Nano-mechanics and materials: theory, multiscale methods and applications
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester [u.a.]
Wiley
2006
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 320 S. Ill., graph. Darst. |
| ISBN: | 0470018518 9780470018514 |
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MARC
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| 100 | 1 | |a Liu, Wing Kam |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Nano-mechanics and materials |b theory, multiscale methods and applications |c Wing Kam Liu ; Eduard G. Karpov ; Harold S. Park |
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 2006 | |
| 300 | |a XIII, 320 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Nanostrukturiertes Material - Mechanik | |
| 650 | 4 | |a Nanostructured materials | |
| 650 | 4 | |a Nanotechnology | |
| 650 | 0 | 7 | |a Nanotechnologie |0 (DE-588)4327470-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Nanotechnologie |0 (DE-588)4327470-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Karpov, Eduard G. |e Verfasser |4 aut | |
| 700 | 1 | |a Park, Harold S. |e Verfasser |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014179052&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-014179052 | ||
Record in the Search Index
| _version_ | 1804134574930788352 |
|---|---|
| adam_text | Contents
Preface
xi
1
Introduction
1
1.1
Potential of Nanoscale Engineering
...................... 1
1.2
Motivation for Multiple Scale Modeling
.................... 2
1.3
Educational Approach
............................. 5
2
Classical Molecular Dynamics
7
2.1
Mechanics of a System of Particles
...................... 7
2.1.1
Generalized Coordinates
........................ 8
2.1.2
Mechanical Forces and Potential Energy
............... 8
2.1.3 Lagrange
Equations of Motion
.................... 10
2.1.4
Integrals of Motion and Symmetric Fields
.............. 12
2.1.5
Newtonian Equations
.......................... 13
2.1.6
Examples
................................ 14
2.2
Molecular Forces
................................ 17
2.2.1
External Fields
............................. 18
2.2.2
Pair-Wise Interaction
.......................... 20
2.2.3
Multibody Interaction
......................... 24
2.2.4
Exercises
................................ 26
2.3
Molecular Dynamics Applications
....................... 28
3
Lattice Mechanics
37
3.1
Elements of Lattice Symmetries
........................ 37
3.1.1
Bravais
Lattices
............................ 38
3.1.2
Basic Symmetry Principles
...................... 40
3.1.3
Crystallographic Directions and Planes
................ 42
3.2
Equation of Motion of a Regular Lattice
................... 42
3.2.1
Unit Cell and the Associate Substructure
............... 43
3.2.2
Lattice Lagrangian and Equations of Motion
............. 45
3.2.3
Examples
................................ 47
3.3
Transforms
................................... 49
3.3.1
Fourier Transform
........................... 50
3.3.2
Laplace Transform
........................... 51
3.3.3
Discrete Fourier Transform
...................... 53
viii CONTENTS
3.4 Standing
Waves in Lattices
........................... 54
3.4.1 Normal
Modes
and Dispersion
Branches
............... 55
3.4.2
Examples
................................ 57
3.5
Green s Function Methods
........................... 58
3.5.1
Solution for a Unit Pulse
....................... 59
3.5.2
Free Lattice with Initial Perturbations
................. 61
3.5.3
Solution for Arbitrary Dynamic Loads
................ 61
3.5.4
General Inhomogeneous Solution
................... 62
3.5.5
Boundary Value Problems and the Time History Kernel
....... 62
3.5.6
Examples
................................ 65
3.6
Quasi-Static Approximation
.......................... 66
3.6.1
Equilibrium State Equation
...................... 66
3.6.2
Quasi-Static Green s Function
..................... 67
3.6.3
Multiscale Boundary Conditions
.................... 67
4
Methods of Thermodynamics and Statistical Mechanics
79
4.1
Basic Results of the Thermodynamic Method
................. 80
4.1.1
State Equations
............................. 81
4.1.2
Energy Conservation Principle
..................... 84
4.1.3
Entropy and the Second Law of Thermodynamics
.......... 86
4.1.4
Nernst s Postulate
........................... 88
4.1.5
Thermodynamic Potentials
....................... 89
4.2
Statistics of Multiparticle Systems in Thermodynamic Equilibrium
..... 91
4.2.1
Hamiltonian Formulation
....................... 92
4.2.2
Statistical Description of Multiparticle Systems
........... 93
4.2.3
Microcanonical Ensemble
....................... 97
4.2.4
Canonical Ensemble
.......................... 101
4.2.5
Maxwell-Boltzmann Distribution
................... 104
4.2.6
Thermal Properties of Periodic Lattices
................ 107
4.3
Numerical Heat Bath Techniques
.......................
