| List of Figures | p. XVII |
| List of Tables | p. LXIII |
| Nomenclature | p. LXV |
| Introduction | |
| Introduction | p. 3 |
| Materials Deformation and Fracture Phenomena: Why and How Things Break | p. 5 |
| Strength of Materials: Flaws, Defects, and a Perfect Material | p. 6 |
| Crystal Structures and Molecular Packing | p. 8 |
| Cracks | p. 10 |
| Dislocations | p. 10 |
| Other Defects in Crystals and Other Structures | p. 12 |
| Brittle vs. Ductile Material Behavior | p. 12 |
| The Need for Atomistic Simulations | p. 15 |
| Applications: Experimental and Computational Mechanics | p. 18 |
| Experimental Techniques | p. 18 |
| Example Applications: The Significance of Mechanics | p. 20 |
| Outline of This Book | p. 27 |
| Basics of Atomistic, Continuum and Multiscale Methods | |
| Basic Atomistic Modeling | p. 31 |
| Introduction | p. 31 |
| Modeling and Simulation | p. 32 |
| Model Building and Physical Representation | p. 34 |
| The Concept of Computational Experiments | p. 35 |
| Basic Statistical Mechanics | p. 36 |
| Formulation of Classical Molecular Dynamics | p. 37 |
| Integrating the Equations of Motion | p. 39 |
| Thermodynamic Ensembles and Their Numerical Implementation | p. 40 |
| Energy Minimization | p. 43 |
| Monte Carlo Techniques | p. 44 |
| Classes of Chemical Bonding | p. 46 |
| The Interatomic Potential or Force Field: Introduction | p. 48 |
| Pair Potentials | p. 50 |
| Multibody Potentials: Embedded Atom Method for Metals | p. 54 |
| Force Fields for Biological Materials and Polymers | p. 56 |
| Bond Order and Reactive Potentials | p. 59 |
| Limitations of Classical Molecular Dynamics | p. 68 |
| Numerical Implementation | p. 69 |
| Periodic Boundary Conditions | p. 70 |
| Force Calculation | p. 71 |
| Neighbor Lists and Bins | p. 72 |
| Property Calculation | p. 73 |
| Temperature Calculation | p. 73 |
| Pressure Calculation | p. 74 |
| Radial Distribution Function | p. 74 |
| Mean Square Displacement Function | p. 75 |
| Velocity Autocorrelation Function | p. 76 |
| Virial Stress Tensor | p. 76 |
| Large-Scale Computing | p. 78 |
| Historical Development of Computing Power | p. 79 |
| Parallel Computing | p. 80 |
| Discussion | p. 82 |
| Visualization and Analysis Methods | p. 83 |
| Energy Method | p. 85 |
| Centrosymmetry Parameter | p. 86 |
| Slip Vector | p. 88 |
| Measurement of Defect Speed | p. 89 |
| Visualization Methods for Biological Structures | p. 89 |
| Other Methods | p. 90 |
| Distinguishing Modeling and Simulation | p. 90 |
| Application of Mechanical Boundary Conditions | p. 90 |
| Summary | p. 93 |
| Basic Continuum Mechanics | p. 95 |
| Newton's Laws of Mechanics | p. 95 |
| Definition of Displacement, Stress, and Strain | p. 97 |
| Stress Tensor | p. 99 |
| Equilibrium Conditions | p. 100 |
| Strain Tensor | p. 103 |
| Energy Approach to Elasticity | p. 105 |
| Isotropic Elasticity | p. 107 |
| Nonlinear Elasticity or Hyperelasticity | p. 108 |
| Elasticity of a Beam | p. 110 |
| Reduction Formulas | p. 110 |
| Equilibrium Equations | p. 111 |
| Example: Solution of a Simple Beam Problem | p. 112 |
| Calculation of Internal Stress Field | p. 113 |
| Differential Beam Equations | p. 116 |
| The Need for Atomistic Elasticity: What's Next | p. 119 |
| Atomistic Elasticity: Linking Atoms and Continuum | p. 121 |
| Thermodynamics as Bridge Between Atomistic and Continuum Viewpoints | p. 121 |
| The Atomic and Molecular Origin of Elasticity: Entropic vs. Energetic Sources | p. 122 |
| The Virial Stress and Strain | p. 123 |
| Elasticity Due to Energetic Contributions | p. 124 |
| Cauchy-Born Rule | p. 124 |
| Elasticity of a One-Dimensional String of Atoms | p. 126 |
| Elasticity and Surface Energy of a Two-Dimensional Triangular Lattice | p. 128 |
| Elasticity and Surface Energy of a Three-Dimensional FCC Lattice | p. 142 |
