Dumitrica Trends in Computational Nanomechanics

Transcending Length and Time Scales
1. Auflage 2010
ISBN: 978-1-4020-9785-0
Verlag: Springer Netherlands
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 9, 628 Seiten

Reihe: Challenges and Advances in Computational Chemistry and Physics

Trends in Computational Nanomechanics reviews recent advances in analytical and computational modeling frameworks to describe the mechanics of materials on scales ranging from the atomistic, through the microstructure or transitional, and up to the continuum. The book presents new approaches in the theory of nanosystems, recent developments in theoretical and computational methods for studying problems in which multiple length and/or time scales must be simultaneously resolved, as well as example applications in nanomechanics. This title will be a useful tool of reference for professionals, graduates and undergraduates interested in Computational Chemistry and Physics, Materials Science, Nanotechnology.

Dr. Traian Dumitrica received a doctorate in physics from Texas A&M University in 2000. Since then he has worked at Rice University, Freie Universitaet Berlin, and Universitaet Kassel. He joined the University of Minnesota faculty in 2005. His research focuses in understanding the mechanical properties of materials using atomistic computational methods. System of interest include carbon nanotubes, silicon nanoparticles, and coherent phonons in semiconductors.

Autoren/Hrsg.

Dumitrica, Traian

Dumitrica, Trajan

Inhaltsverzeichnis

1;Preface;6
2;Contents;10
3;1 Hybrid Quantum/Classical Modeling of Material Systems: The ``Learn on the Fly'' Molecular Dynamics Scheme;20
3.1;1.1 Introduction;20
3.2;1.2 The LOTF Scheme;21
3.2.1;1.3.1 Reconciling the Boundary;21
3.2.2;1.3.2 Evaluation of the QM Forces;23
3.2.3;1.3.3 Force Matching;24
3.2.3.1;1.3.3.1 The Adjustable Potential;25
3.2.4;1.3.4 The LOTF Predictor-Corrector Scheme;26
3.3;1.3 Selection of the QM Region: An Hysteretic Algorithm;29
3.3.1;1.4.1 A Screw Dislocation Study;30
3.3.2;1.4.2 Brittle Fracture;31
3.4;1.4 Towards Chemical Complexity: Hydrogen-Induced Platelets in Silicon;34
3.4.1;1.5.1 The Atom-Resolved Stress Tensor;37
3.5;1.5 Acknowledgments;40
3.6;References;40
4;2 Multiscale Molecular Dynamics and the Reverse Mapping Problem;43
4.1;2.1 Introduction;43
4.1.1;2.2.1 Atomistic and Coarse-Grained Molecular Dynamics;46
4.1.2;2.2.2 Mapping Between Different Representations, or the Reverse Mapping Problem;47
4.2;2.2 Adaptive Multiscale Molecular Dynamics;48
4.2.1;2.3.1 Stage 1: Coupling Atomistic and Coarse-Grained Regions;49
4.2.2;2.3.2 Equations of Motion;55
4.2.3;2.3.3 Stage 2: Freezing the Intra-Bead Motions;56
4.2.4;2.3.4 Case Study 1: Liquid Methane;58
4.2.5;2.3.5 Other Adaptive Multiscale Implementations;60
4.3;2.3 Reverse Mapping Through Rigid Body Rotation;61
4.3.1;2.4.1 Rigid Body Rotational Optimization;62
4.3.2;2.4.2 Rigid Body Rotational Dynamics;65
4.3.3;2.4.3 Coupling Between the Rotational Dynamics and Coarse-Grained Molecular Dynamics;66
4.3.4;2.4.4 Case Study 2: Polyethylene Chain;68
4.4;2.4 Combining Rotational Reverse Mapping with Hybrid MD;71
