Vol. 1, No. 1, 2013

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Dislocations, imperfect interfaces and interface cracks in anisotropic elasticity for quasicrystals

Xu Wang and Peter Schiavone

Vol. 1 (2013), No. 1, 1–17

We derive the detailed structures of the 6 × 6 matrices Ni and Ni(1) (i = 1,2,3) in the Stroh formalism of anisotropic elasticity for quasicrystals. All six matrices are expressed explicitly in terms of the sixty-six reduced elastic compliances. The Green’s functions for bi-quasicrystals are also obtained. Next, we derive compliant and stiff interface models in anisotropic quasicrystalline bimaterials. It is observed that the phonon normal traction is always continuous across the stiff interface. Finally we present the asymptotic fields associated with a traction-free, semi-infinite interface crack in anisotropic quasicrystalline bimaterials and solve the collinear interface crack problem. The interface crack-tip field consists of three two-dimensional oscillatory singularities which are evaluated via the introduction of three complex stress intensity factors.

quasicrystal, anisotropic elasticity, Stroh formalism, dislocation, interface crack
Mathematical Subject Classification 2010
Primary: 74B05, 74E10
Secondary: 74E15
Received: 23 February 2012
Accepted: 5 April 2012
Published: 6 February 2013

Communicated by David Steigmann
Xu Wang
School of Mechanical and Power Engineering
East China University of Science and Technology
130 Meilong Road
Shanghai 200237
Peter Schiavone
Department of Mechanical Engineering
University of Alberta
4-9 Mechanical Engineering Building
Edmonton, AB  T6G 2G8