Preface Chapter 1 Crystals 1.1 Periodicity of crystal structure,crystal cell 1.2 Three-dimensional lattice types 1.3 Symmetry and point groups 1.4 Reciprocal lattice 1.5 Appendix of Chapter 1:Some basic concepts References Chapter 2 Framework of the classical theory of elasticity 2.1 Review on some basic concepts 2.2 Basic assumptions of theory of elasticity 2.3 Displacement and deformation 2.4 Stress analysis and equations of motion 2.5 Generalized Hooke's law 2.6 Elastodynamics,wave motion 2.7 Summary References Chapter 3 Quasicrystal and its properties 3.1 Discovery of quasicrystal 3.2 Structure and symmetry of quasicrystals 3.3 A brief introduction on physical properties of quasicrystals 3.4 One-,two- and three-dimensional quasicrystals 3.5 Two-dimensional quasicrystals and planar quasicrystals References Chapter 4 The physical basis of elasticity of quasicrystals 4.1 Physical basis of elasticity of quasicrystals 4.2 Deformation tensors 4.3 Stress tensors and the equations of motion 4.4 Free energy and elastic constants 4.5 Generalized Hooke's law 4.6 Boundary conditions and initial conditions 4.7 A brief introduction on relevant material constants of quasicrystals 4.8 Summary and mathematical solvability of boundary value or initialboundary value proble 4.9 Appendix of Chapter 4:Description on physical basis of elasticity of quasicrystals based on the Landau density wave theory References Chapter 5 Elasticity theory of one-dimensional quasicrystals and simplification 5.1 Elasticity of hexagonal quasicrystals 5.2 Decomposition of the problem into plane and anti-plane problems 5.3 Elasticity of monoclinic quasicrystals 5.4 Elasticity of orthorhombic quasicrystals 5.5 Tetragonal quasicrystals 5.6 The space elasticity of hexagonal quasicrystals 5.7 Other results of elasticity of one-dimensional quasicrystals References Chapter 6 Elasticity of two-dimensional quasicrystals and simplification 6.1 Basic equations of plane elasticity of two-dimensional quasicrystals:point groups 5m and 10mm in five- and ten-fold symmetries 6.2 Simplification of the basic equation set: displacement potential function method 6.3 Simplification of the basic equations set: stress potential function method 6.4 Plane elasticity of point group 5,5 pentagonal and point group 10,10 decagonal quasicrystals 6.5 Plane elasticity of point group 12mm of dodecagonal quasicrystals 6.6 Plane elasticity of point group 8mm of octagonal quasicrystals,displacement potential 6.7 Stress potential of point group 5;5 pentagonal and point group 10,10 decagonal quasicrystals 6.8 Stress potential of point group 8mm octagonal quasicrystals 6.9 Engineering and mathematical elasticity of quasicrystals References Chapter 7 Application I:Some dislocation and interface problems and solutions in one and two-dimensional quasicrystals 7.1 Dislocations in one-dimensional hexagonal quasicrystals 7.2 Dislocations in quasicrystals with point groups 5m and 10mm symmetries 7.3 Dislocations in quasicrystals with point groups 5,5 five-fold and 10,10 ten-fold symmetries 7.4 Dislocations in quasicrystals with eight-fold symmetry 7.5 Dislocations in dodecagonal quasicrystals 7.6 Interface between quasicrystal and crystal 7.7 Conclusion and discussion References Chapter 8 Application II:Solutions of notch and crack problems of one-and two-dimensional quasicrystals 8.1 Crack problem and solution of one-dimensional quasicrystals 8.2 Crack problem in finite-sized one-dimensional quasicrystals 8.3 Griffth crack problems in point groups 5m and 10mm quasicrystals based on displacement potential function method 8.4 Stress potential function formulation and complex variable function method for solving notch and crack problems of quasicrystals of point groups 5,5 and 10,10 8.5 Solutions of crack/notch problems of two-dimensional octagonal quasicrystals 8.6 Other solutions of crack problems in one-and two-dimensional quasicrystals 8.7 Appendix of Chapter 8: Derivation of solution of Section 8.1 References Chapter 9 Theory of elasticity of three-dimensional quasicrystals and its applications 9.1 Basic equations of elasticity of icosahedral quasicrystals 9.2 Anti-plane elasticity of icosahedral quasicrystals and problem of interface between quasicrystal