Three-dimensional analysis of a spheroidal inclusion in a two-dimensional quasicrystal body

Abstract

This paper deals with the three-dimensional problem of a spheroidal quasicrystalline inclusion, which is embedded in an infinite matrix consisting of a two-dimensional quasicrystal subject to uniform loadings at infinity. Based on the general solution of quasicrystals in cylindrical coordinates, a series of displacement functions is adopted to obtain the explicit real-form results for the coupled fields both inside the inclusion and matrix, when three different types of loadings are studied: axisymmetric, in-plane shear and out-of-plane shear. Furthermore, the present results are reduced to the limiting cases involving inhomogeneities including rigid inclusions, cavities and penny-shaped cracks.

Keywords:

• two-dimensional hexagonal quasicrystals
• spheroidal inclusion
• rigid inclusion
• cavity
• penny-shaped crack

Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 11172319), Chinese Universities Scientific Fund (No. 2011JS046), and the Alexander von Humboldt Foundation in Germany.