每期文章评述的首发平台是微信公众号 :近场动力学PD讨论班。您也可以搜索微信号:peridynamics。或者在本文的末尾有公众号的二维码,欢迎您扫描加入。 本文摘要:你知道“近场动力学”名字的意义吗?你知道在物理和力学中常见的几个英文词汇:Mechanics, Statics, Kinematics, Kinetics和Dynamics的意思和区别吗?本文细细道来,欢迎阅读。 最近连续被两位老先生问到:“近场动力学中的动力学如何体现”? “这个么...”,我一时语塞。脑中飞快得思索如何作答:“近场动力学是由英文‘peri-dynamics’翻译过来的,其中dynamics就是动力学的意思,例如分子动力学,英文就是molecular dynamics”。就这样搪塞过去了。老先生们虽然没有反驳,但是显然对我的回答不够满意。 回来后,赶紧上网查。维基百科中对于动力学的解释如下:“ 动力学(Dynamics)是经典力学的一门分支,主要研究运动的变化与造成这变化的各种因素。... 更仔细地说,动力学研究由于力的作用,物理系统怎样改变。动力学的基础定律是艾萨克·牛顿提出的牛顿运动定律。对于任意物理系统,只要知道其作用力的性质,引用牛顿运动定律,就可以研究这作用力对于这物理系统的影响。... ”。显然,分子动力学正是建立在牛顿运动定律上的,完全符合这个动力学的定义,但是近场动力学似乎有些牵强。至少到目前为止,我所做的近场动力学研究都还停留在拟静态问题的模拟上,还没有考虑过含加速度那一项,好像离牛顿运动定律也很远。 可是,“peridynamics”按英文的字面确实可以分解为“ peri- ”词根和“ dynamics ”两个词。字典上,“peri-”词根的意思是“周围,邻近”,翻译做“近场”挺合适的,还带有学术味道。而“dynamics”大家都知道翻译做“动力学”。所以,从字面看中文的翻译也挺正确的。那么现在的问题就变成了:“为什么‘peridynamics’的提出者Silling博士要把这个理论起名为“peri-dynamics”呢”? 于是,赶紧查Silling博士最早命名“peridynamics”的文献中是否有解释。这篇文献也就是我们现阶段正在评述的Silling博士发表于2000年的文章(S.A. Silling, Reformulation of elasticity theory for discontinuities and long-range forces, Journal of the mechanics and physics of solids , 2000, 48 , 175-209)。在文章的176页倒数第二段末尾,Silling博士写到:“We propose the term peridynamic model for such a formulation, from Greek roots for near and force ”。很明显,Silling博士认为“dynamics”就是指“力”。根据这个认识,中文岂不是应该翻译做“近场力学”更合适!?可是在我印象中“dynmaics”从来都是翻译做“动力学”啊,这又是怎么回事呢? 接着上网搜索... 终于让我搜到中国科学院物理研究所的曹则贤研究员于2015年发表在《物理》杂志上的一篇文章《物理学咬文嚼字之七十 纷繁的运-动-力学》(曹则贤,物理学咬文嚼字之七十纷繁的运-动-力学, 物理 ,2015,44(3),193-198)。读完之后,恍然大悟。在此,与各位分享文章内容的摘要以及我的一些体会。 文中详细介绍了英文中常见的五个与力学相关的词汇:Mechanics, Statics,Kinematics,Kinetics和Dynamics。现在总结如下: Mechanics: 在中文中经常被翻译为“力学”。其实出自希腊文,原意是“having to do with, or having skill in the use of, machinery or tools”,跟手艺人掌握的机械与工具有关。西方古代最令人印象深刻的mechanics是抛石机。Mechanics后来衍生的意思,及其所衍生的其它词的意思,都与机械、手艺有关。比如,物理研究的一个关键内容是弄清楚某事的mechanism,汉译就是机制、机理。Mechanics其实是研究“how things go”,不一定是以力为驱动,更确切的说应该是以interaction(相互作用)作为驱动。然而Mechanics被译为力学,有其历史的原因,但如果我们死抱着mechanics是力学的概念,对mechanics的理解有害无益。 Statics: 静力学,力学中研究静止或者平衡的那部分学问。汉译静力学中的“力”字属于翻译时硬塞进去的。Statics可能是物理学的源头。顺便插一句,昨天现场观看了日本艺术家Miyoko Shida Rigolo表演的羽毛平衡。把一根羽毛和几根特殊的树枝在没有任何粘接的情况下靠重力平衡搭成个不会散的架子。最终,再把羽毛一撤,枝架不再平衡,所有的树枝都散落一地。请见下图(表演中,头顶平衡枝架): 网上有表演的视频,您若感兴趣可以上网观看整个表演过程,场面相当震撼。按照上面的定义,这个就应该属于Statics的学问吧,呵呵。 Kinematics: 汉译成动理学。据说这个词是法国科学家安培在希腊原词的基础上生造出来的。它是一门关于运动的mechanics分支(注意这里的mechanics更多的是指机理,而不是力学哦),不涉及力或者质量,即只谈运动(包括速度和加速度),不涉及原因。