Atomistic Modeling of Materials Failure

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Springer Science & Business Media, Aug 7, 2008 - Technology & Engineering - 492 pages
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Atomistic Modeling of Materials Failure is an introduction to molecular and atomistic modeling techniques applied to solid fracture and deformation. Focusing on a variety of brittle, ductile, geometrically confined and biological materials, this detailed overview includes computational methods at the atomic scale, and describes how these techniques can be used to model the dynamics of cracks and other deformation mechanisms.

A full description of molecular dynamics (MD) as a numerical modeling tool covers the use of classical interatomic potentials and implementation of large-scale massively parallelized computing facilities in addition to the general philosophies of model building, simulation, interpretation and analysis of results. Readers will find an analytical discussion of the numerical techniques along with a review of required mathematical and physics fundamentals. Example applications for specific materials (such as silicon, copper, fibrous proteins) are provided as case studies for each of the techniques, areas and problems discussed.

Providing an extensive review of multi-scale modeling techniques that successfully link atomistic and continuum mechanical methods, Atomistic Modeling of Materials Failure is a valuable reference for engineers, materials scientists, and researchers in academia and industry.

 

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Contents

65 Stress and Deformation Field near Rapidly Propagating Mode I Cracks in a Harmonic Lattice
223
651 Stress and Deformation Fields
225
652 Energy Flow near the Crack Tip
227
653 Limiting Velocities of Mode I Cracks in Harmonic Lattices
229
654 Summary
230
The Significance of Hyperelasticity
234
661 Modeling
236
662 Crack Speed and Energy Flow
238

