Presenting cutting-edge research and development within multiscale modeling techniques and frameworks, Multiscale Analysis of Deformation and Failure of Materials systematically describes the background, principles and methods within this exciting new & interdisciplinary field.
The author&;s approach emphasizes the principles and methods of atomistic simulation and its transition to the nano and sub-micron scale of a continuum, which is technically important for nanotechnology and biotechnology. He also pays close attention to multiscale analysis across the micro/meso/macroscopy of a continuum, which has a broad scope of applications encompassing different disciplines and practices, and is an essential extension of mesomechanics.
Of equal interest to engineers, scientists, academics and students, Multiscale Analysis of Deformation and Failure of Materials is a multidisciplinary text relevant to those working in the areas of materials science, solid and computational mechanics, bioengineering and biomaterials, and aerospace, automotive, civil, and environmental engineering.
- Provides a deep understanding of multiscale analysis and its implementation
- Shows in detail how multiscale models can be developed from practical problems and how to use the multiscale methods and software to carry out simulations
- Discusses two interlinked categories of multiscale analysis; analysis spanning from the atomistic to the micro-continuum scales, and analysis across the micro/meso/macro scale of continuum.
Arvustused
"Provides a deep understanding of multiscale analysis and its implementation. " (Nanotech Cafe, 15 March 2011)
About the Author. Series Preface. Preface. Abbreviations. 1
Introduction. 1.1 Material Properties Based on Hierarchy of Material
Structure. 1.2 Overview of Multiscale Analysis. 1.3 Framework of Multiscale
Analysis Covering a Large Range of Spatial Scales. 1.4 Examples in
Formulating Multiscale Models from Practice. 1.5 Concluding Remarks.
References. 2 Basics of Atomistic Simulation. 2.1 The Role of Atomistic
Simulation. 2.2 Interatomic Force and Potential Function. 2.3 Pair
Potential. 2.4 Numerical Algorithms for Integration and Error Estimation.
2.5 Geometric Model Development of Atomistic System. 2.6 Boundary
Conditions. 2.7 Statistical Ensembles. 2.8 Energy Minimization for
Preprocessing and Statistical Mechanics Data Analyses. 2.9 Statistical
Simulation Using Monte Carlo Methods. 2.10 Concluding Remarks. References.
3 Applications of Atomistic Simulation in Ceramics and Metals. Part 3.1
Applications in Ceramics and Materials with Ionic and Covalent Bonds. 3.1
Covalent and Ionic Potentials and Atomistic Simulation for Ceramics. 3.2
Born Solid Model for Ionic-bonding Materials. 3.3 Shell Model. 3.4
Determination of Parameters of Short-distance Potential for Oxides. 3.5
Applications in Ceramics: Defect Structure in Scandium Doped Ceria Using
Static Lattice Calculation. 3.6 Applications in Ceramics: Combined Study of
Atomistic Simulation with XRD for Nonstoichiometry Mechanisms in Y3Al5O12
(YAG) Garnets. 3.7 Applications in Ceramics: Conductivity of the YSZ Oxide
Fuel Electrolyte and Domain Switching of Ferroelectric Ceramics Using MD.
3.8 Tersoff and Brenner Potentials for Covalent Materials. 3.9 The Atomistic
Stress and Atomistic-based Stress Measure. Part 3.2 Applications in Metallic
Materials and Alloys. 3.10 Metallic Potentials and Atomistic Simulation for
Metals. 3.11 Embedded Atom Methods EAM and MEAM. 3.12 Constructing Binary
and High Order Potentials from Monoatomic Potentials. 3.13 Application
Examples of Metals: MD Simulation Reveals Yield Mechanism of Metallic
Nanowires. 3.14 Collecting Data of Atomistic Potentials from the Internet
Based on a Specific Technical Requirement. Appendix 3.A Potential Tables for
Oxides and Thin-Film Coating Layers. References. 4 Quantum Mechanics and
Its Energy Linkage with Atomistic Analysis. 4.1 Determination of Uranium
Dioxide Atomistic Potential and the Significance of QM. 4.2 Some Basic
Concepts of QM. 4.3 Postulates of QM. 4.4 The Steady State Schr odinger
Equation of a Single Particle. 4.5 Example Solution: Square Potential Well
with Infinite Depth. 4.6 Schr odinger Equation of Multi-body Systems and
Characteristics of its Eigenvalues and Ground State Energy. 4.7 Three Basic
Solution Methods for Multi-body Problems in QM. 4.8 Tight Binding Method.
