本书是微纳技术著作丛书(影印版)之一，对纳米力学和材料的基本概念进行了介绍，侧重于多重尺度建模方法和技术的研究。本书内容包括：分子力学基础，微粒系统、晶格机械及现代多尺度建模理论等。本书是一本相关领域电子工程师、材料科研工作者开发微纳米材料应用的全面的指南，同时也可作为微纳米力学和微纳米技术专业研究生的参考书。

合成与分析纳米物质特性的能力取得了革命性的进展，广泛应用于生物医学、机械、电子、精密材料以及军事工程等领域。纳米力学是研究和描述单个原子、系统和结构在各种载荷条件下响应的机械行为特性的学科，它的发展促进了该技术的进步。尤其是多尺度建模方法，它可以使此领域的工程师更好的理解微纳米材料。

  本书由该领域内资深专家撰写，对纳米力学和材料的基本概念进行了介绍，侧重于多重尺度建模方法和技术的研究。本书内容包括：分子力学基础，微粒系统、晶格机械及现代多尺度建模理论等。

本书是一本相关领域电子工程师、材料科研工作者开发微纳米材料应用的全面的指南，同时也可作为微纳米力学和微纳米技术专业研究生的参考书。

Introduction

1.1 Potential of Nanoscale Engineering

1.2 Motivation for Multiple Scale Modeling

1.3 Educational Approach

Classical Molecular Dynamics

2.1 Mechanics of a System of Particles

 2.1.1 Generalized Coordinates

 2.1.2 Mechanical Forces and Potential Energy

 2.1.3 Lagrange Equations of Motion 

 2.1.4 Integrals of Motion and Symmetric Fields

 2.1.5 Newtonian Equations

 2.1.6 Examples

2.2 Molecular Forces

 2.2.1 External Fields

 2.2.2 Pair-Wise Interaction

 2.2.3 Multibody Interaction

 2.2.4 Exercises

2.3 Molecular Dynamics Applications

Lattice Mechanics

3.1 Elements of Lattice Symmetries

 3.1.1 Bravais Lattices

 3.1.2 Basic Symmetry Principles

 3.1.3 Crystallographic Directions and Planes

3.2 Equation of Motion of a Regular Lattice

 3.2.1 Unit Cell and the Associate Substructure

 3.2.2 Lattice Lagrangian and Equations of Motion

 3.2.3 Examples

3.3 Transforms

  3.3.1 Fourier Transform

  3.3.2 Laplace Transform

  3.3.3 Discrete Fourier Transform

3.4 Standing Waves in Lattices

 3.4.1 Normal Modes and Dispersion Branches

 3.4.2 Examples

3.5 Green's Function Methods

 3.5.1 Solution for a Unit Pulse

 3.5.2 Free Lattice with Initial Perturbations

 3.5.3 Solution for Arbitrary Dynamic Loads

 3.5.4 General Inhomogeneous Solution

 3.5.5 Boundary Value Problems and the Time History Kernel

 3.5.6 Examples

3.6 Q~asi-Static Approximation

 3.6.1 Equilibrium State Equation

 3.6.2 Quasi-Static Green's Function

 3.6.3 Multiscale Boundary Conditions

Methods of Thermodynamics and Statistical Mechanics

4.1 Basic Results of the Thermodynamic Method

 4.1.1 State Equations

 4.1.2 Energy Conservation Principle

 4.1.3 Entropy and the Second Law of Thermodynamics

 4.1.4 Nernst's Postulate

 4.1.5 Thermodynamic Potentials.

4.2 Statistics of Multiparticle Systems in Thermodynamic Equilibrium

 4.2.1 Hamiltonian Formulation

 4.2.2 Statistical Description of Multiparticle Systems

 4.2.3 Microcanonical Ensemble

 4.2.4 Canonical Ensemble

 4.2.5 Maxwell-Boltzmann Distribution

 4.2.6 Thermal Properties of Periodic Lattices

4.3 Numerical Heat Bath Techniques

 4.3.1 Berendsen Thermostat

 4.3.2 Nos6-Hoover Heat Bath

 4.3.3 Phonon Method for Solid-Solid Interfaces

Introduction to Multiple Scale Modeling

5.1 MAAD

5.2 Coarse-Grained Molecular Dynamics

5.3 Quasi-Continuum Method

5.4 CADD

5.5 Bridging Domain

Introduction to Bridging Scale

6.1 Bridging Scale Fundamentals

 6.1.1 Multiscale Equations of Motion

6.2 Removing Fine Scale Degrees of Freedom in Coarse Scale Region . 0

 6.2.1 Relationship of Lattice Mechanics to Finite Elements

 6.2.2 Linearized MD Equation of Motion

 6.2.3 Elimination of Fine Scale Degrees of Freedom

 6.2.4 Commentary on Reduced Multiscale Formulation

