Abstract Using the complex variable function method and the technique of
conformal mapping, the anti-plane shear problem of an elliptic hole
with asymmetric collinear cracks in a one-dimensional hexagonal
quasi-crystal is solved, and the exact analytic solutions of the
stress intensity factors (SIFs) for mode III problem are obtained.
Under the limiting conditions, the present results reduce to the
Griffith crack and many new results obtained as well, such as the
circular hole with asymmetric collinear cracks, the elliptic hole
with a straight crack, the mode T crack, the cross crack and so on.
As far as the phonon field is concerned, these results, which play
an important role in many practical and theoretical applications,
are shown to be in good agreement with the classical results.
Received: 26 November 2007
Revised: 09 January 2008
Published: 09 July 2008