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Index

N2 scaling, 72µVT, 40

Abell-Tersoff approach, 60Adhesion, 439, 452, 453Adhesion strength, 459Advanced molecular dynamics methods,

177Aluminum

nanocrystalline, 379AMBER, 56Analysis techniques, 410Asymptotic stress field, 194Atomic hypothesis, 35Atomic interactions, 35Atomistic simulations, 33Atomistic theory, 16, 121Averaging, 36Avogadro’s number, 79, 155

Barrierdislocation motion, 424

BCC, 9bcc packing, 13Beam elasticity, 110Berendsen thermostat, 40Billion-atom simulation, 341Bimaterial interface, 287Biological materials, 56Biomechanics, 9, 452Bond order potentials, 59, 63Bookkeeping, 73Boundary conditions, 90, 399

displacement, 90

mechanical, 90steered molecular dynamics, 92

Brittle failure, 12Brittle versus ductile, 12Brittle-to-ductile transition, 342Buffer region, 171

CADD, 167Canonical ensemble, 40Carbon nanotubes, 438Catalysis, 66Cauchy relation, 55Centrosymmetry parameter, 86Centrosymmetry technique, 410Charge equilibration, 63CHARMM, 56Chemical bonding, 46Chemical complexity, 56, 62, 63, 304,

359Classical molecular dynamics, 37CMDF, 173Coble creep, 378Cohesive zone, 446Common neighbor analysis, 90Computational efficiency, 54Computational Materials Design

FacilityCMDF, 173

Computer experiments, 35Computer power, 79Computing power, historical

development, 79Concurrent multiscale modeling, 162

484 Index

Concurrent multiscale simulation tools,157

Confinement, 244, 301, 436Constrained grain boundary diffusion,

385atomistic simulations, 396bicrystal model, 396continuum model, 388experimental evidence, 386

Continuum mechanics, 15, 95Continuum theory, 16, 121Copper

nanocrystalline, 379nanostructured, 422

Coulomb potential, 64Coupling

atomistic-continuum, 393atomistic-continuum theories of

plasticity, 339atomistic-experiment, 249, 271atomistic-mesoscopic scale, 432strain, 124stress, 123

Coupling constantheat bath, 41

Crack, 401, 419diffusion wedge, 386hyperelasticity, 207initiation time, 267parallel glide dislocations, 404versus diffusion wedge, 406

Cracks, 10Cross-slip, 352Crystal structure, 9

Deformationdiffusive, 378elastic, 5nanocrystalline materials, 378plastic, 5, 373thin films, 430

Deformation map, 434Deformation mechanisms, 373Deformation tensor, 104Deformation-mechanism map, 374Density functional theory, 48DFT, 164Differential beam equations, 116Differential multiscale modeling, 159

Diffusion, 15, 378Diffusion wedges, 385, 395, 397, 409

crack like, 401dislocation glide, 409formation, 400versus crack, 406, 408

Diffusive displacement, 401Diffusivity

copper, 178dependence, 436surface, 178

Discretization, 76Dislocation

cross slip, 425pileup, 404pilups, 425

Dislocation bowing, 412Dislocation channelling, 382Dislocation climb, 388Dislocation cutting, 346Dislocation density, 418

tensor, 341Dislocation dipole, 396, 403Dislocation dragging force, 349Dislocation motion

grain boundaries, 421Dislocation network, 421Dislocation pinning, 346Dislocations, 10, 11, 341

interaction, 424Displacement, 97DREIDING, 56Ductile failure, 13Dundur’s parameter, 393Dynamic materials failure, 5

EAM, 54, 166, 357, 359Edge dislocation, 329, 390Elastic regime, 5Electron gas, 55Electron volt, 155Electronic properties, 68Embedded atom potential, 48Embedded-atom method, 54Empirical potentials, 50Energetic elasticity, 122Energy approach to elasticity, 105Energy length scale

characteristic, 188, 234, 244, 299

Index 485

Energy method, 85Energy minimization, 43Energy release rate, 190, 196, 447, 453Entropic elasticity, 122Equations of motion, 39Ergodic hypothesis, 36, 41Experiments

polycrystalline films, 409

Failure, 5Failure processes, 32FCC, 9FCC lattice, 142FCC packing, 13FEAt, 163Flaw tolerance, 446, 457Flaws, 10Fleischer mechanism, 351Force calculation, 71Force field, 48Fracture, 12Fracture instability, 197Fracture surface energy, 140Fracture surface energy 3D, 148Free energy minima, 176Friedel-Escaig mechanism, 351