4.9 Hartree-Fock (HF) Methods. 4.10 Electronic Density Functional Theory
(DFT). 4.11 Brief Introduction on Developing Interatomic Potentials by DFT
Calculations. 4.12 Concluding Remarks. Appendix 4.A Solution to Isolated
Hydrogen Atom. References. 5 Concurrent Multiscale Analysis by Generalized
Particle Dynamics Methods. 5.1 Introduction. 5.2 The Geometric Model of the
GP Method. 5.3 Developing Natural Boundaries Between Domains of Different
Scales. 5.4 Verification of Seamless Transition via 1D Model. 5.5 An
Inverse Mapping Method for Dynamics Analysis of Generalized Particles. 5.6
Applications of GP Method. 5.7 Validation by Comparison of Dislocation
Initiation and Evolution Predicted by MD and GP. 5.8 Validation by
Comparison of Slip Patterns Predicted by MD and GP. 5.9 Summary and
Discussions. 5.10 States of Art of Concurrent Multiscale Analysis. 5.11
Concluding Remarks. References. 6 Quasicontinuum Concurrent and
Semi-analytical Hierarchical Multiscale Methods Across Atoms/Continuum. 6.1
Introduction. Part 6.1 Basic Energy Principle and Numerical Solution
Techniques in Solid Mechanics. 6.2 Principle of Minimum Potential Energy of
Solids and Structures. 6.3 Essential Points of Finite Element Methods. Part
6.2 Quasicontinuum (QC) Concurrent Method of Multiscale Analysis. 6.4 The
Idea and Features of the QC Method. 6.5 Fully Non-localized QC Method. 6.6
Applications of the QC Method. 6.7 Short Discussion about the QC Method.
Part 6.3 Analytical and Semi-analytical Multiscale Methods Across
Atomic/Continuum Scales. 6.8 More Discussions about Deformation Gradient and
the Cauchy-Born Rule. 6.9 Analytical/Semi-analytical Methods Across
Atom/Continuum Scales Based on the Cauchy-Born Rule. 6.10 Atomistic-based
Continuum Model of Hydrogen Storage with Carbon Nanotubes. 6.11
Atomistic-based Model for Mechanical, Electrical and Thermal Properties of
Nanotubes. 6.12 A Proof of 3D Inverse Mapping Rule of the GP Method. 6.13
Concluding Remarks. References. 7 Further Introduction to Concurrent
Multiscale Methods. 7.1 General Feature in Geometry of Concurrent Multiscale
Modeling. 7.2 Physical Features of Concurrent Multiscale Models. 7.3 MAAD
Method for Analysis Across ab initio, Atomic and Macroscopic Scales. 7.4
Force-based Formulation of Concurrent Multiscale Modeling. 7.5 Coupled Atom
Discrete Dislocation Dynamics (CADD) Multiscale Method. 7.6 1D Model for a
Multiscale Dynamic Analysis. 7.7 Bridging Domains Method. 7.8 1D Benchmark
Tests of Interface Compatibility for DC Methods. 7.9 Systematic Performance
Benchmark of Most DC Atomistic/Continuum Coupling Methods. 7.10 The Embedded
Statistical Coupling Method (ESCM). References. 8 Hierarchical Multiscale
Methods for Plasticity. 8.1 A Methodology of Hierarchical Multiscale
Analysis Across Micro/meso/macroscopic Scales and Information Transformation
Between These Scales. 8.2 Quantitative Meso-macro Bridging Based on
Self-consistent Schemes. 8.3 Basics of Continuum Plasticity Theory. 8.4
Internal Variable Theory, Back Stress and Elastoplastic Constitutive
Equations. 8.5 Quantitative Micro-meso Bridging by Developing Meso-cell
Constitutive Equations Based on Microscopic Analysis. 8.6 Determining Size
Effect on Yield Stress and Kinematic Hardening Through Dislocation Analysis.
