Inclined mode-I elliptic crack problem in one-dimensional hexagonal quasicrystals

This article investigates an inclined elliptic crack problem in one-dimensional (1D) hexagonal quasicrystals (QCs). The crack lies in a plane perpendicular to the transversely isotropic plane, and its orientation (the major axis of the ellipse) forms an arbitrary angle with the quasi-periodic axis of the QCs. A pair of uniform normal loading is applied symmetrically on the crack surfaces. Using the potential theory method, the governing equation is established and the phonon–phason field is obtained in terms of simple integrals. The fracture parameters including the crack opening displacement (COD) and the stress intensity factor (SIF) are derived. Numerical results validate the solutions and investigate the effects of the phason field, inclination angle and eccentricity on the fracture parameters. A simplified explicit expression for the SIF is developed via symbolic regression. This machine learning-based model offers an efficient and accurate computational alternative to complex theoretical solutions. As a model problem within the framework of QC elasticity theory, the present study offers insights into the fracture behavior of 1D hexagonal QCs and is expected to provide a theoretical reference for structural integrity evaluation and fracture-resistant design of QC materials.