Exact analytic solutions for an elliptic hole with asymmetric collinear cracks in a one-dimensional hexagonal quasi-crystal

Using the complex variable function method and the technique ofconformal mapping, the anti-plane shear problem of an elliptic holewith asymmetric collinear cracks in a one-dimensional hexagonalquasi-crystal is solved, and the exact analytic solutions of thestress intensity factors (SIFs) for mode III problem are obtained.Under the limiting conditions, the present results reduce to theGriffith crack and many new results obtained as well, such as thecircular hole with asymmetric collinear cracks, the elliptic holewith a straight crack, the mode T crack, the cross crack and so on.As far as the phonon field is concerned, these results, which playan important role in many practical and theoretical applications,are shown to be in good agreement with the classical results.