MULTISCALE ANALYSIS OF DEFORMATION AND FAILURE OF MATERIALS -- Contents -- About the Author -- Series Preface -- Preface -- Abbreviations -- 1 Introduction -- 1.1 Material Properties Based on Hierarchy of Material Structure -- 1.1.1 Property-structure Relationship at Fundamental Scale -- 1.1.2 Property-structure Relationship at Different Scales -- 1.1.3 Upgrading Products Based on Material Structure-property Relationships -- 1.1.4 Exploration of In-depth Mechanisms for Deformation and Failure by Multiscale Modeling and Simulation -- 1.2 Overview of Multiscale Analysis -- 1.2.1 Objectives, Contents and Significance of Multiscale Analysis -- 1.2.2 Classification Based on Multiscale Modeling Schemes -- 1.2.3 Classification Based on the Linkage Feature at the Interface Between Different Scales -- 1.3 Framework of Multiscale Analysis Covering a Large Range of Spatial Scales -- 1.3.1 Two Classes of Spatial Multiscale Analysis -- 1.3.2 Links Between the Two Classes of Multiscale Analysis -- 1.3.3 Different Characteristics of Two Classes of Multiscale Analysis -- 1.3.4 Minimum Size of Continuum -- 1.4 Examples in Formulating Multiscale Models from Practice -- 1.4.1 Cyclic Creep (Ratcheting) Analysis of Pearlitic Steel Across Micro/meso/macroscopic Scales -- 1.4.2 Multiscale Analysis for Brittle-ductile Transition of Material Failure -- 1.5 Concluding Remarks -- References -- 2 Basics of Atomistic Simulation -- 2.1 The Role of Atomistic Simulation -- 2.1.1 Characteristics, History and Trends -- 2.1.2 Application Areas of Atomistic Simulation -- 2.1.3 An Outline of Atomistic Simulation Process -- 2.1.4 An Expression of Atomistic System -- 2.2 Interatomic Force and Potential Function -- 2.2.1 The Relation Between Interatomic Force and Potential Function -- 2.2.2 Physical Background and Classifications of Potential Functions -- 2.3 Pair Potential.

2.3.1 Lennard-Jones (LJ) Potential -- 2.3.2 The 6-12 Pair Potential -- 2.3.3 Morse Potential -- 2.3.4 Units for Atomistic Analysis and Atomic Units (au) -- 2.4 Numerical Algorithms for Integration and Error Estimation -- 2.4.1 Motion Equation of Particles -- 2.4.2 Verlet Numerical Algorithm -- 2.4.3 Velocity Verlet (VV) Algorithm -- 2.4.4 Other Algorithms -- 2.5 Geometric Model Development of Atomistic System -- 2.6 Boundary Conditions -- 2.6.1 Periodic Boundary Conditions (PBC) -- 2.6.2 Non-PBC and Mixed Boundary Conditions -- 2.7 Statistical Ensembles -- 2.7.1 Nve Ensemble -- 2.7.2 Nvt Ensemble -- 2.7.3 Npt Ensemble -- 2.8 Energy Minimization for Preprocessing and Statistical Mechanics Data Analyses -- 2.8.1 Energy Minimization -- 2.8.2 Data Analysis Based on Statistical Mechanics -- 2.9 Statistical Simulation Using Monte Carlo Methods -- 2.9.1 Introduction of Statistical Method -- 2.9.2 Metropolis-Hastings Algorithm for Statics Problem -- 2.9.3 Dynamical Monte Carlo Simulations -- 2.9.4 Adsorption-desorption Equilibrium -- 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 -- 3.1.1 Applications of High-performance Ceramics -- 3.1.2 Ceramic Atomic Bonds in terms of Electronegativity -- 3.2 Born Solid Model for Ionic-bonding Materials -- 3.2.1 Born Model -- 3.2.2 Born-Mayer and Buckingham Potentials -- 3.3 Shell Model -- 3.4 Determination of Parameters of Short-distance Potential for Oxides -- 3.4.1 Basic Assumptions -- 3.4.2 General Methods in Determining Potential Parameters -- 3.4.3 Three Basic Methods for Potential Parameter Determination by Experiments.

