The Refined Theory of Axisymmetric Circular Cylinder in One-Dimensional Hexagonal Quasicrystals

A refined theory of axisymmetric cylinder in one-dimensional (1D) hexagonal quasicrystals (QCs) is analyzed. Based on elastic theory with 1D hexagonal QCs, the refined theory of axisymmetric cylinder is derived by using general solution of 1D hexagonal QCs and Lur’e method without ad hoc assumptions. At first, expressions were obtained for all the phonon and phason displacements and stress components in term of the three functions with single independent variable. Based on the boundary conditions, the refined equation for the cylinder is derived directly. And the approximate equation is accurate up to the second-order terms with respect to radius of circular cylinder.

The Interaction between a Dislocation and Circular Inhomogeneity in 1D Hexagonal Quasicrystals

The interaction between a dislocation and circular inhomogeneity in 1D hexagonal quasicrystals is investigated. By using the complex potential method, explicit solutions of complex potentials are obtained. The image force acting on the dislocation are also derived. The results show that the interface attracts the dislocation inside both the matrix and the inhomogeneity under most condition. The attraction increase with the increase of the elastic constant of phason field and the phonon-phason coupling elastic constant.