Ill
4.3.1
Berendsen Thermostat
......................... 112
4.3.2
Nosé-Hoover
Heat Bath
........................ 118
4.3.3
Phonon Method for Solid-Solid Interfaces
.............. 119
5
Introduction to Multiple Scale Modeling
123
5.1
MAAD
..................................... 124
5.2
Coarse-Grained Molecular Dynamics
..................... 126
5.3
Quasi-Continuum Method
........................... 126
5.4
CADD
...................................... 128
5.5
Bridging Domain
................................ 129
6
Introduction to Bridging Scale
131
6.1
Bridging Scale Fundamentals
......................... 131
6.1.1
Multiscale Equations of Motion
.................... 133
6.2
Removing Fine Scale Degrees of Freedom in Coarse Scale Region
..... 136
6.2.1
Relationship of Lattice Mechanics to Finite Elements
........ 137
6.2.2
Linearized MD Equation of Motion
.................. 139
CONTENTS ix
6.2.3 Elimination
of Fine Scale Degrees of Freedom
............141
6.2.4
Commentary on Reduced Multiscale Formulation
..........143
6.2.5
Elimination of Fine Scale Degrees of Freedom:
3D
Generalization
...........................143
6.2.6
Numerical Implementation of Impedance Force
...........150
6.2.7
Numerical Implementation of Coupling Force
............151
6.3
Discussion on the Damping Kernel Technique
................ 152
6.3.1
Programming Algorithm for Time History Kernel
.......... 157
6.4
Cauchy-Born Rule
............................... 158
6.5
Virtual Atom Cluster Method
......................... 159
6.5.1
Motivations and General Formulation
................. 159
6.5.2
General Idea of the VAC Model
.................... 163
6.5.3
Three-Way Concurrent Coupling with QM Method
......... 164
6.5.4
Tight-Binding Method for Carbon Systems
.............. 167
6.5.5
Coupling with the VAC Model
.................... 169
6.6
Staggered Time Integration Algorithm
..................... 170
6.6.1
MD Update
............................... 170
6.6.2
FE Update
............................... 172
6.7
Summary of Bridging Scale Equations
.................... 172
6.8
Discussion on the Bridging Scale Method
................... 173
7
Bridging Scale Numerical Examples
175
7.1
Comments on Time History Kernel
......................175
7.2
ID Bridging Scale Numerical Examples
....................176
7.2.1
Lennard-Jones Numerical Examples
..................176
7.2.2
Comparison of VAC Method and Cauchy-Born Rule
........178
7.2.3
Truncation of Time History Kernel
..................179
7.3
2D/3D Bridging Scale Numerical Examples
..................182
7.4
Two-Dimensional Wave Propagation
.....................184
7.5
Dynamic Crack Propagation in Two Dimensions
...............187
7.6
Dynamic Crack Propagation in Three Dimensions
..............195
7.7
Virtual Atom Cluster Numerical Examples
..................200
7.7.1
Bending of Carbon Nanotubes
.....................200
7.7.2