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 -- 3.6.1 Background -- 3.6.2 Structure and Defect Mechanisms of YAG Garnets -- 3.6.3 Simulation Method and Results -- 3.7 Applications in Ceramics: Conductivity of the YSZ Oxide Fuel Electrolyte and Domain Switching of Ferroelectric Ceramics Using MD -- 3.7.1 MD Simulation of the Motion of Oxygen Ions in SOFC -- 3.8 Tersoff and Brenner Potentials for Covalent Materials -- 3.8.1 Introduction of the Abell-Tersoff Bonder-order Approach -- 3.8.2 Tersoff and Brenner Potential -- 3.9 The Atomistic Stress and Atomistic-based Stress Measure -- 3.9.1 The Virial Stress Measure -- 3.9.2 The Computation Form for the Virial Stress -- 3.9.3 The Atomistic-based Stress Measure for Continuum -- 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 -- 3.11.1 Basic EAM Formulation -- 3.11.2 EAM Physical Background -- 3.11.3 EAM Application for Hydrogen Embrittlement -- 3.11.4 Modified Embedded Atom Method (MEAM) -- 3.11.5 Summary and Discussions -- 3.12 Constructing Binary and High Order Potentials from Monoatomic Potentials -- 3.12.1 Determination of Parameters in LJ Pair Function for Unlike Atoms by Lorentz-Berthelet Mixing Rule -- 3.12.2 Determination of Parameters in Morse and Exponential Potentials for Unlike Atoms -- 3.12.3 Determination of Parameters in EAM Potentials for Alloys -- 3.12.4 Determination of Parameters in MEAM Potentials for Alloys -- 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 -- 3.14.1 Background About Galvanic Corrosion of Magnesium and Nano-Ceramics Coating on Steel -- 3.14.2 Physical and Chemical Vapor Deposition to Produce Ceramics Thin Coating Layers on Steel Substrate -- 3.14.3 Technical Requirement for Potentials and Searching Results -- 3.14.4 Using Obtained Data for Potential Development and Atomistic Simulation -- 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 Schrödinger Equation of a Single Particle -- 4.5 Example Solution: Square Potential Well with Infinite Depth -- 4.5.1 Observations and Discussions -- 4.6 Schrödinger Equation of Multi-body Systems and Characteristics of its Eigenvalues and Ground State Energy -- 4.6.1 General Expression of the Schrödinger Equation and Expectation Value of Multi-body Systems -- 4.6.2 Example: Schrödinger Equation for Hydrogen Atom Systems -- 4.6.3 Variation Principle to Determine Approximate Ground State Energy -- 4.7 Three Basic Solution Methods for Multi-body Problems in QM -- 4.7.1 First-principle or ab initio Methods -- 4.7.2 An Approximate Method -- 4.8 Tight Binding Method -- 4.9 Hartree-Fock (HF) Methods -- 4.9.1 Hartree Method for a Multi-body Problem -- 4.9.2 Hartree-Fock (HF) Method for the Multi-body Problem -- 4.10 Electronic Density Functional Theory (DFT) -- 4.11 Brief Introduction on Developing Interatomic Potentials by DFT Calculations -- 4.11.1 Energy Linkage Between QM and Atomistic Simulation.

4.11.2 More Information about Basis Set and Plane-wave Pseudopotential Method for Determining Atomistic Potential -- 4.11.3 Using Spline Functions to Express Potential Energy Functions -- 4.11.4 A Systematic Method to Determine Potential Functions by First-principle Calculations and Experimental Data -- 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 -- 5.1.1 Existing Needs for Concurrent Multiscale Modeling -- 5.1.2 Expanding Model Size by Concurrent Multiscale Methods -- 5.1.3 Applications to Nanotechnology and Biotechnology -- 5.1.4 Plan for Study of Concurrent Multiscale Methods -- 5.2 The Geometric Model of the GP Method -- 5.3 Developing Natural Boundaries Between Domains of Different Scales -- 5.3.1 Two Imaginary Domains Next to the Scale Boundary -- 5.3.2 Neighbor-link Cells (NLC) of Imaginary Particles -- 5.3.3 Mechanisms for Seamless Transition -- 5.3.4 Linkage of Position Vectors at Different Scales by Spatial and Temporal Averaging -- 5.3.5 Discussions -- 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 -- 5.10.1 MAAD Concurrent Multiscale Method -- 5.10.2 Incompatibility Problems at Scale Boundary Illustrated with the MAAD Method -- 5.10.3 Quasicontinuum (QC) Method -- 5.10.4 Coupling Atomistic Analysis with Discrete Dislocation (CADD) Method -- 5.10.5 Existing Efforts to Eliminate Artificial Phenomena at the Boundary.

5.10.6 Embedded Statistical Coupling Method (ESCM) with Comments on Direct Coupling (DC) Methods.