4.4.1;2.5.1 Case Study 3: Hybrid Simulation of a Polyethylene Chain;72
4.5;2.5 Summary;75
4.6;2.6 Acknowledgments;75
4.7;References;76
5;3 Transition Path Sampling Studies of Solid-Solid Transformations in Nanocrystals under Pressure;78
5.1;3.1 Rare Events in Computer Simulations;78
5.2;3.2 Transition Path Sampling;81
5.2.1;3.3.1 The Transition Path Ensemble;81
5.2.2;3.3.2 Monte Carlo in Trajectory Space;83
5.2.3;3.3.3 Analyzing Trajectories;86
5.2.4;3.3.4 Calculating Rate Constants;88
5.3;3.3 A TPS Algorithm for Nanocrystals in a Pressure Bath;91
5.3.1;3.4.1 Ideal Gas Pressure Bath;91
5.3.1.1;3.4.1.1 Algorithm;92
5.3.2;3.4.2 Simple Shooting Moves;94
5.4;3.4 The Wurtzite to Rocksalt Transformation in CdSe Nanocrystals;95
5.4.1;3.5.1 Straightforward MD Simulations;96
5.4.2;3.5.2 TPS Reveals the Main Mechanism;98
5.5;3.5 Concluding Remarks;98
5.6;3.6 Acknowledgments;99
5.7;References;99
6;4 Nonequilibrium Molecular Dynamics and Multiscale Modeling of Heat Conduction in Solids;102
6.1;4.1 Introduction;102
6.2;4.2 Molecular Dynamics and its Applicability to the Simulation of Heat Transport;104
6.2.1;4.3.1 Introduction to Equilibrium MD;104
6.2.2;4.3.2 Temperature Control;106
6.2.3;4.3.3 Lattice Vibrations;107
6.2.4;4.3.4 The Quantum Model of Phonon Heat Transport;108
6.2.5;4.3.5 The Classical Limit;112
6.2.6;4.3.6 Heat Transport in Metals;115
6.3;4.3 Nonequilibrium Molecular Dynamics;116
6.3.1;4.4.1 The Green-Kubo Method;117
6.3.2;4.4.2 The Direct Method;117
6.3.3;4.4.3 Size Effects;123
6.4;4.4 Isothermal Concurrent Multiscale Methods;126
6.4.1;4.5.1 Coarse-Grained Dynamics;128
6.4.2;4.5.2 Coarse-Grained Thermal Properties;132
6.4.3;4.5.3 Boundary Conditions for the Atomistic/Continuum Interface;134
6.4.4;4.5.4 Isothermal Dynamic Multiscale Models;138
6.5;4.5 Non-Isothermal Concurrent Multiscale Methods;139
6.5.1;4.6.1 Quasi-Static Phonon Models for Insulators;140
6.5.2;4.6.2 Dynamic Phonon Models for Insulators;143
6.5.3;4.6.3 Quasi-Static Models for Metals;144
6.5.4;4.6.4 Dynamic Coarse-Grained Models for Metals;145
6.5.5;4.6.5 Conclusions;146
6.6;4.6 ACKNOWLEDGEMENT;147
6.7;REFERENCES;147
7;5 A Multiscale Methodology to Approach Nanoscale Thermal Transport;152
7.1;5.1 Introduction;152
7.1.1;5.2.1 Interfacial Resistance;153
7.1.2;5.2.2 Phonon Behavior Through Acoustic Waves;153
7.1.3;5.2.3 Strategies to Modulate the Interfacial Resistance;154
7.1.4;5.2.4 Role of Surface Modifications;154
7.2;5.2 Continuum Limits;155
7.3;5.3 Multiscale Investigations;156
7.3.1;5.4.1 Atomistic and Multiscale Simulations;156
7.3.2;5.4.2 Molecular Dynamics (MD) Simulations;158
7.3.3;5.4.3 Thermal Lattice Boltzmann Method (LBM);159
7.3.4;5.4.4 Hybrid Multiscale Methodology;160
7.3.5;5.4.5 Coupling MD and LBM;161
7.4;5.4 Example Problems;163
7.5;5.5 Acknowledgments;163
7.6;REFERENCES;163
8;6 Multiscale Modeling of Contact-Induced Plasticity in Nanocrystalline Metals;168
8.1;6.1 Introduction;168
8.2;6.2 Atomistic Modeling of Nanoscale Contact in Nanocrystalline Films;171
8.2.1;6.3.1 Simulation Methods;172
8.2.1.1;6.3.1.1 Molecular Dynamics;172
8.2.1.2;6.3.1.2 Quasicontinuum (QC) Method;172
8.2.2;6.3.2 Modeling of Spherical/Cylindrical Contact in Nanocrystalline Metals;173