VAC Coupling with Tight Binding
..................200
8
Non-Nearest Neighbor MD Boundary Condition
203
8.1
Introduction
...................................203
8.2
Theoretical Formulation in
3D.........................203
8.2.1
Force Boundary Condition: ID Illustration
..............207
8.2.2
Displacement Boundary Condition: ID Illustration
..........210
8.2.3
Comparison to Nearest Neighbors Formulation
............211
8.2.4
Advantages of Displacement Formulation
...............212
8.3
Numerical Examples: ID Wave Propagation
.................212
8.4
Time-History Kernels for FCC Gold
......................213
8.5
Conclusion for the Bridging Scale Method
..................215
8.5.1
Bridging Scale Perspectives
......................220
x
CONTENTS
9
Multiscale Methods for Material Design
223
9.1
Multiresolution Continuum Analysis
......................225
9.1.1
Generalized Stress and Deformation Measures
............227
9.1.2
Interaction between Scales
.......................231
9.1.3
Multiscale Materials Modeling
....................232
9.2
Multiscale Constitutive Modeling of Steels
..................234
9.2.1
Methodology and Approach
......................235
9.2.2
First-Principles Calculation
......................235
9.2.3
Hierarchical Unit Cell and Constitutive Model
............237
9.2.4
Laboratory Specimen Scale: Simulation and Results
.........239
9.3
Bio-Inspired Materials
.............................244
9.3.1
Mechanisms of Self-Healing in Materials
...............244
9.3.2
Shape-Memory Composites
......................246
9.3.3
Multiscale Continuum Modeling of SMA Composites
........250
9.3.4
Issues of Modeling and Simulation
..................256
9.4
Summary and Future Research Directions
...................260
10
Bio-Nano
Interface
263
10.
1 Introduction
...................................263
10.2
Immersed Finite Element Method
.......................265
10.2.1
Formulation
...............................265
10.2.2
Computational Algorithm of IFEM
..................268
10.3
Vascular Flow and Blood Rheology
......................269
10.3.1
Heart Model
..............................269
10.3.2
Flexible Valve-Viscous Fluid Interaction
...............270
10.3.3
Angioplasty Stent
...........................270
10.3.4
Monocyte Deposition
.........................272
10.3.5
Platelet Adhesion and Blood Clotting
.................272
10.3.6
RBC Aggregation and Interaction
...................274
10.4
Electrohydrodynamic Coupling
........................280
10.4.1
Maxwell Equations
...........................281
10.4.2
Electro-manipulation
..........................283
10.4.3
Rotation of CNTs Induced by Electroosmotic Flow
.........285
10.5
CNT/DNA Assembly Simulation
.......................287
10.6
Cell Migration and Cell-Substrate Adhesion
.................290
10.7
Conclusions
...................................295
Appendix A Kernel Matrices for EAM Potential
297
