4.2 Integration of Normal Contact Force -- 4.3 Tangential Force -- 4.4 Equivalent Nodal Forces -- Further Reading -- 5 Ball to Surface Contact Interaction in 3D -- 5.1 Problem Description -- 5.2 Integration of Normal Contact Force -- 5.3 Tangential Force -- 5.4 Equivalent Nodal Forces -- Further Reading -- 6 Tetrahedron to Points Contact Interaction in 3D -- 6.1 Problem Description -- 6.2 Integration of Normal Contact Force -- 6.3 Tangential Force -- 6.4 Equivalent Nodal Forces -- Further Reading.

7 Tetrahedron to Triangle Contact Interaction in 3D -- 7.1 Problem Description -- 7.2 Integration of Normal Contact Force -- 7.3 Tangential Force -- 7.4 Equivalent Nodal Forces -- Further Reading -- 8 Rock Joints -- 8.1 Introduction -- 8.2 Interaction between Mesh Entities in 2D -- 8.2.1 Interaction between a 2D Disk and a Straight Edge -- 8.2.2 Numerical Integration of the Roller-Edge Interaction -- 8.3 Joint Dilation -- 8.4 Shear Resistance of a 2D Rock Joint -- 8.5 Numerical Examples -- References -- Further Reading -- 9 MR Contact Detection Algorithm for Bodies of Similar Size -- 9.1 The Challenge -- 9.2 Constraints of MR Contact Detection Algorithm -- 9.3 Space Decomposition -- 9.4 Mapping of Spherical Bounding Boxes onto Cells -- 9.5 Spatial Sorting -- 9.6 Quick Sort Algorithm -- 9.7 MR-Linear Sort Algorithm -- 9.8 Implementation of the MR-Linear Sort Algorithm -- 9.9 Quick Search Algorithm -- 9.10 MR-Linear Search Algorithm -- 9.11 CPU and RAM Performance -- 9.12 CPU Performance and RAM Consumption -- References -- Further Reading -- 10 MR Contact Detection Algorithm for Bodies of Different Sizes -- 10.1 Introduction -- 10.2 Description of the Multi-Step-MR Algorithm (MMR) -- 10.3 Polydispersity -- 10.4 CPU Performance -- 10.5 RAM Requirements -- 10.6 Robustness -- 10.7 Applications -- Further Reading -- 11 MR Contact Detection Algorithm for Complex Shapes in 2D -- 11.1 Introduction -- 11.2 Contactor Circle to Target Point MR Contact Detection Algorithm -- 11.2.1 Cell Size and Space Boundaries -- 11.2.2 Rendering of 2D Target Points onto Cells -- 11.2.3 Sorting of Target Cells -- 11.2.4 Interrogation Tools for Sorted Target Cells -- 11.2.5 Rendering of 2D Contactor Circles onto Cells -- 11.3 Contactor Circle to Target Edge MR Contact Detection Algorithm -- 11.3.1 Rendering 2D Target Edges onto Cells -- 11.3.2 Searching for Contacts.

11.4 Contactor Triangle to Target Edge MR Contact Detection Algorithm -- 11.4.1 Rendering 2D Triangles onto Cells -- 11.5 Extension to Other Shapes -- 11.6 Reporting of Contacting Couples -- Further Reading -- 12 MR Contact Detection Algorithm for Complex Shapes in 3D -- 12.1 Introduction -- 12.2 Rendering Target Simplex Shapes -- 12.2.1 Rendering 3D Points onto Cells -- 12.2.2 Rendering 3D Edges onto Cells -- 12.3 Sorting Target Cells -- 12.4 Target Cells Interrogation Tools -- 12.5 Searching for Contacts -- 12.5.1 Rendering Contactor Tetrahedron -- 12.5.2 Rendering Contactor Triangular Facet -- 12.5.3 Rendering Other Contactor Simplex Shapes -- Further Reading -- 13 Parallelization -- 13.1 Introduction -- 13.2 Domain Decomposition Approach -- 13.2.1 Communication Engine -- 13.2.2 Broadcasting Engine -- 13.2.3 Summing Engine -- 13.2.4 Gathering Engine -- 13.2.5 Distribution of Physical Objects across Processors -- 13.2.6 Creating Proxies -- 13.2.7 Relocating Originals -- 13.3 Graphics Processing Units (GPU) -- 13.4 Structured Parallelization -- Further Reading -- Index.