8.2.3;6.3.3 Calculations of Local Stresses and Mean Contact Pressures;175
8.2.4;6.3.4 Tools for the Visualization of Defects and Grain Boundaries;177
8.2.4.1;6.3.4.1 Centro-Symmetry Parameter;177
8.2.4.2;6.3.4.2 Local Crystal Structure by Ackland and Jones;178
8.3;6.3 Effects of Interatomic Potentials on Equilibrium Microstructures;178
8.4;6.4 Effects of a Grain Boundary Network on Incipient Plasticity During Nanoscale Contact;180
8.5;6.5 Mechanisms of Grain Boundary Motion During Contact Plasticity;183
8.6;6.6 Concluding Remarks;187
8.7;6.7 Acknowledgment;187
8.8;References;188
9;7 Silicon Nanowires: From Empirical to First Principles Modeling;190
9.1;7.1 Introduction;190
9.2;7.2 Methodological Considerations;193
9.2.1;7.3.1 Empirical Models;194
9.2.2;7.3.2 Semi-Empirical Models;195
9.3;7.3 Structural Properties: Application of Empirical Methods;197
9.4;7.4 Morphology of Thin Silicon Nanowires: Application of Tight Binding and First Principles Methods;200
9.5;7.5 Conclusions;205
9.6;References;206
10;8 Multiscale Modeling of Surface Effects on the Mechanical Behavior and Properties of Nanowires;209
10.1;8.1 Introduction;209
10.2;8.2 Methodology;212
10.2.1;8.3.1 Continuum Mechanics Preliminaries;212
10.2.2;8.3.2 Surface and Bulk Energy Densities;213
10.2.3;8.3.3 Formulation for Embedded Atom Method/FCC Metals;215
10.2.4;8.3.4 Formulation for Diamond Cubic Lattices;219
10.2.4.1;8.3.4.1 Bulk Cauchy-Born Model for Silicon;219
10.2.4.2;8.3.4.2 Surface Cauchy-Born Model for Silicon;222
10.3;8.3 Finite Element Formulation and Implementation;224
10.3.1;8.4.1 Variational Formulation;224
10.3.2;8.4.2 Finite Element Eigenvalue Problem for Nanowire Resonant Frequencies;225
10.4;8.4 Applications of Surface Cauchy-Born Model;226
10.5;8.5 Direct Surface Cauchy-Born/Molecular Statics Comparison;226
10.6;8.6 Surface Stress Effects on the Resonant Properties of Silicon Nanowires;228
10.6.1;8.7.1 Constant Cross Sectional Area;231
10.6.2;8.7.2 Constant Length;233
10.6.3;8.7.3 Constant Surface Area to Volume Ratio;234
10.7;8.7 Discussion and Analysis;235
10.7.1;8.8.1 Comparison to Experiment;237
10.8;8.8 Conclusions and Perspectives;239
10.9;8.9 Acknowledgments;240
10.10;References;240
11;9 Predicting the Atomic Configuration of 1- and 2-Dimensional Nanostructures via Global Optimization Methods;246
11.1;9.1 Introduction;246
11.2;9.2 Reconstruction of Silicon Surfaces as a Problem of Global Optimization;249
11.2.1;9.3.1 The Parallel-Tempering Monte Carlo;250
11.2.2;9.3.2 Genetic Algorithm;254
11.2.3;9.3.3 Selected Results on Si(114);256
11.3;9.3 The Structure of Freestanding Nanowires;258
11.3.1;9.4.1 A Genetic Algorithm for 1-D Nanowire Systems;258
11.3.2;9.4.2 Magic Structures of H-Passivated Si-[110] Nanowires;261
11.3.3;9.4.3 Growth of 1-D Nanostructures into Global Minima Under Radial Confinement;262
11.4;9.4 Future Directions;265
11.5;9.5 Acknowledgments;266
11.6;References;266
12;10 Atomic-Scale Simulations of the Mechanical Behavior of Carbon Nanotube Systems;269
12.1;10.1 Introduction;269
12.2;10.2 Computational Details;270
12.2.1;10.3.1 Interatomic Potentials;271
12.2.2;10.3.2 Important Approximations;274