Bibliography
301
Index
315
|
| adam_txt |
Contents
Preface
xi
1
Introduction
1
1.1
Potential of Nanoscale Engineering
. 1
1.2
Motivation for Multiple Scale Modeling
. 2
1.3
Educational Approach
. 5
2
Classical Molecular Dynamics
7
2.1
Mechanics of a System of Particles
. 7
2.1.1
Generalized Coordinates
. 8
2.1.2
Mechanical Forces and Potential Energy
. 8
2.1.3 Lagrange
Equations of Motion
. 10
2.1.4
Integrals of Motion and Symmetric Fields
. 12
2.1.5
Newtonian Equations
. 13
2.1.6
Examples
. 14
2.2
Molecular Forces
. 17
2.2.1
External Fields
. 18
2.2.2
Pair-Wise Interaction
. 20
2.2.3
Multibody Interaction
. 24
2.2.4
Exercises
. 26
2.3
Molecular Dynamics Applications
. 28
3
Lattice Mechanics
37
3.1
Elements of Lattice Symmetries
. 37
3.1.1
Bravais
Lattices
. 38
3.1.2
Basic Symmetry Principles
. 40
3.1.3
Crystallographic Directions and Planes
. 42
3.2
Equation of Motion of a Regular Lattice
. 42
3.2.1
Unit Cell and the Associate Substructure
. 43
3.2.2
Lattice Lagrangian and Equations of Motion
. 45
3.2.3
Examples
. 47
3.3
Transforms
. 49
3.3.1
Fourier Transform
. 50
3.3.2
Laplace Transform
. 51
3.3.3
Discrete Fourier Transform
. 53
viii CONTENTS
3.4 Standing
Waves in Lattices
. 54
3.4.1 Normal
Modes
and Dispersion
Branches
. 55
3.4.2
Examples
. 57
3.5
Green's Function Methods
. 58
3.5.1
Solution for a Unit Pulse
. 59
3.5.2
Free Lattice with Initial Perturbations
. 61
3.5.3
Solution for Arbitrary Dynamic Loads
. 61
3.5.4
General Inhomogeneous Solution
. 62
3.5.5
Boundary Value Problems and the Time History Kernel
. 62
3.5.6
Examples
. 65
3.6
Quasi-Static Approximation
. 66
3.6.1
Equilibrium State Equation
. 66
3.6.2
Quasi-Static Green's Function
. 67
3.6.3
Multiscale Boundary Conditions
. 67
4
Methods of Thermodynamics and Statistical Mechanics
79
4.1
Basic Results of the Thermodynamic Method
. 80
4.1.1
State Equations
. 81
4.1.2
Energy Conservation Principle
. 84
4.1.3
Entropy and the Second Law of Thermodynamics
. 86
4.1.4
Nernst's Postulate
. 88
4.1.5
Thermodynamic Potentials
. 89
4.2
Statistics of Multiparticle Systems in Thermodynamic Equilibrium
. 91
4.2.1
Hamiltonian Formulation
. 92
4.2.2
Statistical Description of Multiparticle Systems
. 93
4.2.3
Microcanonical Ensemble
. 97
4.2.4
Canonical Ensemble
. 101
4.2.5
Maxwell-Boltzmann Distribution
. 104
4.2.6
Thermal Properties of Periodic Lattices
. 107
4.3
Numerical Heat Bath Techniques
.
Ill
4.3.1
Berendsen Thermostat
. 112
4.3.2
Nosé-Hoover
Heat Bath
. 118
4.3.3
Phonon Method for Solid-Solid Interfaces
. 119
5
Introduction to Multiple Scale Modeling
123
5.1
MAAD
. 124
5.2
Coarse-Grained Molecular Dynamics
. 126
5.3
Quasi-Continuum Method
. 126
5.4
CADD
. 128
5.5
Bridging Domain
. 129
6
Introduction to Bridging Scale
131
6.1
Bridging Scale Fundamentals
. 131
6.1.1
Multiscale Equations of Motion
. 133
6.2
Removing Fine Scale Degrees of Freedom in Coarse Scale Region
. 136
6.2.1