| Concluding Remarks | p. 149 |
| Elasticity Due to Entropic Contributions | p. 149 |
| Elasticity of Single Molecules: Worm-Like-Chain Model | p. 150 |
| Elasticity of Polymers | p. 152 |
| Discussion | p. 154 |
| Multiscale Modeling and Simulation Methods | p. 157 |
| Introduction | p. 157 |
| Direct Numerical Simulation vs. Multiscale and Multiparadigm Modeling | p. 158 |
| Differential Multiscale Modeling | p. 159 |
| Detailed Description of Selected Multiscale Methods to Span Vast Lengthscales | p. 160 |
| Examples of Hierarchical Multiscale Coupling | p. 160 |
| Concurrent Integration of Tight-Binding, Empirical Force Fields and Continuum Theory | p. 162 |
| The Quasicontinuum Method and Related Approaches | p. 165 |
| Continuum Approaches Incorporating Atomistic Information | p. 168 |
| Hybrid ReaxFF Model: Integration of Chemistry and Mechanics | p. 169 |
| Advanced Molecular Dynamics Techniques to Span Vast Timescales | p. 175 |
| Discussion | p. 180 |
| Material Deformation and Failure | |
| Deformation and Dynamical Failure of Brittle Materials | p. 185 |
| The Nature of Brittle Fracture | p. 186 |
| Basics of Linear Elastic Fracture Mechanics | p. 189 |
| Energy Balance Considerations: Griffith's Model of Fracture | p. 189 |
| Asymptotic Stress Field and Stress Intensity Factor | p. 194 |
| Crack Limiting Speed in Dynamic Fracture | p. 196 |
| Atomistic Modeling of Brittle Materials | p. 197 |
| A One-Dimensional Example of Brittle Fracture: Joint Continuum-Atomistic Approach | p. 201 |
| Introduction | p. 202 |
| Linear-Elastic Continuum Model | p. 204 |
| Hyperelastic Continuum Mechanics Model for Bilinear Stress-Strain Law | p. 207 |
| Molecular Dynamics Simulations of the One-Dimensional Crack Model: The Harmonic Case | p. 211 |
| Molecular Dynamics Simulations of the One-Dimensional Crack Model: The Supersonic Case | p. 217 |
| Discussion and Conclusions | p. 219 |
| Stress and Deformation Field near Rapidly Propagating Mode I Cracks in a Harmonic Lattice | p. 223 |
| Stress and Deformation Fields | p. 225 |
| Energy Flow near the Crack Tip | p. 227 |
| Limiting Velocities of Mode I Cracks in Harmonic Lattices | p. 229 |
| Summary | p. 230 |
| Crack Limiting Speeds of Cracks: The Significance of Hyperelasticity | p. 234 |
| Modeling | p. 236 |
| Crack Speed and Energy Flow | p. 238 |
| Hyperelastic Area | p. 239 |
| How Fast can Cracks Propagate? | p. 242 |
| Characteristic Energy Length Scale in Dynamic Fracture | p. 244 |
| Summary | p. 248 |
| Crack Instabilities and Hyperelastic Material Behavior | p. 249 |
| Introduction | p. 251 |
| Design of Computational Model | p. 252 |
| Computational Experiments | p. 255 |
| Discussion and Conclusion | p. 258 |
| Suddenly Stopping Cracks: Linking Atomistic Modeling, Theory, and Experiment | p. 260 |
| Introduction | p. 260 |
| Theoretical Background of Suddenly Stopping Cracks | p. 262 |
| Atomistic Simulation Setup | p. 264 |
| Atomistic Simulation Results of a Suddenly Stopping Mode I Crack | p. 268 |
| Atomistic Simulation Results of a Suddenly Stopping Mode II Crack | p. 278 |
| Discussion | p. 286 |
| Crack Propagation Along Interfaces of Dissimilar Materials | p. 287 |
| Mode I Dominated Cracks at Bimaterial Interfaces | p. 289 |
| Mode II Cracks at Bimaterial Interfaces | p. 294 |
| Summary | p. 297 |
| Dynamic Fracture Under Mode III Loading | p. 299 |
| Atomistic Modeling of Mode III Cracks | p. 300 |
| Mode III Cracks in a Harmonic Lattice - The Reference Systems | p. 300 |
| Mode III Crack Propagation in a Thin Stiff Layer Embedded in a Soft Matrix | p. 301 |
| Suddenly Stopping Mode III Crack | p. 303 |
| Discussion | p. 303 |
| Brittle Fracture of Chemically Complex Materials | p. 304 |
| Introduction | p. 305 |
| Hybrid Atomistic Modeling of Cracking in Silicon: Mixed Hamiltonian Gormulation | p. 307 |