 6.2.5 Elimination of Fine Scale Degrees of Freedom:

      3D Generalization

 6.2.6 Numerical Implementation of Impedance Force

 6.2.7 Numerical Implementation of Coupling Force

6.3 Discussion on the Damping Kernel Technique

 6.3.1 Programming Algorithm for Time History Kernel

6.4 Cauchy-Born Rule

6.5 Virtual Atom Cluster Method

 6.5.1 Motivations and General Formulation

 6.5.2 General Idea of the VAC Model

 6.5.3 Three-Way Concurrent Coupling with QM Method

 6.5.4 Tight-Binding Method for Carbon Systems

 6.5.5 Coupling with the VAC Model

6.6 Staggered Time Integration Algorithm

 6.6.1 MD Update

 6.6.2 FE Update

6.7 Summary of Bridging Scale Equations

6.8 Discussion on the Bridging Scale Method

Bridging Scale Numerical Examples

7.1 Comments on Time History Kernel

7.2 1D Bridging Scale Numerical Examples

 7.2.1 Lennard-Jones Numerical Examples

 7.2.2 Comparison of VAC Method and Cauchy-Born Rule

 7.2.3 Truncation of Time History Kernel

7.3 2D/3D Bridging Scale Numerical Examples

7.4 Two-Dimensional Wave Propagation

7.5 Dynamic Crack Propagation in Two Dimensions

7.6 Dynamic Crack Propagation in Three Dimensions

7.7 Virtual Atom Cluster Numerical Examples

 7.7.1 Bending of Carbon Nanotubes

 7,7.2 VAC Coupling with Tight Binding

Non-Nearest Neighbor MD Boundary Condition

8.1 Introduction

8.2 Theoretical Formulation in 3D

 8.2.1 Force Boundary Condition: 1D Illustration

 8.2.2 Displacement Boundary Condition: 1D Illustration

 8.2.3 Comparison to Nearest Neighbors Formulation

 8.2.4 Advantages of Displacement Formulation

8.3 Numerical Examples: ID Wave Propagation

8.4 Time-History Kernels for FCC Gold

8.5 Conclusion for the Bridging Scale Method

 8.5.1 Bridging Scale Perspectives _

9 Multiscale Methods for Material Design

9.1 Multiresolution Continuum Analysis

    9.1.1 Generalized Stress and Deformation Measures

    9.1.2 Interaction between Scales

    9.1.3 Multiscale Materials Modeling

9.2 Multiscale Constitutive Modeling of Steels

    9.2.1 Methodology and Approach

    9.2.2 First-Principles Caldulation

   9.2.3 Hierarchical Unit Cell and Constitutive Model

    9.2.4 Laboratory Specimen Scale: Simulation and Results

9.3 Bid-Inspired Materials

   9.3.1 Mechanisms of Self-Healing in Materials

   9.3.2 Shape-Memory Composites

   9.3.3 Multiscale Continuum Modeling of SMA Composites

   9.3.4 Issues of Modeling and Simulation

9.4 Summary and Future Research Directions

10 Bio-Nano Interface

10.1 Introduction

10.2 Immersed Finite Element Method

    10.2.1 Formulation

    10.2.2 Computational Algorithm of IFEM

10.3 Vascular Flow and Blood Rheology

    10.3.1 Heart Model

    10.3.2 Flexible Valve-Viscous Fluid Interaction

    10.3.3 Angioplasty Stent

    10.3.4 Monocyte Deposition

    10.3.5 Platelet Adhesion and Blood Clotting

   10.3.6 RBC Aggregation and Interaction

10.4 Electrohydrodynamic Coupling

   10.4.1 Maxwell Equations

   10.4.2 Electro-manipulation

   10.4.3 Rotation of CNTs Induced by Electroosmotic Flow

10.5 CNT/DNA Assembly Simulation

10.6 Cell Migration and Cell-Suhstrate Adhesion

10.7 Conclusions

Appendix A Kernel Matrices for EAM Potential

Bibliography

Index