Relationship of Lattice Mechanics to Finite Elements
. 137
6.2.2
Linearized MD Equation of Motion
. 139
CONTENTS ix
6.2.3 Elimination
of Fine Scale Degrees of Freedom
.141
6.2.4
Commentary on Reduced Multiscale Formulation
.143
6.2.5
Elimination of Fine Scale Degrees of Freedom:
3D
Generalization
.143
6.2.6
Numerical Implementation of Impedance Force
.150
6.2.7
Numerical Implementation of Coupling Force
.151
6.3
Discussion on the Damping Kernel Technique
. 152
6.3.1
Programming Algorithm for Time History Kernel
. 157
6.4
Cauchy-Born Rule
. 158
6.5
Virtual Atom Cluster Method
. 159
6.5.1
Motivations and General Formulation
. 159
6.5.2
General Idea of the VAC Model
. 163
6.5.3
Three-Way Concurrent Coupling with QM Method
. 164
6.5.4
Tight-Binding Method for Carbon Systems
. 167
6.5.5
Coupling with the VAC Model
. 169
6.6
Staggered Time Integration Algorithm
. 170
6.6.1
MD Update
. 170
6.6.2
FE Update
. 172
6.7
Summary of Bridging Scale Equations
. 172
6.8
Discussion on the Bridging Scale Method
. 173
7
Bridging Scale Numerical Examples
175
7.1
Comments on Time History Kernel
.175
7.2
ID Bridging Scale Numerical Examples
.176
7.2.1
Lennard-Jones Numerical Examples
.176
7.2.2
Comparison of VAC Method and Cauchy-Born Rule
.178
7.2.3
Truncation of Time History Kernel
.179
7.3
2D/3D Bridging Scale Numerical Examples
.182
7.4
Two-Dimensional Wave Propagation
.184
7.5
Dynamic Crack Propagation in Two Dimensions
.187
7.6
Dynamic Crack Propagation in Three Dimensions
.195
7.7
Virtual Atom Cluster Numerical Examples
.200
7.7.1
Bending of Carbon Nanotubes
.200
7.7.2
VAC Coupling with Tight Binding
.200
8
Non-Nearest Neighbor MD Boundary Condition
203
8.1
Introduction
.203
8.2
Theoretical Formulation in
3D.203
8.2.1
Force Boundary Condition: ID Illustration
.207
8.2.2
Displacement Boundary Condition: ID Illustration
.210
8.2.3
Comparison to Nearest Neighbors Formulation
.211
8.2.4
Advantages of Displacement Formulation
.212
8.3
Numerical Examples: ID Wave Propagation
.212
8.4
Time-History Kernels for FCC Gold
.213
8.5
Conclusion for the Bridging Scale Method
.215
8.5.1
Bridging Scale Perspectives
.220
x
CONTENTS
9
Multiscale Methods for Material Design
223
9.1
Multiresolution Continuum Analysis
.225
9.1.1
Generalized Stress and Deformation Measures
.227
9.1.2
Interaction between Scales
.231
9.1.3
Multiscale Materials Modeling
.232
9.2
Multiscale Constitutive Modeling of Steels
.234
9.2.1
Methodology and Approach
.235
9.2.2
First-Principles Calculation
.235
9.2.3
Hierarchical Unit Cell and Constitutive Model
.237
9.2.4
Laboratory Specimen Scale: Simulation and Results
.239
9.3
Bio-Inspired Materials
.244
9.3.1
Mechanisms of Self-Healing in Materials
.244
9.3.2
Shape-Memory Composites
.246
9.3.3
Multiscale Continuum Modeling of SMA Composites
.250
9.3.4
Issues of Modeling and Simulation
.256
9.4
Summary and Future Research Directions
.260
10
Bio-Nano
Interface
263
10.