8.7 Numerical Methods to Link Plastic Strains at the Mesoscopic and
Macroscopic Scales. 8.8 Experimental Study on Layer-thickness Effects on
Cyclic Creep (Ratcheting). 8.9 Numerical Results and Comparison Between
Experiments and Multiscale Simulation. 8.10 Findings in Microscopic Scale by
Multiscale Analysis. 8.11 Summary and Conclusions. Appendix 8.A
Constitutive Equations and Expressions of Parameters. Appendix 8.B
Derivation of Equation (8.12e) and Matrix Elements. References. 9 Topics in
Materials Design, Temporal Multiscale Problems and Bio-materials. Part 9.1
Materials Design. 9.1 Multiscale Modeling in Materials Design. Part 9.2
Temporal Multiscale Problems. 9.2 Introduction to Temporal Multiscale
Problems. 9.3 Concepts of Infrequent Events. 9.4 Minimum Energy Path (MEP)
and Transition State Theory in Atomistic Simulation. 9.5 Applications and
Impacts of NEB Methods. Part 9.3 Multiscale Analysis of Protein Materials
and Medical Implant Problems. 9.6 Multiscale Analysis of Protein Materials.
9.7 Multiscale Analysis of Medical Implants. 9.8 Concluding Remarks.
Appendix 9A Derivation of Governing Equation (9.11) for Implicit Relationship
of Stress, Strain Rate, Temperature in Terms of Activation Energy and
Activation Volume. References. 10 Simulation Schemes, Softwares, Lab
Practice and Applications. Part 10.1 Basics of Computer Simulations. 10.1
Basic Knowledge of UNIX System and Shell Commands. 10.2 A Simple MD Program.
10.3 Static Lattice Calculations Using GULP. 10.4 Introduction of
Visualization Tools and Gnuplot. 10.5 Running an Atomistic Simulation Using
a Public MD Software DL-POLY. 10.6 Nve and npt Ensemble in MD Simulation.
Part 10.2: Simulation Applications in Metals and Ceramics by MD. 10.7
Non-equilibrium MD Simulation of One-phase Model Under External Shearing (1).
10.8 Non-equilibrium MD Simulation of a One-phase Model Under External
Shearing (2). 10.9 Non-equilibrium MD Simulation of a Two-phase Model Under
External Shearing. Part 10.3: Atomistic Simulation for Protein-Water System
and Brief Introduction of Large-scale Atomic/Molecular System (LAMMPS) and
the GP Simulation. 10.10 Using NAMD Software for Biological Atomistic
Simulation. 10.11 Stretching of a Protein Module (1): System Building and
Equilibration with VMD/NAMD. 10.12 Stretching of a Protein Module (2):
Non-equilibrium MD Simulation with NAMD. 10.13 Brief Introduction to LAMMPS.
10.14 Multiscale Simulation by Generalized Particle (GP) Dynamics Method.
Appendix 10.A Code Installation Guide. Prerequisites. 10.A.1 Introduction.
10.A.2 Using the KNOPPIX CD to Install the GNU/Linux System. 10.A.3 ssh and
scp. 10.A.4 Fortran and C Compiler. 10.A.5 Visual Molecular Dynamics (VMD).
10.A.6 Installation of AtomEye. Appendix 10.B Brief Introduction to Fortran
90. 10.B.1 Program Structure, Write to Terminal and Write to File. 10.B.2
Do Cycle, Formatted Output. 10.B.3 Arrays and Allocation. 10.B.4 IF THEN
ELSE. Appendix 10.C Brief Introduction to VIM. 10.C.1 Introduction. 10.C.2
Simple Commands. Appendix 10.D Basic Knowledge of Numerical Algorithm for
Force Calculation. 10.D.1 Force Calculation in Atomistic Simulation.
Appendix 10.E Basic Knowledge of Parallel Numerical Algorithm. 10.E.1
General Information. 10.E.2 Atom Decomposition. 10.E.3 Force Decomposition.
10.E.4 Domain Decomposition. Appendix 10.F Supplemental Materials and
Software for Geometric Model Development in Atomistic Simulation. 10.F.1
Model Development for Model Coordinates Coincident with Main Crystal Axes.
10.F.2 Model Development for Model Coordinates not Coincident with Crystal
Axes. References. Postface. Index.
Jinghong Fan, Kazuo Inamori School of Engineering, Alfred University, Alfred, New York Dr. Jinghong Fan is a Professor of Mechanical Engineering at the Kazuo Inamori School of Engineering at Alfred University, Alfred, New York, USA. Dr. Fan serves as the Chairman of the Scientific Committee of the Research Center on Materials Mechanics at Chongqing University. He co-chaired the First and Second International Conference on Heterogeneous Materials Mechanics in 2004 and 2008. He has received several awards in his field, including the National Prize for Natural Science in China in 1987. Publications include books such as Foundation of Nonlinear Continuum Mechanics, 1988, and circa140 papers conference and journal papers. Dr. Fan has served as a guest editor of a number of journal special issues.
