| This inter-disciplinary work covering the continuum mechanics of novel materials, condensed matter phvsics and partial differential equations discusses the mathematical theory of elasticity of quasicrystals (a new condensed matter) and its applications by setting up new partial differential equations of higher order and their solutions under complicated boundary value and initial value conditions. |
| preface chapter1 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 chapter1: 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 initial- boundary value problem 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 and10mm 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, pentagonal and point group10, decagonal quasicrystals 6.5 plane elasticity of point group12mm of dodecagonal quasicrystals 6.6 plane elasticity of point group 8mm of octagonal quasicrystals, displacement potential 6.7 stress potential of point group 5, pentagonal and point group10, 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 and10mm symmetries 7.3 dislocations in quasicrystals with point groups 5, five-fold and10, 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 griffith crack problems in point groups 5m and10mm 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, and10, 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/griffith 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 griftith crack in anti-plane elasticity 10.5 elast0-/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 chapter10: the detail of finite difference scheme references chapter 11 complex variable function method for elasticity of quasicrystals chapter 12 variational principle of elasticity of quasicrystals chapter 13 some mathematical principles on solutions of elasticity of quasicrystals chapter 14 nonlinear behaviour of quasicrystals chapter 15 fracture theory of quasicrystals chapter 16 remarkable conclusion references major appendix: on some mathematical materials appendix i outline of complex variable functions and some additional calculations appendix ii dual integral equations and some additional calculations. a references index |
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