The Significance of Mechanics
20
16 Outline of This Book
27
Basics of Atomistic Continuum and Multiscale Methods
29
Basic Atomistic Modeling
31
22 Modeling and Simulation
32
221 Model Building and Physical Representation
34
222 The Concept of Computational Experiments
35
23 Basic Statistical Mechanics
36
24 Formulation of Classical Molecular Dynamics
37
241 Integrating the Equations of Motion
39
242 Thermodynamic Ensembles and Their Numerical Implementation
40
243 Energy Minimization
43
244 Monte Carlo Techniques
44
25 Classes of Chemical Bonding
46
Introduction
48
261 Pair Potentials
50
Embedded Atom Method for Metals
54
263 Force Fields for Biological Materials and Polymers
56
264 Bond Order and Reactive Potentials
59
265 Limitations of Classical Molecular Dynamics
68
27 Numerical Implementation
69
271 Periodic Boundary Conditions
70
272 Force Calculation
71
273 Neighbor Lists and Bins
72
28 Property Calculation
73
282 Pressure Calculation
74
284 Mean Square Displacement Function
75
285 Velocity Autocorrelation Function
76
29 LargeScale Computing
78
291 Historical Development of Computing Power
79
292 Parallel Computing
80
293 Discussion
82
210 Visualization and Analysis Methods
83
2101 Energy Method
85
2102 Centrosymmetry Parameter
86
2103 Slip Vector
88
2104 Measurement of Defect Speed
89
2106 Other Methods
90
213 Summary
93
Basic Continuum Mechanics
95
32 Definition of Displacement Stress and Strain
97
321 Stress Tensor
99
322 Equilibrium Conditions
100
323 Strain Tensor
103
33 Energy Approach to Elasticity
105
34 Isotropic Elasticity
107
35 Nonlinear Elasticity or Hyperelasticity
108
36 Elasticity of a Beam
110
362 Equilibrium Equations
111
Solution of a Simple Beam Problem
112
364 Calculation of Internal Stress Field
113
365 Differential Beam Equations
116
Whats Next
119
Atomistic Elasticity Linking Atoms and Continuum
121
Entropic vs Energetic Sources
122
43 The Virial Stress and Strain
123
44 Elasticity Due to Energetic Contributions
124
442 Elasticity of a OneDimensional String of Atoms
126
443 Elasticity and Surface Energy of a TwoDimensional Triangular Lattice
128
444 Elasticity and Surface Energy of a ThreeDimensional FCC Lattice
142
445 Concluding Remarks
149
WormLikeChain Model
150
452 Elasticity of Polymers
152
46 Discussion
154
Multiscale Modeling and Simulation Methods
156
52 Direct Numerical Simulation vs Multiscale and Multiparadigm Modeling
158
53 Differential Multiscale Modeling
159
54 Detailed Description of Selected Multiscale Methods to Span Vast Lengthscales
160
542 Concurrent Integration of TightBinding Empirical Force Fields and Continuum Theory
162
543 The Quasicontinuum Method and Related Approaches
165
544 Continuum Approaches Incorporating Atomistic Information
168
Integration of Chemistry and Mechanics
169
55 Advanced Molecular Dynamics Techniques to Span Vast Timescales
175
56 Discussion
180
Material Deformation and Failure
182
Deformation and Dynamical Failure of Brittle Materials
183
61 The Nature of Brittle Fracture
186
62 Basics of Linear Elastic Fracture Mechanics
189
622 Asymptotic Stress Field and Stress Intensity Factor
194
623 Crack Limiting Speed in Dynamic Fracture
196
63 Atomistic Modeling of Brittle Materials
197
Joint ContinuumAtomistic Approach
201
641 Introduction
202
642 LinearElastic Continuum Model
204
643 Hyperelastic Continuum Mechanics Model for Bilinear StressStrain Law
207
The Harmonic Case
211
The Supersonic Case
217
646 Discussion and Conclusions
219
663 Hyperelastic Area
239
664 How Fast can Cracks Propagate?
242
665 Characteristic Energy Length Scale in Dynamic Fracture
244
666 Summary
248
67 Crack Instabilities and Hyperelastic Material Behavior
249
671 Introduction
251
672 Design of Computational Model
252
673 Computational Experiments
255
674 Discussion and Conclusion
258
Linking Atomistic Modeling Theory and Experiment
260
682 Theoretical Background of Suddenly Stopping Cracks
262
683 Atomistic Simulation Setup
264
684 Atomistic Simulation Results of a Suddenly Stopping Mode I Crack
268
685 Atomistic Simulation Results of a Suddenly Stopping Mode II Crack
278
686 Discussion
286
69 Crack Propagation Along Interfaces of Dissimilar Materials
287
691 Mode I Dominated Cracks at Bimaterial Interfaces
289
692 Mode II Cracks at Bimaterial Interfaces
294
693 Summary
297
610 Dynamic Fracture Under Mode III Loading
299
6101 Atomistic Modeling of Mode III Cracks
300
6103 Mode III Crack Propagation in a Thin Stiff Layer Embedded in a Soft Matrix
301
6104 Suddenly Stopping Mode III Crack
303
611 Brittle Fracture of Chemically Complex Materials
304
6111 Introduction
305
Mixed Hamiltonian Gormulation
307
6114 Simulation Results
308
6115 Dynamical Fracture Mechanisms
311
6116 Reactive Chemical Processes and Fracture Initiation
316
6117 Summary
317
Brittle Fracture
320
6121 Hyperelasticity can Govern Dynamic Fracture
323
6122 Interfaces and Geometric Confinement
326
Deformation and Fracture of Ductile Materials
327
72 Continuum Theoretical Concepts of Dislocations and Their Interactions
328
721 Properties of Dislocations
329
722 Forces on Dislocations
331
723 RiceThomson Model for Dislocation Nucleation
332
724 RicePeierls Model
337
725 Link with Atomistic Concepts
338
727 Linking Atomistic Simulation Results to Continuum Mechanics Theories of Plasticity
339
73 Modeling Plasticity Using LargeScale Atomistic Simulations
341
Deformation Mechanics of Model FCC Copper LJ Potential
343
742 Visualization Procedure
345
744 Summary
355
Deformation Mechanics of a Nickel Nanocrystal EAM Potential
357
MultiParadigm Modeling of Chemical Complexity in Mechanical Deformation of Metals
359
761 Atomistic Model and Validation
360
Modeling Hybrid MetalOrganic Systems
364
Deformation and Fracture Mechanics of Geometrically Confined Materials
373
82 Thin Metal Films and Nanocrystalline Metals
381
821 Constrained Diffusional Creep in UltraThin Metal Films
385
822 Single Edge Dislocations in Nanoscale Thin Films
390
823 RiceThompson Model for Nucleation of Parallel Glide Dislocations
393
824 Discussion and Summary
396
831 Introduction and Modeling Procedure
397
832 Formation of the Diffusion Wedge
400
833 Development of the CrackLike Stress Field and Nucleation of Parallel Glide Dislocations
402
834 Discussion
404
835 Summary
408
841 Atomistic Modeling of the Grain Triple Junction
409
842 Atomistic Simulation Results
410
843 Discussion
414
851 Atomistic Modeling of Polycrystalline Thin Films
415
852 Atomistic Simulation Results
416
853 Plasticity of Nanocrystalline Bulk Materials with Twin Lamella
422
854 Modeling of Constrained Diffusional Creep in Polycrystalline Films
426
855 Discussion
428
Results of Modeling of Thin Films
430
86 Use of Atomistic Simulation Results in Hierarchical Multiscale Modeling
432
861 Mechanisms of Plastic Deformation of Ultrathin Uncapped Copper Films
434
863 Yield Stress in UltraThin Copper Films
435
864 The Role of Interfaces and Geometric Confinement
436
87 Deformation and Fracture Mechanics of Carbon Nanotubes
438
871 Mesoscale Modeling of CNT Bundles
441
872 Mesoscale Simulation Results
444
873 Discussion
445
Bulk Fracture and Deformation
446
882 Simulation Results
450
89 Nanoscale Adhesion Systems
452
891 Strength of Fibrillar Adhesion Systems
453
892 Theoretical Considerations of Shape Optimization of Adhesion Elements
455
893 Atomistic Modeling
456
894 Simulation Results
457
895 Summary
460
References
463
Index
482
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