近场动力学领域最新、最全研究汇总：《Handbook of Peridynamic Modeling》一书终于出版发行了！

自2013年9月开始，在Bobaru教授、Foster教授、Geubelle教授和Silling博士的领导下组织国际上各个近场动力学理论的知名研究团队编写了此书，历时三年，将近600页，汇集了近年来各家关于近场动力学理论的重要研究成果。我也参与其中，撰写了本书第14章中关于能量基的耦合框架部分。

这本书对希望学习和从事近场动力学理论研究的同学和老师会有很大的借鉴作用。不过价格不菲，亚马逊上精装版卖200刀。经费充足的小伙伴们可以考虑购买，也可以购买电子版：首先需要一个Bookshelf账号，然后有在线和离线软件两种阅读方式。电子书的具体价格我不知道，应该比纸质书要便宜吧。

电子书在线阅读登陆界面（需要购买哦）：

http://bookshelf.vitalsource.com/

电子书桌面阅读软件下载：

http://www.vitalsource.com/downloads

我把目录贴在下面，大家先睹为快：

Handbook of Peridynamic Modeling

Contents

Foreword

Preface

List of Figures

List of Tables

Contributors

I   The Need for Nonlocal Modeling and Introduction to Peridynamics

1   Why Peridynamics?

Stewart A. Silling

1.1   The mixed blessing of locality

1.2   Origins of nonlocality in a model

1.2.1   Long-range forces

1.2.2   Coarsening a fine-scale material system

1.2.3    Smoothing of a heterogeneous material system

1.3   Nonlocality at the macroscale

1.4   The mixed blessing of nonlocality

References

2   Introduction to Peridynamics

Stewart A. Silling

2.1   Equilibrium interms of integral equations

2.2   Material modeling

2.2.1   Bond-based materials

2.2.2   Relation between bond densities and flux

2.2.3   Peridynamic states

2.2.4   Ordinary state-based materials

2.2.5   Correspondence materials

2.2.6   Discrete particles as peridynamic bodies

2.2.7   Setting the horizon

2.2.8   Linearized peridynamics

2.3   Plasticity

2.3.1   Bond-based microplastic material

2.3.2   LPS material with plasticity

2.4   Damage and fracture

2.4.1   Damage in bond-based models

2.4.2   Damage in ordinary state-based material models

2.4.3   Damage in correspondence material models

2.4.4   Nucleation strain

2.5   Treatment of boundaries and interfaces

2.5.1   Bond-based materials

2.5.2   State-based materials

2.6   Emu numerical method

2.7   Conclusions

References

II   Mathematics,Numerics, and Software Tools of Peridynamics

3   Nonlocal Calculus of Variations and Well-Posedness of Peridynamics

Qiang Du

3.1   Introduction

3.2   A brief review of well-posedness results

3.3   Nonlocal balance laws and nonlocal vector calculus

3.4   Nonlocal calculus of variations — an illustration

3.5   Nonlocal calculus of variations — further discussions

3.6   Summary

References

4   Local Limits and Asymptotically Compatible Discretizations

Qiang Du

4.1   Introduction

4.2   Local PDE limits of linear peridynamic models

4.3   Discretization schemes and discrete local limits

4.4   Asymptotically compatible schemes for peridynamics

4.5   Summary

References

5   Roadmap for Software Implementation

David Littlewood

5.1   Introduction

5.2   Evaluating the internal force density

5.3   Bond damage and failure

5.4   The tangent stiffness matrix

5.5   Modeling contact

5.6   Mesh free discretizations for peridynamics

5.7   Proximity search for identification of pairwise interactions

5.8   Time integration

5.8.1   Explicit time integration for transient dynamics

5.8.2   Estimating the maximum stable time step

5.8.3   Implicit time integration for quasi-statics

5.9   Example simulations

5.9.1   Fragmentation of a brittle disk resulting from impact

5.9.2   Quasi-static simulation of a tensile test

5.10   Summary

References

III   Material Models and Links to Atomistic Models

6   Constitutive Modeling in Peridynamics

John T. Foster

6.1   Introduction

6.2   Kinematics, momentum conservation, and terminology

6.3   Linear peridynamic isotropic solid

6.3.1   Plane elasticity

6.3.1.1   Plane stress

6.3.1.2   Plane strain

6.3.2   “Bond-based” theories as a special case

6.3.3   On the role of the influence function

6.3.4   Other elasticity theories

6.4   Finite Deformations

6.4.1   Invariants of peridynamic scalar-states

6.5   Correspondence models

6.5.1   Non-ordinary correspondence models for solid mechanics

6.5.2   Ordinary correspondence models for solid mechanics

6.6   Plasticity

6.6.1   Yield surface and flow rule

6.6.2   Loading/unloading and consistency

6.6.3   Discussion

6.7   Non-ordinary models

6.7.1   A non-ordinary beam model

6.7.2   A non-ordinary plate/shell model

6.7.3   Other non-ordinary models

6.8   Final Comments

References

7   Links between Peridynamic and Atomistic Models

Pablo Seleson and Michael L. Parks

7.1   Introduction

7.2   Molecular dynamics

7.3   A meshfree discretization of peridynamic models

