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准晶数学弹性理论及应用（第二版）英文版
  • 书号：9787030474292
    作者：Tianyou Fan
  • 外文书名：
  • 装帧：圆脊精装
    开本：B5
  • 页数：472
    字数：无
    语种：zh-Hans
  • 出版社：科学出版社
    出版时间：1900-01-01
  • 所属分类：
  • 定价： ￥198.00元
    售价： ￥156.42元
  • 图书介质:
    纸质书

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本书介绍了固体准晶弹性和软物质准晶弹性-流体动力学理论好应用，为国内外第一本该领域的专著，为原始创新成就。内容包括晶体，经典弹性基础，固体准晶及其性质，固体准晶弹性的物理基础，一维准晶弹性和化简，二维准晶弹性与化简，应用之一----一维和二维准晶的位错和界面问题及解，应用之二----一维和二维准晶的缺口和裂纹问题及解，三维准晶弹性和应用，准晶弹性与缺陷动力学，准晶弹性和缺陷的复分析，准晶弹性的变分原理和数值解，准晶弹性解的若干数学原理，固体准晶的非线性，固体准晶的断裂理论，可能的7次和14次固体准晶，可能的9次和18次固体准晶，准晶流体动力学，软物质准晶的弹性-流体动力学及其应用。

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目录

  • Contents
    1 Crystals1
    1.1 Periodicity of Crystal Structure, Crystal Cell 1
    1.2 Three-Dimensional LatticeTypes2
    1.3 Symmetry and Point Groups 2
    1.4 Reciprocal Lattice 5
    1.5 Appendix of Chapter 1: Some Basic Concepts6
    1.5.1 ConceptofPhonon6
    1.5.2 Incommensurate Crystals 10
    1.5.3 Glassy Structure 11
    1.5.4 Mathematical Aspect of Group 11
    References 12
    2 Framework of Crystal Elasticity13
    2.1 Review on Some Basic Concepts13
    2.1.1 Vector13
    2.1.2 Coordinate Frame 14
    2.1.3 Coordinate Transformation 14
    2.1.4 Tensor16
    2.1.5 Algebraic Operation of Tensor 16
    2.2 Basic Assumptions of Theory of Elasticity17
    2.3 Displacement and Deformation17
    2.4 Stress Analysis 19
    2.5 Generalized Hooke’sLaw20
    2.6 Elastodynamics, Wave Motion 24
    2.7 Summary25
    References 26
    3 Quasicrystal and Its Properties27
    3.1 Discovery of Quasicrystal 27
    3.2 Structure and Symmetry of Quasicrystals 29
    3.3 A Brief Introduction on Physical Properties of Quasicrystals 31
    3.4 One-, Two-and Three-Dimensional Quasicrystals 32
    3.5 Two-Dimensional Quasicrystals and Planar Quasicrystals 32
    References 33
    4 The Physical Basis of Elasticity of Solid Quasicrystals37
    4.1 Physical Basis of Elasticity of Quasicrystals 37
    4.2 Deformation Tensors38
    4.3 Stress Tensors and Equations of Motion 40
    4.4 Free Energy Density and Elastic Constants 42
    4.5 Generalized Hooke’sLaw44
    4.6 Boundary Conditions and Initial Conditions 44
    4.7 A Brief Introduction on Relevant Material Constants of Solid Quasicrystals 46
    4.8 Summary and Mathematical Solvability of Boundary Value or Initial-Boundary Value Problem47
    4.9 Appendix of Chapter 4: Description on Physical Basis of Elasticity of Quasicrystals Based on the Landau Density WaveTheory48
    References 53
    5 Elasticity Theory of One-Dimensional Quasicrystals and Simplification 55
    5.1 Elasticity of Hexagonal Quasicrystals55
    5.2 Decomposition of the Elasticity into a Superposition of Plane and Anti-plane Elasticity58
    5.3 Elasticity of Monoclinic Quasicrystals61
    5.4 Elasticity of Orthorhombic Quasicrystals64
    5.5 Tetragonal Quasicrystals 65
    5.6 The Space Elasticity of Hexagonal Quasicrystals 66
    5.7 Other Results of Elasticity of One-Dimensional Quasicrystals 68
    References 68
    6 Elasticity of Two-Dimensional Quasicrystals and Simplification 71
    6.1 Basic Equations of Plane Elasticity of Two-Dimensional Quasicrystals: Point Groups 5m and 10mm in Five-and TenfoldSymmetries75
    6.2 Simplification of the Basic Equation Set: Displacement Potential Function Method81
    6.3 Simplification of Basic Equations Set: Stress Potential Function Method 83
    6.4 Plane Elasticity of Point Group 5, 5 and 10, 10 Pentagonal and Decagonal Quasicrystals85
    6.5 Plane Elasticity of Point Group 12mm of Dodecagonal Quasicrystals 89
