Abstract
A model of a thin elastic inclusion embedded in an infinite 1D hexagonal quasicrystal is discussed. The atomic arrangements of the matrix and the inclusion are both periodic along the $$x_{1}$$ -direction and quasiperiodic along the $$x_{2}$$ -direction in the $$ox_{1}x_{2}$$ -coordinate system. Using the hypersingular integral equation method, the inclusion problem is reduced to solving a set of hypersingular integral equations. Based on the exact analytical solution of the singular phonon and phason stresses near the inclusion front, a numerical method of the hypersingular integral equation is proposed using the finite-part integral method. Finally, the numerical solutions for the phonon and phason stress intensity factors of some examples are given.
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