7.4   Upscaling molecular dynamics to peridynamics

7.4.1   A one-dimensional nonlocal linear springs model

7.4.2   A three-dimensional embedded-atom model

7.5   Computational speedup through upscaling

7.6   Concluding remarks

References

8   Absorbing Boundary Conditions with Verification

Raymond A. Wildman and George A. Gazonas

8.1   Introduction

8.2   A PML for state-based peridynamics

8.2.1  Two-dimensional (2D), state-based peridynamics review

8.2.2   Auxiliary field formulation and PML application

8.2.3   Numerical examples

8.3   Verification of cone and center crack problems

8.3.1   Dimension alanalysis of Hertzian cone crack development in brittle elastic solids

8.3.2   State-based verification of a cone crack

8.3.3   Bond-based verification of a center crack

8.4   Verification of an axisymmetric indentation problem

8.4.1   Formulation

8.4.2   Analytical verification

References

IV   Modeling Material Failure and Damage

9   Dynamic Brittle Fracture as an Upscaling of Unstable Mesoscopic Dynamics

Robert P. Lipton

9.1   Introduction

9.2   The macroscopice volution of brittle fracture as a small horizon limit of mesoscopic dynamics

9.3   Dynamic instability and fracture initiation

9.4   Localization of dynamic instability in the small horizon-macroscopic limit

9.5   Free crack propagation in the small horizon-macroscopic limit

9.6   Summary

References

10   Crack Branching in Dynamic Brittle Fracture

Florin Bobaru and Guanfeng Zhang

10.1   Introduction

10.2   A brief review of literature on crack branching

10.2.1   Theoretical models and experimental results on dynamic brittle fracture and crack branching

10.2.2   Computations of dynamic brittle fracture based on FEM

10.2.3   Dynamic brittle fracture results based on atomistic modeling

10.2.4   Dynamic brittle fracture based on particle and lattice-based methods

10.2.5   Phase-field models in dynamic fracture

10.2.6   Results on dynamic brittle fracture from peridynamic models

10.3   Brief review of the bond-based peridynamic model

10.4   An accurate and efficient quadrature scheme

10.5   Peridynamic results for dynamic fracture and crack branching

10.5.1   Crack branching in soda-lime glass

10.5.1.1   Load case1: stress on boundaries

10.5.1.2   Load case2: stress on pre-crack surfaces

10.5.1.3   Load case3: velocity boundary conditions

10.5.2   Crack branching in homalite

10.5.2.1   Load case1: stress on boundaries

10.5.2.2   Load case2: stress on pre-crack surfaces

10.5.2.3   Load case3: velocity boundary conditions

10.5.3   Influence of sample geometry

10.5.3.1   Load case1: stress on boundaries

10.5.3.2   Load case 2: stress on pre-crack surfaces

10.5.3.3   Load case3: velocity boundary conditions

10.6   Discussion of crack branching results

10.7   Why do cracks branch?

10.8   The importance of nonlocal modeling in crack branching

10.9   Conclusions

References

11   Relations between Peridynamic and Classical Cohesive Models

Scot M. Breitenfeld, Philippe H. Geubelle, Olaf Weckner, and Stewart A. Silling

11.1   Introduction

11.2   Analytical PD-based normal cohesive law

11.2.1   Case 1 — No bonds have reached critical stretch

11.2.2   Case 2 — Bonds have exceeded the critical stretch

11.2.3   Numerical approximation of PD-based cohesive law

11.3   PD-based tangential cohesive law

11.3.1   Case 1 — No bonds have reached critical stretch

11.3.2   Case 2 — Bonds have exceeded the critical stretch

11.4   PD-based mixed-mode cohesive law

11.5   Conclusions

References

12   Peridynamic Modeling of Fiber-reinforced Composites

Erdogan Madenci and Erkan Oterkus

12.1   Introduction

12.2   Peridynamic analysis of a lamina

12.3   Peridynamic analysis of a laminate

12.4   Numerical results

12.5   Conclusions

12.6   Appendix A: PD material constants of a lamina

12.6.1   Simple shear

12.6.2   Uniaxial stretch in the fiber direction

12.6.3   Uniaxial stretch in the transverse direction

12.6.4   Biaxial stretch

12.7   Appendix B: Surface correction factors for a composite lamina

12.8   Appendix C: PD interlayer and shear bond constants of a laminate

12.9   Appendix D: Critical Stretch Values for Bond Constants

References

13   Peridynamic Modeling of Impact and Fragmentation

Florin Bobaru, Zhanping Xu, and Yenan Wang

13.1   Introduction

13.2   Convergence studies and damage models that influence the damage behavior