    6.6 Plane Elasticity of Point Group8mm of Octagonal Quasicrystals, Displacement Potential93
    6.7 Stress Potential of Point Group5;5 Pentagonal and Point Group 10;10 Decagonal Quasicrystals98
    6.8 Stress Potential ofPointGroup8mm Octagonal Quasicrystals 100
    6.9 Engineering and Mathematical Elasticity of Quasicrystals 103 References 106
    7 Application I—Some Dislocation and Interface Problems and Solutions in One-and Two-Dimensional Quasicrystals109
    7.1 Dislocations in One-Dimensional Hexagonal Quasicrystals 110
    7.2 Dislocations in Quasicrystals with Point Groups 5m and 10 mm Symmetries112
    7.3 Dislocations in Quasicrystals with Point Groups 5; 5 Fivefold and 10, 10 Tenfold Symmetries 119
    7.4 Dislocations in Quasicrystals with Eightfold Symmetry124
    7.4.1 Fourier Transform Method 125
    7.4.2 Complex Variable Function Method 127
    7.5 Dislocations in Dodecagonal Quasicrystals 128
    7.6 Interface Between Quasicrystal and Crystal 129
    7.7 Dislocation Pile up, Dislocation Group and Plastic Zone133
    7.8 Discussions and Conclusions134
    References 134
    8Application II—Solutions of Notch and Crack Problems of One-and Two-Dimensional Quasicrystals137
    8.1 Crack Problem and Solution of One-Dimensional Quasicrystals 138
    8.1.1 GriffithCrack138
    8.1.2 Brittle Fracture Theory 143
    8.2 Crack Problem in Finite-Sized One-Dimensional Quasicrystals 145
    8.2.1 Cracked Quasicrystal Strip with Finite Height 145
    8.2.2 Finite Strip with Two Cracks 149
    8.3 Griffith Crack Problems in Point Groups5m and 10mm Quasicrystal Based on Displacement Potential Function Method150
    8.4 Stress Potential Function Formulation and Complex Analysis Method for Solving Notch/Crack Problem of Quasicrystals of Point Groups5,5and10;10155
    8.4.1 Complex Analysis Method 156
    8.4.2 The Complex Representation of Stresses and Displacements 156
    8.4.3 Elliptic Notch Problem158
    8.4.4 Elastic Field Caused by a Griffith Crack 162
    8.5 Solutions of Crack/Notch Problems of Two-Dimensional Octagonal Quasicrystals 163
    8.6 Approximate Analytic Solutions of Notch/Crack of Two-Dimensional Quasicrystals with5-and 10-Fold Symmetries165
    8.7 Cracked Strip with Finite Height of Two-Dimensional Quasicrystals with 5-and 10-Fold Symmetries and Exact Analytic Solution 168
    8.8 Exact Analytic Solution of Single Edge Crack in a Finite Width Specimen of a Two-Dimensional Quasicrystal of 10-FoldSymmetry 172
    8.9 Perturbation Solution of Three-Dimensional Elliptic Disk Crack in One-Dimensional Hexagonal Quasicrystals 175
    8.10 Other Crack Problems in One-and Two-Dimensional Quasicrystals 179
    8.11 Plastic Zone Around Crack Tip 179
    8.12 Appendix1 ofChapter8: Some Derivations in Sect.8.1179
    8.13 Appendix2 of Chapter8: Some Further Derivation of Solution in Sect.8.9 181
    References 186
    9 Theory of Elasticity of Three-Dimensional Quasicrystals and Its Applications189
    9.1 Basic Equations of Elasticity of Icosahedral Quasicrystals190
    9.2 Anti-plane Elasticity of Icosahedral Quasicrystals and Problem of Interface of Quasicrystal–Crystal194
    9.3 Phonon-Phason Decoupled Plane Elasticity of Icosahedral Quasicrystals 200
    9.4 Phonon-Phason Coupled Plane Elasticity of Icosahedral Quasicrystals—Displacement Potential Formulation 202
    9.5 Phonon-Phason Coupled Plane Elasticity of Icosahedral Quasicrystals—Stress Potential Formulation 205
    9.6 A Straight Dislocation in an Icosahedral Quasicrystal 207
    9.7 Application of Displacement Potential to Crack Problem of Icosahedral Quasicrystal212
    9.8 An Elliptic Notch/Griffith Crack in an Icosahedral Quasicrystal220
    9.8.1 The Complex Representation of Stresses and Displacements 220
    9.8.2 Elliptic Notch Problem222
    9.8.3 BriefSummary226
    9.9 Elasticity of Cubic Quasicrystals—The Anti-plane and AxisymmetricDeformation226
    References 231
    10 Phonon-Phason Dynamics and Defect Dynamics of Solid Quasicrystals 233
    10.1 Elastodynamics of Quasicrystals Followed Bak’s Argument 234
    10.2 Elastodynamics of Anti-plane Elasticity for Some Quasicrystals 235
    10.3 Moving Screw Dislocation in Anti-plane Elasticity236
    10.4 Mode III Moving Griffith Crack in Anti-plane Elasticity 240
    10.5 Two-Dimensional Phonon-Phason Dynamics, Fundamental Solution 243
    10.6 Phonon-Phason Dynamics and Solutions of Two-Dimensional Decagonal Quasicrystals 249
    10.6.1 The Mathematical Formalism of Dynamic Crack Problems of Decagonal Quasicrystals 249
    10.6.2 Examination on the Physical Model 252
    10.6.3 Testing the Scheme and the Computer Programme254
    10.6.4 Results of Dynamic Initiation of Crack Growth 256
    10.6.5 Results of the Fast Crack Propagation257
    10.7 Phonon-Phason Dynamics and Applications to Fracture Dynamics of Icosahedral Quasicrystals259
    10.7.1 Basic Equations, Boundary and Initial Conditions259
    10.7.2 Some Results 261
    10.7.3 Conclusion and Discussion 263
    10.8 Appendix of Chapter 10: The Detail of Finite Difference Scheme264
    References 268
    11 Complex Analysis Method for Elasticity of Quasicrystals271
    11.1 Harmonic and Biharmonic in Anti-Plane Elasticity of One-Dimensional Quasicrystals272
    11.2 Biharmonic Equations in Plane Elasticity of Point Group 12mm Two-Dimensional Quasicrystals 272
    11.3 The Complex Analysis of Quadruple Harmonic Equations and Applications in Two-Dimensional Quasicrystals273
    11.3.1 Complex Representation of Solution of the Governing Equation 273
    11.3.2 Complex Representation of the Stresses and Displacements 274
    11.3.3 The Complex Representation of Boundary Conditions275
    11.3.4 Structure of Complex Potentials276
    11.3.5 Conformal Mapping 281
    11.3.6 Reduction in the Boundary Value Problem to Function Equations 282
    11.3.7 Solution of the Function Equations283
    11.3.8 Example1 Elliptic Notch/Crack Problem and Solution284
    11.3.9 Example2 Infinite Plane with an Elliptic Hole Subjected to a Tension at Infinity 286
    11.3.10 Example3 Infinite Plane with an Elliptic Hole Subjected to a Distributed Pressure at a Part of Surface of the Hole 286
    11.4 Complex Analysis for Sextuple Harmonic Equation and Applications to Three-Dimensional Icosahedral Quasicrystals 287
    11.4.1 The Complex Representation of Stresses and Displacements288
    11.4.2 The Complex Representation of Boundary Conditions290
    11.4.3 Structure of Complex Potentials291
    11.4.4 Case of InfiniteRegions294
    11.4.5 Conformal Mapping and Function Equations at f-Plane295
    11.4.6 Example: Elliptic Notch Problem and Solution297
    11.5 Complex Analysis of Generalized Quadruple Harmonic Equation 300
    11.6 Conclusion and Discussion 301
    11.7 Appendix of Chapter 11: Basic Formulas of Complex Analysis302
    11.7.1 Complex Functions, Analytic Functions 302
    11.7.2 Cauchy’s formula 303
    11.7.3 Poles 306
    11.7.4 Residual Theorem 306
    11.7.5 Analytic Extension309
    11.7.6 Conformal Mapping 309
    References 311
    12 Variational Principle of Elasticity of Quasicrystals, Numerical Analysis and Applications 313
    12.1 Review of Basic Relations of Elasticity of Icosahedral Quasicrystals 314
    12.2 General Variational Principle for Static Elasticity of Quasicrystals 315
    12.3 Finite Element Method for Elasticity of Icosahedral Quasicrystals 319
    12.4 Numerical Results 323
    12.5 Conclusion332
    References 332
    13 Some Mathematical Principles on Solutions of Elasticity of Quasicrystals333
    13.1 Uniqueness of Solution of Elasticity of Quasicrystals 333
    13.2 Generalized Lax–Milgram Theorem 335
    13.3 Matrix Expression of Elasticity of Three-Dimensional Quasicrystals 339
    13.4 The Weak Solution of Boundary Value Problem of Elasticity of Quasicrystals 343
    13.5 The Uniqueness of Weak Solution 344
    13.6 Conclusion and Discussion 347
    References 347
    14 Nonlinear Behaviour of Quasicrystals349
    14.1 Macroscopic Behaviour of Plastic Deformation of Quasicrystals 350
    14.2 Possible Scheme of Plastic Constitutive Equations 352
    14.3 Nonlinear Elasticity and Its Formulation 355
    14.4 Nonlinear Solutions Based on Some Simple Models356
    14.4.1 Generalized Dugdale–Barenblatt Model for Anti-plane Elasticity for Some Quasicrystals 356
    14.4.2 Generalized Dugdale–Barenblatt Model for Plane Elasticity of Two-Dimensional Point Groups 5 m, 10 mm and 5;5, 10;10 Quasicrystals 359
    14.4.3 Generalized Dugdale–Barenblatt Model for Plane Elasticity of Three-Dimensional Icosahedral Quasicrystals 361
    14.5 Nonlinear Analysis Based on the Generalized Eshelby Theory 362
    14.5.1 Generalized Eshelby Energy-Momentum Tensor and Generalized Eshelby Integral 362
    14.5.2 Relation Between Crack Tip Opening Displacement and the Generalized Eshelby Integral 364
    14.5.3 Some Further Interpretation on Application of E-Integral to the Nonlinear Fracture Analysis of Quasicrystals 365
    14.6 Nonlinear Analysis Based on the Dislocation Model366
    14.6.1 Screw Dislocation Pile-Up for Hexagonal or Icosahedral or Cubic Quasicrystals 366
    14.6.2 Edge Dislocation Pile-Up for Pentagonal or Decagonal Two-Dimensional Quasicrystals 369
    14.6.3 Edge Dislocation Pile-Up for Three-Dimensional Icosahedral Quasicrystals 370
    14.7 Conclusion and Discussion 371
    14.8 Appendix of Chapter 14: Some Mathematical Details 371
    14.8.1 Proof on Path-Independency of E-Integral 371
    14.8.2 Proof on the Equivalency of E-Integral to Energy Release Rate Under Linear Elastic Case for Quasicrystals373
    14.8.3 On the Evaluation of the Critic Value ofE-Integral376
    References 377
    15 Fracture Theory of Solid Quasicrystals379
    15.1 Linear Fracture Theory of Quasicrystals 379
    15.2 Crack Extension Force Expressions of Standard Quasicrystal Samples and Related Testing Strategy for Determining Critical Value GIC383
    15.2.1 Characterization of GI and GIC of Three-Point Bending Quasicrystal Samples 383
    15.2.2 Characterization of GI and GIC of Compact Tension Quasicrystal Sample 384
    15.3 Nonlinear Fracture Mechanics 385
    15.4 Dynamic Fracture387
    15.5 Measurement of Fracture Toughness and Relevant Mechanical Parameters of Quasicrystalline Material 388
    15.5.1 FractureToughness389
    15.5.2 Tension Strength389
    References 391
    16 Hydrodynamics of Solid Quasicrystals393
    16.1 ViscosityofSolid393
    16.2 Generalized Hydrodynamics of Solid Quasicrystals 394
    16.3 Simplification of Plane Field Equations in Two-Dimensional 5-and 10-Fold Symmetrical Solid Quasicrystals 396
    16.4 Numerical Solution 396
    16.5 Conclusion and Discussion 405
    References 405
    17 Remarkable Conclusion 407
    References 408
    Major Appendix: On Some Mathematical Additional Materials411
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