Gecko, 452, 453Geometric analysis, 85Geometric confinement, 14, 373, 381Geometrically necessary dislocations,

389Glassy phase, 398Glide

parallel glide dislocations, 409Grain boundary, 401

dislocation source, 414, 415jogs, 402stability, 402

Grain boundary processes, 378Grain boundary structure

elevated temperature, 400Grain boundary traction relaxation,

410, 415Grain boundary tractions, 430Grain triple junction, 408Grand canonical ensemble ensemble, 40Green-Kubo relations, 76Griffith condition, 13, 266

Hall-Petch, 373Hamiltonian, 37Hardening, 424Harmonic potential, 54, 128, 142HCP, 9Heat bath, 41Hierarchical multiscale methods, 157High-energy grain boundary, 410, 414Homologous temperature, 400Hooke’s law, 97Hybrid models, 169, 304, 359Hyperelasticity, 62, 108, 260

Image force, 392Image stress, 406Insects, 452Interface

crack-grain boundary, 419Interface effect, 381Interfaces, 287, 436

dissimilar materials, 287Interfaces and geometric confinement,

436Interfacial dislocations, 382, 418Intersonic mode I cracks, 242Interstitial tubes, 351Inverse Hall-Petch effect, 375, 376Isobaric-isothermal ensemble, 40

Jog dragging, 412Jogs, 413

kcal/mole, 155

Langevin dynamics, 41Large-scale computing, 78Leap-frog algorithm, 39Length-and time scale

Classical molecular dynamics, 341Lennard-Jones, 48, 52Limitations, classical molecular

dynamics, 68LINUX

supercomputers, 82Liquid-like grain boundary, 398Loading

strain field, 399Lomer-Cottrell locks, 355Long-time limit, 179Low-energy grain boundary, 410

486 Index

MAAD, 163Materials failure

ductile, 85nickel, 85

Materials in small dimensions, 381Mathews-Freund-Nix mechanism, 386Mean square displacement function, 75Measurement, 37Mechanical properties, 142Medium-range-order analysis, 90Melting temperature

copper, 399Mesoscopic simulations, 50, 434Message passing, 80Metropolis-Hastings algorithm, 45Microcanonical ensemble, 40Microelectronic devices, 381Microscopic configurations, 41Microstructure, 9, 76Miniaturization, 381Mirror-mist-hackle, 197Mode I fracture

Mother-daughter mechanism, 289Mode II fracture, 243, 294Mode III fracture, 142, 299Model materials, 35, 341Modeling, 32Modeling and simulation, 32, 33, 90Molecular dynamics, 37Molecular statics, 44Monte Carlo, 37, 45Morse potential, 53Mother-daughter mechanism, 289Mother-daughter-granddaughter

mechanism, 294MPI, 80Multi-body potential, 54Multi-scale phenomena, 35Multi-scale simulations

hierarchical, 432Multiparadigm modeling, 158, 170, 357Multiscale, 157Multiscale modeling and simulation,

157

Nanocrystalline copper, 376Nanocrystalline materials, 15, 353Nanoindentation, 167Nanomaterials, 26, 438, 446

Nanoscale, 381confinement, 391deformation phenomena, 435

Nanoscale adhesion, 453Nanostructured materials, 376

strain rate, 379yield stress, 379

Nanostructures, 446Nanotechnology, 3, 381Navier-Bernouilli, 114Newton, 155Newton’s laws, 96Nickel, 85

nanocrystalline, 379Nonlinear elasticity, 108NPT, 40NVE, 40NVT, 40

On-the-fly concurrent multiscalemethods, 158

Organic materials, 56Oxidation, 357

Pair potential, 48, 50Parallel glide dislocations, 167, 384, 419

experimental evidence, 386minimum film thickness, 403nucleation, 393, 396, 402nucleation mechanism, 394

