Fundamental solutions for penny-shaped and half-plane cracks in one-dimensional hexagonal quasicrystals: Shear mode

The present article is to investigate the penny-shaped and half-plane crack problems in an infinite space of one-dimensional hexagonal quasicrystals. The cracks are subjected to a pair of anti-symmetrical point shear loads exerted on the crack surfaces. By means of the potential theory method, the governing integral equation is developed and the complete fundamental solutions of the phonon and phason fields are obtained. Moreover, the important quantities on the crack plane, including the crack slip displacement and the stress intensity factor, are derived in terms of elementary functions. The fundamental solutions presented in the article are important to boundary element analysis and may serve as benchmarks for numerical research. (C) 2022 Elsevier Inc. All rights reserved.

Automated summary

This article investigates the penny-shaped and half-plane crack problems in an infinite space of one-dimensional hexagonal quasicrystals. The complete fundamental solutions of the phonon and phason fields are obtained, and important quantities on the crack plane are derived. These fundamental solutions are significant for boundary element analysis and numerical research.