1 Introduction
.263
10.2
Immersed Finite Element Method
.265
10.2.1
Formulation
.265
10.2.2
Computational Algorithm of IFEM
.268
10.3
Vascular Flow and Blood Rheology
.269
10.3.1
Heart Model
.269
10.3.2
Flexible Valve-Viscous Fluid Interaction
.270
10.3.3
Angioplasty Stent
.270
10.3.4
Monocyte Deposition
.272
10.3.5
Platelet Adhesion and Blood Clotting
.272
10.3.6
RBC Aggregation and Interaction
.274
10.4
Electrohydrodynamic Coupling
.280
10.4.1
Maxwell Equations
.281
10.4.2
Electro-manipulation
.283
10.4.3
Rotation of CNTs Induced by Electroosmotic Flow
.285
10.5
CNT/DNA Assembly Simulation
.287
10.6
Cell Migration and Cell-Substrate Adhesion
.290
10.7
Conclusions
.295
Appendix A Kernel Matrices for EAM Potential
297
Bibliography
301
Index
315 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Liu, Wing Kam Karpov, Eduard G. Park, Harold S. |
| author_facet | Liu, Wing Kam Karpov, Eduard G. Park, Harold S. |
| author_role | aut aut aut |
| author_sort | Liu, Wing Kam |
| author_variant | w k l wk wkl e g k eg egk h s p hs hsp |
| building | Verbundindex |
| bvnumber | BV020857440 |
| callnumber-first | T - Technology |
| callnumber-label | TA418 |
| callnumber-raw | TA418.9.N35 |
| callnumber-search | TA418.9.N35 |
| callnumber-sort | TA 3418.9 N35 |
| callnumber-subject | TA - General and Civil Engineering |
| classification_rvk | UP 7500 VE 9850 ZN 3700 |
| ctrlnum | (OCoLC)255159354 (DE-599)BVBBV020857440 |
| dewey-full | 620.5 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.5 |
| dewey-search | 620.5 |
| dewey-sort | 3620.5 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Chemie / Pharmazie Physik Elektrotechnik / Elektronik / Nachrichtentechnik |
| discipline_str_mv | Chemie / Pharmazie Physik Elektrotechnik / Elektronik / Nachrichtentechnik |
| format | Book |
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| id | DE-604.BV020857440 |
| illustrated | Illustrated |
| index_date | 2024-07-02T13:21:49Z |
| indexdate | 2024-07-09T20:26:47Z |
| institution | BVB |
| isbn | 0470018518 9780470018514 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014179052 |
| oclc_num | 255159354 |
| open_access_boolean | |
| owner | DE-703 DE-20 DE-1043 DE-29T DE-355 DE-BY-UBR |
| owner_facet | DE-703 DE-20 DE-1043 DE-29T DE-355 DE-BY-UBR |
| physical | XIII, 320 S. Ill., graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Wiley |
| record_format | marc |
| spelling | Liu, Wing Kam Verfasser aut Nano-mechanics and materials theory, multiscale methods and applications Wing Kam Liu ; Eduard G. Karpov ; Harold S. Park Chichester [u.a.] Wiley 2006 XIII, 320 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Nanostrukturiertes Material - Mechanik Nanostructured materials Nanotechnology Nanotechnologie (DE-588)4327470-5 gnd rswk-swf Nanotechnologie (DE-588)4327470-5 s DE-604 Karpov, Eduard G. Verfasser aut Park, Harold S. Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014179052&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Liu, Wing Kam Karpov, Eduard G. Park, Harold S. Nano-mechanics and materials theory, multiscale methods and applications Nanostrukturiertes Material - Mechanik Nanostructured materials Nanotechnology Nanotechnologie (DE-588)4327470-5 gnd |
| subject_GND | (DE-588)4327470-5 |
| title | Nano-mechanics and materials theory, multiscale methods and applications |
| title_auth | Nano-mechanics and materials theory, multiscale methods and applications |
| title_exact_search | Nano-mechanics and materials theory, multiscale methods and applications |
| title_exact_search_txtP | Nano-mechanics and materials theory, multiscale methods and applications |
| title_full | Nano-mechanics and materials theory, multiscale methods and applications Wing Kam Liu ; Eduard G. Karpov ; Harold S. Park |
| title_fullStr | Nano-mechanics and materials theory, multiscale methods and applications Wing Kam Liu ; Eduard G. Karpov ; Harold S. Park |
| title_full_unstemmed | Nano-mechanics and materials theory, multiscale methods and applications Wing Kam Liu ; Eduard G. Karpov ; Harold S. Park |
| title_short | Nano-mechanics and materials |
| title_sort | nano mechanics and materials theory multiscale methods and applications |
| title_sub | theory, multiscale methods and applications |
| topic | Nanostrukturiertes Material - Mechanik Nanostructured materials Nanotechnology Nanotechnologie (DE-588)4327470-5 gnd |
| topic_facet | Nanostrukturiertes Material - Mechanik Nanostructured materials Nanotechnology Nanotechnologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014179052&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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