Parallel molecular dynamics, 80Parrinello-Rahman, 41Partial dislocations, 348, 350, 422Partial point defects, 413Pascal, 155PBC, 70Peach-Koehler force, 392Periodic boundary conditions, 70Petaflop computers, 80Phonons, 164Pinning potential, 399Plane strain, 399Plastic deformation, 5Plasticity, 341

atomistic modeling, 414nanocrystalline materials, 422polycrystalline thin films, 414thin films, 409

Point defect generation, 413

Index 487

Polycrystalline films, 409Polycrystalline thin films

atomistic modeling, 415Polycrystalline thin metal films, 381Polymers, 9, 56Post-processing, 85Potential, 48Property calculation, 73, 93Protein unfolding, 92Proteins, 9, 56

Quantizationstress, 392

Quantum mechanics, 32, 35, 68Quasicontinuum method, QC, 165Quasicrystals, 201, 343

Brittle fracture, 201Dislocations, 343Ductile failure, 343

Radial distribution function, 74Reactive potentials, 59ReaxFF, 59, 62, 169, 304, 359Reduced units, 155Reference units, 155Relaxation, 399Relaxation mechanisms, 430Rice-Thomson model, 404Richard Feynman, 35Rigid boundaries, 403Rise time, 41Robustness, 459

SC, 9Screw dislocation, 329Self-folding, 439Sessile locks, 353Shielded Coulomb potential, 64Shock loading, 364Silicon, 55Simulation, 32Simulation techniques, 49Single atoms, 179Single edge dislocations, 390Size effects, 373, 381, 438, 452Slip planes, 353Slip vector, 88, 341, 410, 412Small-scale materials, 199Speedup, 81

Spring constant ratio, 236Stacking fault, 358State transition, 179Statistical mechanics, 36Strain, 97Strain rate, 266, 400Stress, 97Stress intensity, 393Stress intensity factor, 194, 266, 390,

396parallel glide dislocations, 402

Stress tensor, 99Sub-micron scale, 381Sub-nano structure, 422Submicron thin films, 385Suddenly stopping crack, 260

mode I, 268mode II, 278, 280mode III, 303

Super-Rayleigh fracture, 242, 274Supercomputers, 79Supercomputing, 78, 80, 201, 342Supersonic fracture, 207, 210, 280, 281,

289Supersonic mode I cracks, 289Supersonic mode II cracks, 243Surface diffusion, 177Surface diffusivity, 177Surface effects, 381, 436Surface steps, 178, 417

Temperature, 73Temperature accelerated method, 177Tersoff potential, 61The strongest size, 376Thermodynamics, 41, 105, 121Thin films, 167, 381

deformation map, 434yield stress, 384, 433, 435

Threading dislocations, 382, 383, 386,402, 417

versus parallel glide dislocations, 416,430

Three-dimensional molecular dynamicssimulations, 142

Threshold stress, 433Tight-Binding approach, 162Tight-binding potential, 48Tilt grain boundary, 399

488 Index

Time scale, 407Time scale dilemma, 175, 176Time scale methods, 175Time step, 43top500.org, 80Transition region, 171Transport properties, 76Triangular lattice, 9Triple junction, 410Twin grain boundary, 424Twin lamella, 422Two-dimensional lattice, 128

UFF, 56Unit conversion, 155Unstable stacking fault energy, 14

Vacancy tubes, 351Velocity autocorrelation function, 76Velocity verlet, 398Velocity Verlet algorithm, 40

Verlet algorithm, 39Virial strain, 124Virial stress, 76, 77, 123Virtual internal bond method, VIB, 168Viscoelasticity, 169Visualization, 83, 85, 345, 401

distributed computing, 83movies, 83Richard Hamming, 84virtual reality, 83

Volterra edge dislocations, 388

Water formation, 66Work-hardening, 354

Yield stress, 435Young’s modulus, 97, 120, 133, 142, 204

bilinear, 138, 207FCC, 142, 144

Zhou’s virial stress, 77