Titlebook: Mathematical Theory of Elasticity of Quasicrystals and Its Applications; Tian-You‘Fan Book 2016Latest edition Science Press and Springer

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,Application II—Solutions of Notch and Crack Problems of One- and Two-Dimensional Quasicrystals,Quasicrystals are potential material to be developed for structural use, and their strength and toughness attract the attention of researchers. Experimental observations [Hu et al. in Adv Phy 17:345–376, 1997 ., Meng et al. in Acta Metal Sinica 30:61–64, 1994 .] have shown that quasicrystals are brittle under low and middle temperature.

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Phonon-Phason Dynamics and Defect Dynamics of Solid Quasicrystals,Elastodynamics or phonon-phason dynamics of quasicrystals is a topic with different points of view. The focus of contradictions between different scholar circles lies in the role of phason variables in the dynamic process.

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Variational Principle of Elasticity of Quasicrystals, Numerical Analysis and Applications,From Chaps. .–., we developed analytic theories and methods.

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Some Mathematical Principles on Solutions of Elasticity of Quasicrystals,Starting from Chap. ., we studied several mathematical models of the elasticity of quasicrystals and gave different kinds of solutions.

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Fracture Theory of Solid Quasicrystals,Solid quasicrystals are brittle, and the study on fracture behaviour of the material is significant. In the previous chapters, many of crack problems are investigated, and the exact analytic, approximate and numerical solutions are constructed; this provides a basis for discussing the fracture theory.