Three-Dimensional Analysis Of Decagonal Symmetrical Two-Dimensional Quasicrystal Composites

Quasicrystals is a solid structure first discovered by D.Shechtman,that is different from crystals and non-crystals.This discovery aroused a strong responses in the crystallography,chemistry,physics,materials science and field of mathematics.The mechanical properties of quasicrystals have received extensive attention from researchers,specially the fracture mechanics of quasicrystals with defects such as cracks,dislocations,inclusions and holes.In this paper,the effective elastic properties of two-dimensional quasicrystals composites are analyzed by combining the anisotropic properties,structural properties and phonon field,phason field coupling of quasicrystals materials.Based on Green’s function method,the elastic problems of two-dimensional decagonal quasicrystals materials with ellipsoid inclusions are analyzed,and analytical expressions of phonon and phason field strain inside the inclusions are obtained.Based on the above results,the analytical expression of the effective elastic constant with elliptical cylindrical inclusions is further given.At the same time,the effects of inclusion shape and volume fraction on the effective elastic properties of quasicrystals composites are discussed.Using Mori-Tanaka theory,equivalent inclusion method and distribution density function,a method for predicting the effective electroelastic constant of two-dimensional piezoelectric quasicrystals composites containing spatially oriented inclusions is proposed.In particular,the analytical expressions of the effective electroelastic constant of piezoelectric quasicrystals composites with four special inclusion orientation are obtained.And the effects of volume fraction,shape and orientation of inclusions on the effective electroelastic properties of piezoelectric quasicrystal composites are discussed.With the help of Mori-Tanaka theory,the effect of imperfect interface on the effective elastic properties of two-dimensional decagonal quasicrystals composites was studied.By replacing the interface phase with a zero-thickness surface in the middle of the interphase in the three-phase model,the general imperfect interface of the quasicrystals composite is degenerated to the spring-type imperfect interface in the two-phase model.Based on the jump relationship of physical quantities in the interface,the analytical expression of the effective elastic constant of the two-dimensional decagonal quasicrystals composite with spring-type imperfect interface is further derived.The effect of inclusion shape and volume fraction on the effective elastic properties of quasicrystals composites was analyzed in detail.