12.2.2.1;10.3.2.1 Periodic Boundary Conditions;274
12.2.2.2;10.3.2.2 Temperature Control;275
12.2.2.3;10.3.2.3 Predictor-Corrector Algorithm;276
12.2.2.4;10.3.2.4 Simulation Methods for Mechanical Behavior;277
12.3;10.3 Mechanical Behavior of Nanotubes;278
12.3.1;10.4.1 Tensile Behavior;279
12.3.1.1;10.4.1.1 Young's Modulus;279
12.3.1.2;10.4.1.2 Fracture or Plastic Behavior;280
12.3.1.3;10.4.1.3 Effect of Filling, Functionalization, and Temperature;281
12.3.1.4;10.4.1.4 Effect of Combined Loads;282
12.3.2;10.4.2 Compressive Behavior;285
12.3.2.1;10.4.2.1 Buckling Instability;285
12.3.2.2;10.4.2.2 Effect of Filling, Functionalization, and Temperature;287
12.3.2.3;10.4.2.3 Nanotube Proximal Probe Tips;289
12.3.2.4;10.4.2.4 Crystalline Bundle;290
12.3.3;10.4.3 Bending Behavior;290
12.3.3.1;10.4.3.1 Bending Modulus;290
12.3.3.2;10.4.3.2 Buckling Instability;291
12.3.3.3;10.4.3.3 Effect of Filling, Functionalization, and Temperature;291
12.3.3.4;10.4.3.4 Effect of External Gases;292
12.3.4;10.4.4 Torsional Behavior;294
12.3.4.1;10.4.4.1 Shear Modulus and Stiffness;294
12.3.4.2;10.4.4.2 Buckling Instability;296
12.3.4.3;10.4.4.3 Effect of Filling, Functionalization, and Temperature;297
12.3.4.4;10.4.4.4 Effect of Combined Loads;300
12.3.4.5;10.4.4.5 Crystalline Bundle;305
12.4;10.4 Conclusions;305
12.5;10.5 Acknowledgments;306
12.6;REFERENCES;306
13;11 Stick-Spiral Model for Studying Mechanical Properties of Carbon Nanotubes;310
13.1;11.1 Introduction;310
13.2;11.2 Carbon Nanotubes and Their Mechanical Properties;311
13.2.1;11.3.1 Carbon Nanotubes (CNTs);311
13.2.2;11.3.2 Mechanical Properties of CNTs;313
13.2.3;11.3.3 Theoretical Modeling on Geometry Dependent Mechanical Properties of CNTs;313
13.3;11.3 Stick-Spiral Model For Carbon Nanotubes;315
13.3.1;11.4.1 Model Description;315
13.3.2;11.4.2 Governing Equations of the Stick-Spiral Model;317
13.3.3;11.4.3 Linear Stick-Spiral Model and its Applications;319
13.3.3.1;11.4.3.1 Linear Stick-Spiral Model;319
13.3.3.2;11.4.3.2 Elastic Mechanical Properties of SWCNTs;319
13.3.3.3;11.4.3.3 Explicit Expressions for Vibrating Frequencies of Some Raman Modes;321
13.3.4;11.4.4 Nonlinear Stick-Spiral Model and its Applications;323
13.3.4.1;11.4.4.1 Nonlinear Stick-Spiral Model;323
13.3.4.2;11.4.4.2 Mechanical Behavior of SWCNTs Under Large Strains;324
13.4;11.4 Concluding Remarks;327
13.5;11.5 Acknowledgments;328
13.6;11.5 Appendix;328
13.7;References;330
14;12 Potentials for van der Waals Interaction in Nano-Scale Computation;336
14.1;12.1 Introduction;336
14.2;12.2 Potentials for van der Waals Interaction;337
14.2.1;12.3.1 The Lennard-Jones Potential;337
14.2.2;12.3.2 The Registry-Dependent Interlayer Potential;337
14.3;12.3 Computational Method;337
14.4;12.4 Comparison Between the Two Potentials;340
14.4.1;12.5.1 On the Lattice Registry Effect;340
14.4.2;12.5.2 On the Deformation of Carbon Nanotubes;342
14.5;12.5 Concluding Remarks;345
14.6;REFERENCES;345
15;13 Electrical Conduction in Carbon Nanotubes under Mechanical Deformations;347
15.1;13.1 Introduction;347
15.2;13.2 Modeling Procedures;351
15.2.1;13.3.1 The Carbon Nanotube Wall;352
15.2.2;13.3.2 Initial Internal Stress State;354