伽利略的力学中没有力与能量的概念的,他那时无法测量这些量,因此只能以定性的方式谈到它们。伽利略关于运动的描述构成了Kinematics的大部分内容。动理学包括对质点、物体和物质体系的运动的描述,因此也叫geometry of motion(运动的几何学)。 Kinetics: 运动学,它的希腊文的原词与Kinematics的希腊文原词同源。Kinetics也有汉译为动力学的,但是其字面上没有“力”字。作为经典力学的分支,kinetics脱胎于kinematics(只关注运动本身的动理学),它研究运动及其原因——通过质量及质量二阶矩即惯量张量的概念建立起运动同力、力矩之间的关系。Kinetics(运动学)研究运动,不可能不涉及到力的。进入二十世纪,kinetics在物理学领域已经逐渐被dynamics或者analytical dynamics所取代(我们必须注意到是涉及力的那些用法才被dynamics所取代),但kinetics和力至少到目前还脱不了干系。 Dynamics: 希腊文原意是力、能力(power,strength,force)。形容词为dynamic或dynamical。除了有“强有力的,有活力的(energetic,vigorous,forceful)”这些与力、运动有关的意思以外,它还有与变化有关的意思,汉语翻译成“动态的”,如dynamic response(动态响应),即响应要跟得上刺激的时间变化。动力学是物理学的重要组成部分。 以某个时刻的状态作为初始条件,能确定物理系统是如何随时间演化的物理理论就可以被看做是动力学 。 曹则贤研究员还特别比较了 kinematics 和 dynamics 的区别:“按物理学家的说法,kinematics在不考虑力的因素的前提下研究运动是如何发生的,如果考虑了力,kinematics就变成了dynamics。相比较,数学家的概念更清晰:一个孤立的系统包括:(a)相空间,即系统运动之所有可能的瞬时状态的集合;(b)在相空间中描述系统所有可能历史(history)的曲线的集合,即系统随着时间的推移可以经过的状态之序列。前者是kinematics,后者是dynamics。有必要区分系统的状态和系统之运动的状态”。 我把上述定义简单地总结为:kinematics是关于某一时刻运动物体的状态(比如,物体在此时刻有多少动能和多少势能),而dynamics更关注物体运动的整个变化过程。于是,我立刻想起Silling博士在2000年发表的文章中开篇就提到:“Many problems of fundamental importance in solid mechanics involve the spontaneous formation of discontinuities. Here, 'spontaneous' means that a discontinuity forms where one was not present initially.” 这句话明确指出问题的根本是固体材料中不连续(如裂纹)自发形成的过程。Peridynamics理论的提出也正是为了 研究 从完好材料开始,裂纹自发产生及扩展的过程 ,而且研究者预先并不知道裂纹将会在哪里出现或者向哪里扩展。也就是说,近场动力学关注的是物理系统的变化过程。 综上所述,近场动力学中的“近场”表明是物质点周围一定距离内的区域;“力”表明所研究的是物质点间的相互作用;而“动”表明是一个变化的过程;“学”则是指一套理论体系。整个连起来就可以解释为: 近场动力学是假设每个物质点在承受其周围一定范围内的非接触相互作用下,研究整个物理系统的变化过程的一套理论 。 到目前为止,近场动力学不仅限于模拟固体材料从连续状态到不连续发生和发展的整个变化过程,而且已经被推广到热扩散、波的传播、细胞膜碎裂等各个动态演变系统的研究领域中。因此,“近场-动-力学”的命名“动”感十足,且恰到好处地描述了它的应用范畴。 封面图简介: (左图)杜尚于1912年画的《下楼梯的裸女》;(右图)Elisofon于1952年采用连续曝光的手法拍摄的《下楼梯的杜尚》。两图都动态地表现了活力的艺术。 本文部分内容引用和参考下文(请点击链接阅读原文:http://ccftp.scu.edu.cn:8090/Download/20150516235353542.pdf) —————————————————————————————————————————————————————— 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 ,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! 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. 每期文章评述的首发平台是微信公众号 :近场动力学PD讨论班 也可以搜索微信号:peridynamics 或扫如下二维码加入公众号:
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 ,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! 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. 每期文章评述的首发平台是微信公众号 :近场动力学PD讨论班 也可以搜索微信号:peridynamics 或扫如下二维码加入公众号: