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 Asc&bsp;of Group 11
References 12
2 Framework of Crystal Elasticity13
2.1 Review on Some Basic Concepts13
2.1.1 Vectr3
2.1.2 Coordinate Frame 14
2.1.3 Coordinate Transformation 14
2.1.4 Tensr6
2.1.5 Algebraic Oraio of Tensor 16
2.2 Basic Assutin of Theory of Elasticity17
. 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 sicrystal and Its Properties27
3.1 Discovery of sicrystal 27
3.2 Structure and Symmetry of sicrystals 29
3.3 A Brief Introduction on Physical Properties of sicrystals 31
3.4 One-， Two-and Three-Dimensional sicrystals 32
3.5 Two-Dimensional sicrystals and Planar sicrystals 32
References 33
4 The Physical Basis of Elasticity of Solid sicrystals37
4.1 Physical Basis of Elasticity of sicrystals 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 sicrystals 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 sicrystals Based on the Landau Density WaveTheory48
References 53
5 Elasticity Theory of One-Dimensional sicrystals and Simpiction 55
5.1 Elasticity of Hexagonal sicrystals55
5.2 Decoition of the Elasticity into a Superposition of Plane and Anti-plane Elasticity58
5.3 Elasticity of Monoclinic sicrystals61
5.4 Elasticity of Orthorhombic sicrystals64
5.5 Tetragonal sicrystals 65
5.6 The Space Elasticity of Hexagonal sicrystals 66
5.7 Other Results of Elasticity of One-Dimensional sicrystals 68
References 68
6 Elasticity of Two-Dimensional sicrystals and Simpiction 71
6.1 Basic Equations of Plane Elasticity of Two-Dimensional sicrystals：Point Groups 5m and 10mm in Five-and TenfoldSymmetries75
6.2 Simpiction of the Basic Equation Set：Displacement Potential Function Methd8
6.3 Simpiction of Basic Equations Set：Stress Potential Function Method 83
6.4 Plane Elasticity of Point Group 5， 5 and 10， 10 Pentagonal and Decagonal sicrystals85
6.5 Plane Elasticity of Point Group 12mm of Dodecagonal sicrystals 89
6.6 Plane Elasticity of Point Group8mm of Octagonal sicrystals， Displacement Potential93
6.7 Stress Potential of Point Group5；5 Pentagonal and Point Group 10；10 Decagonal sicrystals98
6.8 Stress Potential ofPointGroup8mm Octagonal sicrystals 100
6.9 Engineering and Mathematical Elasticity of sicrystals 103 References 106
7 Application I-Some Dislocation and Interface Problems and Solutions in One-and Two-Dimensional sicrystals109
7.1 Dislocations in One-Dimensional Hexagonal sicrystals 110
7.2 Dislocations in sicrystals with Point Groups 5m and 10 mm Symmetries112
7.3 Dislocations in sicrystals with Point Groups 5；5 Fivefold and 10，10 Tenfold Symmetries 119
7.4 Dislocations in sicrystals with Eightfold Symmetry124
7.4.1 Fourier Transform Method 125
7.4.2 Complex Variable Function Method 127
7.5 Dislocations in Dodecagonal sicrystals 128
7.6 Interface Between sicrystal 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 sicrystals137
8.1 Crack Problem and Solution of One-Dimensional sicrystals 138
8.1.1 GriffithCrack138
8.1.2 Brittle Fracture Theory 143
8.2 Crack Problem in Finite-Sized One-Dimensional sicrystals 145
8.2.1 Cracked sicrystal Strip with Finite Height 145
8.2.2 Finite Strip with Two Cracks 149
8.3 Griffith Crack Problems in Point Groups5m and 10mm sicrystal Based on Displacement Potential Function Methd50
8.4 Stress Potential Function Formulation and Complex Analysis Method for Solving Notch/Crack Problem of sicrystals 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 sicrystals 163
8.6 Approximate Analytic Solutions of Notch/Crack of Two-Dimen
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