15.2.3;13.3.3 Construction of Special Interaction Elements;355
15.2.4;13.3.4 Model of the Inter-Layer Shear Resistance;356
15.2.5;13.3.5 Electrical Transport Model;356
15.3;13.3 Numerical Results;357
15.3.1;13.4.1 Bending of SWNTs;357
15.3.2;13.4.2 Tube-Tube-Substrate Interaction;358
15.3.3;13.4.3 Deformation of MWNTs Under Bending;359
15.3.4;13.4.4 Laterally-Squeezed (8, 8) SWNT;363
15.3.5;13.4.5 Bent (10, 0) SWNT;365
15.3.6;13.4.6 Simulation of Laboratory Experiments on a MWNT;366
15.3.7;13.4.7 Effect of the Outer Diameter on the Conductance of MWNTs Under Bending;368
15.3.8;13.4.8 Effect of the Outer Diameter on the Conductance of MWNTs Under Stretching;372
15.3.9;13.4.9 Effect of Current Saturation -- Non-Linear I-V Response;373
15.4;13.4 Conclusions;374
15.5;References;375
16;14 Multiscale Modeling of Carbon Nanotubes;378
16.1;14.1 Introduction;378
16.2;14.2 Multiscale Coupling Approaches;379
16.2.1;14.3.1 Quasi-Continuum Method;380
16.2.2;14.3.2 Bridging Domain Method;381
16.2.3;14.3.3 Bridging Scale Method;382
16.3;14.3 Brenner Potential;383
16.4;14.4 An Atomic Simulation Method;385
16.5;14.5 A Higher-Order Continuum Model;387
16.5.1;14.6.1 Higher-Order Gradient Continuum;388
16.5.2;14.6.2 Constitutive Relationship;390
16.5.3;14.6.3 Mesh-Free Numerical Simulation;391
16.6;14.6 Multiscale Coupling Scheme;392
16.7;14.7 Multiscale Computational Examples;393
16.7.1;14.8.1 Bending Test;394
16.7.2;14.8.2 Tensile Failure of SWCNTs with a Single-Atom Vacancy Defect;395
16.8;14.8 Summary;397
16.9;References;398
17;15 Quasicontinuum Simulations of Deformations of CarbonNanotubes;400
17.1;15.1 Introduction;400
17.2;15.2 Quasicontinuum Method for Carbon Nanotubes;402
17.2.1;15.3.1 Deformations of Single-Walled CNTs;403
17.2.2;15.3.2 Bravais Multilattice and Inner Displacement;405
17.2.3;15.3.3 Interpolation Function;407
17.2.4;15.3.4 Summation and Minimization of Energy;409
17.2.5;15.3.5 Adaptive Meshing Scheme;413
17.2.6;15.3.6 Deformation of Multiwalled Carbon Nanotubes (MWCNTs);413
17.2.7;15.3.7 Numerical Examples;414
17.2.7.1;15.3.7.1 Bonding and Nonbonding Interaction for CNT;414
17.2.7.2;15.3.7.2 Bending Simulations for a SWCNT;415
17.3;15.3 QC Method for CNTS by Use of Variable-Node Elements;417
17.3.1;15.4.1 Variable Node Elements for QC;418
17.3.2;15.4.2 Numerical Examples;422
17.4;15.4 Conclusions;424
17.5;15.5 Acknowledgment;425
17.6;15.5 Appendix A. The Green Strain in Deformation of a CNT;425
17.7;15.5 Appendix B. The Functions and the Parameters in the Tersoff-Brenner Potential;426
17.8;15.5 Appendix C. The Shape Functions for a 24-noded Variable-Node Element;427
17.9;References;430
18;16 Electronic Properties and Reactivities of Perfect, Defected, and Doped Single-Walled Carbon Nanotubes;431
18.1;16.1 Scope;431
18.2;16.2 Introduction;431
18.3;16.3 Theoretical Methods;433
18.3.1;16.4.1 First-Principles Calculations;433
18.3.2;16.4.2 Semiempirical Quantum Mechanical Methods;434
18.3.3;16.4.3 Density-Functional Theory;436
18.3.4;16.4.4 ONIOM Model;436
18.3.5;16.4.5 Molecular Dynamical Simulations;437
18.4;16.4 Single-Walled Carbon Nanotubes;438
18.4.1;16.5.1 Perfect SWCNT Rods;438
18.4.2;16.5.2 Open-End SWCNT Segment;441
