Multiscale Analysis of Deformation and Failure of Materials / Edition 1

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Editorial Reviews

From the Publisher
"Provides a deep understanding of multiscale analysis and its implementation. " (Nanotech Cafe, 15 March 2011)
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Product Details

Meet the Author

Jinghong Fan, Kazuo Inamori School of Engineering, AlfredUniversity, Alfred, New York
Dr. Jinghong Fan is a Professor of Mechanical Engineering atthe Kazuo Inamori School of Engineering at Alfred University,Alfred, New York, USA. Dr. Fan serves as the Chairman of theScientific Committee of the Research Center on Materials Mechanicsat Chongqing University. He co-chaired the First and SecondInternational Conference on Heterogeneous Materials Mechanics in2004 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 NonlinearContinuum Mechanics, 1988, and circa140 papers conference andjournal papers. Dr. Fan has served as a guest editor of a number ofjournal special issues.

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Table of Contents

About the Author.

Series Preface.

Preface.

Abbreviations.

1 Introduction.

1.1 Material Properties Based on Hierarchy of MaterialStructure.

1.2 Overview of Multiscale Analysis.

1.3 Framework of Multiscale Analysis Covering a Large Range ofSpatial 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 ErrorEstimation.

2.5 Geometric Model Development of Atomistic System.

2.6 Boundary Conditions.

2.7 Statistical Ensembles.

2.8 Energy Minimization for Preprocessing and StatisticalMechanics Data Analyses.

2.9 Statistical Simulation Using Monte Carlo Methods.

2.10 Concluding Remarks.

References.

3 Applications of Atomistic Simulation in Ceramics andMetals.

Part 3.1 Applications in Ceramics and Materials with Ionic andCovalent Bonds.

3.1 Covalent and Ionic Potentials and Atomistic Simulation forCeramics.

3.2 Born Solid Model for Ionic-bonding Materials.

3.3 Shell Model.

3.4 Determination of Parameters of Short-distance Potential forOxides.

3.5 Applications in Ceramics: Defect Structure in Scandium DopedCeria Using Static Lattice Calculation.

3.6 Applications in Ceramics: Combined Study of AtomisticSimulation with XRD for Nonstoichiometry Mechanisms inY3Al5O12 (YAG) Garnets.

3.7 Applications in Ceramics: Conductivity of the YSZ Oxide FuelElectrolyte and Domain Switching of Ferroelectric Ceramics UsingMD.

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 forMetals.

3.11 Embedded Atom Methods EAM and MEAM.

3.12 Constructing Binary and High Order Potentials fromMonoatomic Potentials.

3.13 Application Examples of Metals: MD Simulation Reveals YieldMechanism of Metallic Nanowires.

3.14 Collecting Data of Atomistic Potentials from the InternetBased on a Specific Technical Requirement.

Appendix 3.A Potential Tables for Oxides and Thin-Film CoatingLayers.

References.

4 Quantum Mechanics and Its Energy Linkage with AtomisticAnalysis.

4.1 Determination of Uranium Dioxide Atomistic Potential and theSignificance of QM.

4.2 Some Basic Concepts of QM.

4.3 Postulates of QM.

4.4 The Steady State Schrödinger Equation of a SingleParticle.

4.5 Example Solution: Square Potential Well with InfiniteDepth.

4.6 Schrödinger Equation of Multi-body Systems andCharacteristics of its Eigenvalues and Ground State Energy.

4.7 Three Basic Solution Methods for Multi-body Problems inQM.

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 byDFT Calculations.

4.12 Concluding Remarks.

Appendix 4.A Solution to Isolated Hydrogen Atom.

References.

5 Concurrent Multiscale Analysis by Generalized ParticleDynamics Methods.

5.1 Introduction.

5.2 The Geometric Model of the GP Method.

5.3 Developing Natural Boundaries Between Domains of DifferentScales.

5.4 Verification of Seamless Transition via 1D Model.

5.5 An Inverse Mapping Method for Dynamics Analysis ofGeneralized Particles.

5.6 Applications of GP Method.

5.7 Validation by Comparison of Dislocation Initiation andEvolution Predicted by MD and GP.

5.8 Validation by Comparison of Slip Patterns Predicted by MDand 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 HierarchicalMultiscale Methods Across Atoms/Continuum.