and crystal 9.3 Phonon-phason decoupled plane elasticity of icosahedral quasicrystals 9.4 Phonon-phason coupled plane elasticity of icosahedral quasicrystals-displacement potential formulation 9.5 Phonon-phason coupled plane elasticity of icosahedral quasicrystals-stress potential formulation 9.6 A straight dislocation in an icosahedral quasicrystal 9.7 An elliptic notch/Griffth crack in an icosahedral quasicrystal 9.8 Elasticity of cubic quasicrystals-the anti-plane and axisymmetric deformation References Chapter 10 Dynamics of elasticity and defects of quasicrystals 10.1 Elastodynamics of quasicrystals followed the Bak's argument 10.2 Elastodynamics of anti-plane elasticity for some quasicrystals 10.3 Moving screw dislocation in anti-plane elasticity 10.4 Mode III moving Griffth crack in anti-plane elasticity 10.5 Elasto-/hydro-dynamics of quasicrystals and approximate analytic solution for moving screw dislocation in anti-plane elasticity 10.6 Elasto-/hydro-dynamics and solutions of two-dimensional decagonal quasicrystals 10.7 Elasto-/hydro-dynamics and applications to fracture dynamics of icosahedral quasicrystals 10.8 Appendix of Chapter 10: The detail of finite difference scheme References Chapter 11 Complex variable function method for elasticity of quasicrystals 11.1 Harmonic and quasi-biharmonic equations in anti-plane elasticity of onedimensional quasicrystals 11.2 Biharmonic equations in plane elasticity of point group 12mm two-dimensional quasicrystals 11.3 The complex variable function method of quadruple harmonic equations and applications in two-dimensional quasicrystals 11.4 Complex variable function method for sextuple harmonic equation and applications to icosahedral quasicrystals 11.5 Complex analysis and solution of quadruple quasiharmonic equation 11.6 Conclusion and discussion References Chapter 12 Variational principle of elasticity of quasicrystals,numerical analysis and applications 12.1 Basic relations of plane elasticity of two-dimensional quasicrystals 12.2 Generalized variational principle for static elasticity of quasicrystals 12.3 Finite element method 12.4 Numerical examples References Chapter 13 Some mathematical principles on solutions of elasticity of quasicrystals 13.1 Uniqueness of solution of elasticity of quasicrystals 13.2 Generalized Lax-Milgram theorem 13.3 Matrix expression of elasticity of three-dimensional quasicrystals 13.4 The weak solution of boundary value problem of elasticity of quasicrystals 13.5 The uniqueness of weak solution 13.6 Conclusion and discussion References Chapter 14 Nonlinear behaviour of quasicrystals 14.1 Macroscopic behaviour of plastic deformation of quasicrystals 14.2 Possible scheme of plastic constitutive equations 14.3 Nonlinear elasticity and its formulation 14.4 Nonlinear solutions based on simple models 14.5 Nonlinear analysis based on the generalized Eshelby theory 14.6 Nonlinear analysis based on the dislocation model 14.7 Conclusion and discussion 14.8 Appendix of Chapter 14: Some mathematical details References Chapter 15 Fracture theory of quasicrystals 15.1 Linear fracture theory of quasicrystals 15.2 Measurement of G_IC 15.3 Nonlinear fracture mechanics 15.4 Dynamic fracture 15.5 Measurement of fracture toughness and relevant mechanical parameters of quasicrystalline material References Chapter 16 Remarkable conclusion References Major Appendix: On some mathematical materials Appendix I Outline of complex variable functions and some additional calculations A.I.1 Complex functions,analytic functions A.I.2 Cauchy's formula A.I.3 Poles A.I.4 Residue theorem A.I.5 Analytic extension A.I.6 Conformal mapping A.I.7 Additional derivation of solution(8.2-19) A.I.8 Additional derivation of solution(11.3-53) A.I.9 Detail of complex analysis of generalized cohesive force model for plane elasticity of two-dimensional point groups 5m,10mm and 10,10quasicrystals A.I.10 On the calculation of integral(9.2-14) Appendix II Dual integral equations and some additional calculations A.II.1 Dual integral equations A.II.2 Additional derivation on the solution of dual integral equations(8.3-8) A.II.3 Additional derivation on the solution of dual integral equations(9.8-8) References Index
京公网安备 11010102004214号