18.5;16.5 Vacancy-Defected Fullerenes and Swcnts;441
18.5.1;16.6.1 Vacancy-Defected Fullerenes;442
18.5.2;16.6.2 Vacancy-Defected SWCNTs;449
18.5.2.1;16.6.2.1 Vacancy-Defected (5,5) and (10,0) SWCNTs;449
18.5.2.2;16.6.2.2 Vacancy-Defected (5,5) SWCNT Clip;454
18.6;16.6 Doped SWCNTs;455
18.6.1;16.7.1 B- and N-Doped SWCNTs;455
18.6.2;16.7.2 Ni-, Pd-, and Sn-Doped SWCNTs;455
18.6.3;16.7.3 Chalcogen Se- and Te-Doped SWCNTs;458
18.6.4;16.7.4 Pt-Doped SWCNTs;458
18.6.5;16.7.5 Gas Adsorptions on Pt-Doped SWCNTs;461
18.7;16.7 Chemical Reactions of Vacancy-Defected SWCNT;463
18.7.1;16.8.1 Computational Details and Model Selection;463
18.7.2;16.8.2 Chemical Reaction of NO with Vacancy-Defected SWCNT;464
18.7.3;16.8.3 Chemical Reaction of O 3 with Vacancy-Defected SWCNT;467
18.7.3.1;16.8.3.1 Reaction of O 3 with the Active Carbon Atom;468
18.7.3.2;16.8.3.2 Reaction of O 3 with the C8-C9 Bond (Position 1);468
18.7.3.3;16.8.3.3 Reaction of O 3 with the C6-C7 Bond (Position 2);470
18.7.3.4;16.8.3.4 Reaction of O 3 with the C4-C5 Bond (Position 3);471
18.7.3.5;16.8.3.5 Reaction of O 3 with the C2-C3 Bond (Position 4);472
18.7.3.6;16.8.3.6 Ab initio Molecular Dynamics Studies;472
18.8;16.8 Conclusions and Outlooks;474
18.9;16.9 ACKNOWLEDGMENTS;475
18.10;References;475
19;17 Multiscale Modeling of Biological Protein Materials -- Deformation and Failure;482
19.1;17.1 Introduction;482
19.1.1;17.2.1 Nanomechanics of Protein Materials: Challenges and Opportunities;484
19.1.2;17.2.2 Strategy of Investigation;485
19.1.3;17.2.3 Impact of Materiomics;486
19.1.4;17.2.4 Transfer from Biological Protein Materials to Synthetic Materials;488
19.2;17.2 Atomistic Simulation Methods;488
19.2.1;17.3.1 Molecular Dynamics Formulation;488
19.2.2;17.3.2 CHARMM Force Field;491
19.2.3;17.3.3 ReaxFF Force Field;493
19.2.4;17.3.4 Coarse-Graining Approaches of Protein Structures;495
19.2.4.1;17.3.4.1 Single-Bead Models;496
19.2.4.2;17.3.4.2 Multi-Bead Models;498
19.2.4.3;17.3.4.3 Coarser Models;498
19.2.4.4;17.3.4.4 Implicit Solvent;498
19.2.4.5;17.3.4.5 Case Study: Coarse-Grained Model of Alpha-Helical Protein Domains;499
19.2.4.6;17.3.4.6 Case Study: Network Model of Alpha Helices;502
19.3;17.3 Theoretical Strength Models of Protein Constituents;505
19.3.1;17.4.1 Strength of a Single Bond;506
19.3.1.1;17.4.1.1 Bell's Model: A Force Dependent Dissociation Rate;506
19.3.1.2;17.4.1.2 Evans' Extension: A Loading Rate Dependence of Strength;507
19.3.1.3;17.4.1.3 Other Refinements of Bell's Model;509
19.3.2;17.4.2 Strength of Complex Molecular Bonds;509
19.3.2.1;17.4.2.1 Multiple Bonds in Parallel;510
19.3.2.2;17.4.2.2 Coupled Strength Models;511
19.3.2.3;17.4.2.3 Hierarchical Bell Model;512
19.3.3;17.4.3 Size Effects in H-Bond Clusters;514
19.3.4;17.4.4 Asymptotic Strength Model for Alpha Helix Protein Domains;515
19.3.4.1;17.4.4.1 Modeling and Results;517
19.3.4.2;17.4.4.2 Summary and Discussion;521
19.4;17.4 Complementary Experimental Methods;522
19.4.1;17.5.1 Structural Characterization;522
19.4.2;17.5.2 Manipulation and Mechanical Testing;522
19.4.3;17.5.3 Synthesis Methods for Hierarchical Materials;524
19.5;17.5 De Novo Design of Bioinspired and Biomimetic Nanomaterials;524