6.1 Introduction.

Part 6.1 Basic Energy Principle and Numerical SolutionTechniques in Solid Mechanics.

6.2 Principle of Minimum Potential Energy of Solids andStructures.

6.3 Essential Points of Finite Element Methods.

Part 6.2 Quasicontinuum (QC) Concurrent Method of MultiscaleAnalysis.

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 MethodsAcross Atomic/Continuum Scales.

6.8 More Discussions about Deformation Gradient and theCauchy-Born Rule.

6.9 Analytical/Semi-analytical Methods Across Atom/ContinuumScales Based on the Cauchy-Born Rule.

6.10 Atomistic-based Continuum Model of Hydrogen Storage withCarbon Nanotubes.

6.11 Atomistic-based Model for Mechanical, Electrical andThermal 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 MultiscaleModeling.

7.2 Physical Features of Concurrent Multiscale Models.

7.3 MAAD Method for Analysis Across ab initio, Atomic andMacroscopic Scales.

7.4 Force-based Formulation of Concurrent MultiscaleModeling.

7.5 Coupled Atom Discrete Dislocation Dynamics (CADD) MultiscaleMethod.

7.6 1D Model for a Multiscale Dynamic Analysis.

7.7 Bridging Domains Method.

7.8 1D Benchmark Tests of Interface Compatibility for DCMethods.

7.9 Systematic Performance Benchmark of Most DCAtomistic/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 AcrossMicro/meso/macroscopic Scales and Information TransformationBetween These Scales.

8.2 Quantitative Meso-macro Bridging Based on Self-consistentSchemes.

8.3 Basics of Continuum Plasticity Theory.

8.4 Internal Variable Theory, Back Stress and ElastoplasticConstitutive Equations.

8.5 Quantitative Micro-meso Bridging by Developing Meso-cellConstitutive Equations Based on Microscopic Analysis.

8.6 Determining Size Effect on Yield Stress and KinematicHardening Through Dislocation Analysis.

8.7 Numerical Methods to Link Plastic Strains at the Mesoscopicand Macroscopic Scales.

8.8 Experimental Study on Layer-thickness Effects on CyclicCreep (Ratcheting).

8.9 Numerical Results and Comparison Between Experiments andMultiscale Simulation.

8.10 Findings in Microscopic Scale by Multiscale Analysis.

8.11 Summary and Conclusions.

Appendix 8.A Constitutive Equations and Expressions ofParameters.

Appendix 8.B Derivation of Equation (8.12e) and MatrixElements.

References.

9 Topics in Materials Design, Temporal Multiscale Problems andBio-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 inAtomistic Simulation.

9.5 Applications and Impacts of NEB Methods.

Part 9.3 Multiscale Analysis of Protein Materials and MedicalImplant 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 ImplicitRelationship of Stress, Strain Rate, Temperature in Terms ofActivation Energy and Activation Volume.

References.

10 Simulation Schemes, Softwares, Lab Practice andApplications.

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 SoftwareDL_POLY.

10.6 Nve and npt Ensemble in MD Simulation.

Part 10.2: Simulation Applications in Metals and Ceramics byMD.

10.7 Non-equilibrium MD Simulation of One-phase Model UnderExternal Shearing (1).

10.8 Non-equilibrium MD Simulation of a One-phase Model UnderExternal Shearing (2).

10.9 Non-equilibrium MD Simulation of a Two-phase Model UnderExternal Shearing.

Part 10.3: Atomistic Simulation for Protein-Water System andBrief Introduction of Large-scale Atomic/Molecular System (LAMMPS)and the GP Simulation.

10.10 Using NAMD Software for Biological AtomisticSimulation.

10.11 Stretching of a Protein Module (1): System Building andEquilibration with VMD/NAMD.

10.12 Stretching of a Protein Module (2): Non-equilibrium MDSimulation 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 toFile.

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 ForceCalculation.

10.D.1 Force Calculation in Atomistic Simulation.

Appendix 10.E Basic Knowledge of Parallel NumericalAlgorithm.

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 GeometricModel Development in Atomistic Simulation.

10.F.1 Model Development for Model Coordinates Coincident withMain Crystal Axes.

10.F.2 Model Development for Model Coordinates not Coincidentwith Crystal Axes.

References.

Postface.

Index.

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