| Atomistic Model | p. 307 |
| Simulation Results | p. 308 |
| Dynamical Fracture Mechanisms | p. 311 |
| Reactive Chemical Processes and Fracture Initiation | p. 316 |
| Summary | p. 317 |
| Summary: Brittle Fracture | p. 320 |
| Hyperelasticity can Govern Dynamic Fracture | p. 323 |
| Interfaces and Geometric Confinement | p. 326 |
| Deformation and Fracture of Ductile Materials | p. 327 |
| Introduction | p. 327 |
| Continuum Theoretical Concepts of Dislocations and Their Interactions | p. 328 |
| Properties of Dislocations | p. 329 |
| Forces on Dislocations | p. 331 |
| Rice-Thomson Model for Dislocation Nucleation | p. 332 |
| Rice-Peierls Model | p. 337 |
| Link with Atomistic Concepts | p. 338 |
| Generalized Stacking Fault Curves | p. 338 |
| Linking Atomistic Simulation Results to Continuum Mechanics Theories of Plasticity | p. 339 |
| Modeling Plasticity Using Large-Scale Atomistic Simulations | p. 341 |
| Case Study: Deformation Mechanics of Model FCC Copper - LJ Potential | p. 343 |
| Model Setup | p. 343 |
| Visualization Procedure | p. 345 |
| Simulation Results | p. 345 |
| Summary | p. 355 |
| Case Study: Deformation Mechanics of a Nickel Nanocrystal - EAM Potential | p. 357 |
| Case Study: Multi-Paradigm Modeling of Chemical Complexity in Mechanical Deformation of Metals | p. 359 |
| Atomistic Model and Validation | p. 360 |
| Example Application: Modeling Hybrid Metal-Organic Systems | p. 364 |
| Deformation and Fracture Mechanics of Geometrically Confined Materials | p. 373 |
| Introduction | p. 373 |
| Thin Metal Films and Nanocrystalline Metals | p. 381 |
| Constrained Diffusional Creep in Ultra-Thin Metal Films | p. 385 |
| Single Edge Dislocations in Nanoscale Thin Films | p. 390 |
| Rice-Thompson Model for Nucleation of Parallel Glide Dislocations | p. 393 |
| Discussion and Summary | p. 396 |
| Atomistic Modeling of Constrained Grain Boundary Diffusion in a Bicrystal Model | p. 396 |
| Introduction and Modeling Procedure | p. 397 |
| Formation of the Diffusion Wedge | p. 400 |
| Development of the Crack-Like Stress Field and Nucleation of Parallel Glide Dislocations | p. 402 |
| Discussion | p. 404 |
| Summary | p. 408 |
| Dislocation Nucleation from Grain Triple Junction | p. 408 |
| Atomistic Modeling of the Grain Triple Junction | p. 409 |
| Atomistic Simulation Results | p. 410 |
| Discussion | p. 414 |
| Atomistic Modeling of Plasticity of Polycrystalline Thin Films | p. 414 |
| Atomistic Modeling of Polycrystalline Thin Films | p. 415 |
| Atomistic Simulation Results | p. 416 |
| Plasticity of Nanocrystalline Bulk Materials with Twin Lamella | p. 422 |
| Modeling of Constrained Diffusional Creep in Polycrystalline Films | p. 426 |
| Discussion | p. 428 |
| Summary: Results of Modeling of Thin Films | p. 430 |
| Use of Atomistic Simulation Results in Hierarchical Multiscale Modeling | p. 432 |
| Mechanisms of Plastic Deformation of Ultra-thin Uncapped Copper Films | p. 434 |
| Deformation Map of Thin Films | p. 434 |
| Yield Stress in Ultra-Thin Copper Films | p. 435 |
| The Role of Interfaces and Geometric Confinement | p. 436 |
| Deformation and Fracture Mechanics of Carbon Nanotubes | p. 438 |
| Mesoscale Modeling of CNT Bundles | p. 441 |
| Mesoscale Simulation Results | p. 444 |
| Discussion | p. 445 |
| Flaw-Tolerant Nanomaterials: Bulk Fracture and Deformation | p. 446 |
| Strength of Brittle Nanoparticles | p. 446 |
| Simulation Results | p. 450 |
| Nanoscale Adhesion Systems | p. 452 |
| Strength of Fibrillar Adhesion Systems | p. 453 |
| Theoretical Considerations of Shape Optimization of Adhesion Elements | p. 455 |
| Atomistic Modeling | p. 456 |
| Simulation Results | p. 457 |
| Summary | p. 460 |
| References | p. 463 |
| Index | p. 483 |
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