19.5.1;17.6.1 Development of Bioinspired Metallic Nanocomposites;527
19.5.2;17.6.2 Nanostructure Design Effects Under Tensile and Shock Loading;528
19.5.3;17.6.3 Outlook and Opportunities;530
19.6;17.6 Discussion and Conclusion;531
19.7;17.7 Acknowledgements;533
19.8;References;533
20;18 Computational Molecular Biomechanics: A Hierarchical Multiscale Framework with Applications to Gating of Mechanosensitive Channels of Large Conductance;543
20.1;18.1 Introduction;543
20.2;18.2 Brief Overview of Mechanosensitive (Ms) Channels;544
20.2.1;18.3.1 Structural Components of MS Channel of Large Conductance (MscL);544
20.2.2;18.3.2 Previous Experimental and Theoretical Investigations;547
20.2.3;18.3.3 Previous Numerical Approaches;548
20.3;18.3 Continuum-Based Approach: Model and Methods for Studying Mscl;549
20.4;18.4 Gating Mechanisms of Mscl and Insights for Mechanotransduction;551
20.4.1;18.5.1 Effect of Different Loading Modes;551
20.4.1.1;18.5.1.1 Gating Behaviors Upon Equi-Biaxial Tension;551
20.4.1.2;18.5.1.2 Gating Behaviors Upon Bending;554
20.4.1.3;18.5.1.3 Insights of Loading Modes Vs. Mechanotransduction;555
20.4.2;18.5.2 Effects of Structural Motifs;556
20.4.3;18.5.3 Co-operativity of MS Channels;557
20.4.4;18.5.4 Large Scale Simulations of Lab Experiments;559
20.5;18.5 Future Look and Improvements of Continuum Framework;560
20.6;18.6 Conclusion;562
20.7;18.7 Acknowledgment;563
20.8;References;563
21;19 Out of Many, One: Modeling Schemes for Biopolymer and Biofibril Networks;565
21.1;19.1 Introduction;565
21.2;19.2 Biopolymers of Interest;566
21.2.1;19.3.1 Intracellular Networks;567
21.2.1.1;19.3.1.1 Actin;567
21.2.1.2;19.3.1.2 Microtubules;568
21.2.1.3;19.3.1.3 Intermediate Filaments;569
21.2.1.4;19.3.1.4 Spectrin;569
21.2.2;19.3.2 Extracellular Networks;569
21.2.2.1;19.3.2.1 Collagen I;569
21.2.2.2;19.3.2.2 Collagen IV;570
21.2.2.3;19.3.2.3 Laminin;570
21.2.2.4;19.3.2.4 Fibronectin;570
21.2.2.5;19.3.2.5 Fibrin;571
21.2.3;19.3.3 The Mechanical Behavior of Biopolymers;571
21.3;19.3 Network Imaging, Extraction, and Generation;574
21.3.1;19.4.1 Imaging;575
21.3.1.1;19.4.1.1 Fiber-Level Imaging;575
21.3.1.2;19.4.1.2 Indirect (Population-Level) Imaging;576
21.3.2;19.4.2 Network Extraction;576
21.3.3;19.4.3 Model Network Generation;577
21.3.4;19.4.4 Network Generation via Energy Minimization;578
21.4;19.4 General Modeling Approaches for Biopolymer Networks;580
21.4.1;19.5.1 Definitions;580
21.4.2;19.5.2 Affine Theory;581
21.4.3;19.5.3 Nonaffine Models;582
21.4.3.1;19.5.3.1 Spring Model;582
21.4.3.2;19.5.3.2 Beam Models;584
21.4.3.3;19.5.3.3 Entropic Beam Model;585
21.4.4;19.5.4 Finite Strain;586
21.4.4.1;19.5.4.1 Strain Stiffening;586
21.4.5;19.5.5 Bridging Scales -- Multiscale Behavior of Networks;586
21.4.5.1;19.5.5.1 Representative Volume Element;586
21.4.5.2;19.5.5.2 Volume Averaging;587
21.5;19.5 Applications to Biopolymers;590
21.5.1;19.6.1 Actin;590
21.5.2;19.6.2 Microtubules, IFs, and the Cytoskeleton;591
21.5.3;19.6.3 Spectrin;592
21.5.4;19.6.4 Collagen I;593
21.5.5;19.6.5 Type IV Collagen;596
21.5.6;19.6.6 Fibronectin, Laminin, and the ECM;596
21.6;19.6 Summary;596
21.7;19.7 Nomenclature;597
21.8;REFERENCES;599
22;Index;611