13.2.1  Damage-dependent critical bond strain

13.2.2  Critical bond strain dependence on compressive strains along other directions

13.2.3   Surface effect in impact problems

13.2.4   Convergence study for impact on a glass plate

13.3   Impact on a multilayered glass system

13.3.1   Modelde scription

13.3.2   A comparison between FEM and peridynamics for the elastic response of a multilayered systemto impact

13.4   Computational results for damage progression in the seven-layer glass system

13.4.1   Damage evolution for the cross section

13.4.2   Damage evolution in the first layer

13.4.3   Damage evolution in the second layer

13.4.4   Damage evolution in the fourth layer

13.4.5   Damage evolution in the seventh layer

13.5   Conclusions

References

V   Multiphysics and Multiscale Modeling

14   Coupling Local and Nonlocal Models

Yan Azdoud, Fei Han, David J. Littlewood, Gilles Lubineau,and Pablo Seleson

14.1   Introduction

14.2   Energy-based blending schemes

14.2.1   The Arlequín method

14.2.1.1   Description of the coupling model

14.2.1.2   A numerical example

14.2.2   The morphing method

14.2.2.1   Overview

14.2.2.2   Description of the morphing method

14.2.2.3  One-dimensional analysis of ghost forces

14.2.2.4   Numerical examples

14.3   Force-based blending schemes

14.3.1   Convergence of peridynamic models to classical models

14.3.2   Derivation of force-based blending schemes

14.3.3   A numerical example

14.4   Summary

References

15   A Peridynamic Model for Corrosion Damage

Ziguang Chen and Florin Bobaru

15.1   Introduction

15.2   Electrochemical kinetics

15.3   Problem formulation of ID pitting corrosion

15.4   The peridynamicformulation for ID pitting corrosion

15.5   Results and discussion of ID pitting corrosion

15.5.1   Pit corrosion depth proportional to √t  

15.5.2   Activation-controlled, diffusion-controlled, and IR-controlled corrosion

15.6   Corrosion damage and the Concentration-Dependent Damage (CDD) model

15.6.1   Damage evolution

15.6.2   Saturated concentration

15.7   Formulation and results of 2D and 3D pitting corrosion

15.7.1   PD formulation of 2D and 3D pitting corrosion

15.7.2   The Concentration-Dependent Damage (CDD) model for pitting corrosion: example in 2D

15.7.3   A coupled corrosion/damage model for pitting corrosion: 2D example

15.7.4   Diffusivity affects the corrosion rate

15.7.5   Pitting corrosion with the CDD+DDC model in 3D

15.8   Pitting corrosion in heterogeneous materials: examples in 2D

15.8.1   Pitting corrosion in layer structures

15.8.2   Pitting corrosion in a material with inclusions: a 2D example

15.9   Conclusions

15.10   Appendix

15.10.1   Convergence study for ID diffusion-controlled corrosion

15.10.2   Convergence study for 2D activation-controlled corrosion with Concentration-Dependent Damage model

References

16   Peridynamics for Coupled Field Equations

Erdogan Madenci and Selda Oterkus

16.1   Introduction

16.2   Diffusion equation

16.2.1   Thermal diffusion

16.2.2   Moisture diffusion

16.2.3   Electrical conduction

16.3   Coupled field equations

16.3.1  Thermomechanics

16.3.1.1   Thermal diffusion with a structural coupling term

16.3.1.2   Equation of motion with a thermal coupling term

16.3.2   Porelasticity

16.3.2.1   Mechanical deformation due to fluid pressure

16.3.2.2   Fluid flow in porous medium

16.3.3  Electromigration

16.3.4  Hygrothermomechanics

16.4   Numerical solution to peridynamic field equations

16.4.1   Correction of PD material parameters

16.4.2   Boundary conditions

16.4.2.1   Essential boundary conditions

16.4.2.2   Natural boundary conditions

16.4.2.3   Example 1

16.4.2.4   Example 2

16.4.2.5   Example 3

16.5   Applications

16.5.1   Coupled nonuniform heating and deformation

16.5.2   Coupled nonuniform moisture and deformation in a square plate

16.5.3   Coupled fluid pore pressure and deformation

16.5.4   Coupled electrical, temperature, deformation, and vacancy diffusion

16.6   Remarks

References

Index

近场动力学(简称PD)理论是国际上刚兴起的基于非局部作用思想建立的一整套力学理论体系，该理论通过求解空间积分方程描述物质力学行为，避免了基于连续性假设建模和求解空间微分方程的传统宏观方法在面临不连续问题时的奇异性[1]，所以特别适用于模拟材料的损伤和断裂过程。然而，因为PD模型的数学理论较深，且新概念多用英文表述，所以很多朋友在学习时会遇到一些困难。在朋友的启发下，我想到在微信上建立此公众号，希望将研究PD理论的朋友们聚集起来，分享PD研习路上的点点滴滴，一起解决各自的难题，共同推动PD理论的发展！

[1] 黄 丹, 章 青,  乔丕忠, 沈 峰, 近场动力学方法及其应用. 力学进展, 2010. 40(4): p. 448-459.

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