Crack solutions and weight functions for plane problems in three-dimensional quasicrystals

Junction problem for rigid and semirigid inclusions in elastic bodies

“…It is well known that classical linear crack models are characterized by linear boundary conditions imposed at the crack faces; see, for example [3,25]. Such a linear approach allows the opposite crack faces to penetrate each other which leads to inconsistency from the mechanical viewpoint; see examples with a mutual penetration of crack faces in [24,31].…”

Crack tip plasticity of a half-infinite Dugdale crack embedded in an infinite space of one-dimensional hexagonal quasicrystal

“…For the anti-plane crack problems in 1D hexagonal QCs, some works [31,14,15] have been achieved under the framework of elasticity of QCs, to explore the effect of phason field on the deformations of the cracked materials. For the plane problems of an elliptic hole and a crack in three-dimensional (3D) QCs, Gao et al [12,13] derived the explicit solutions for the phononphason coupled fields are obtained in closed forms, by a complex potential approach and the generalized Stroh formalism. Fan et al [11] made a comprehensive review on the fracture theory of QCs concerning with linear, nonlinear and dynamic crack problems for QCs of various types.…”

Fundamental elastic field in an infinite medium of two-dimensional hexagonal quasicrystal with a planar crack: 3D exact analysis

“…Introducing the Westerggaard's stress functions, Guo et al (2013) developed a semi-inverse method of a Griffith crack in a plane of 1D hexagonal QC. For an elliptical hole and a planar crack embedded in a 3D QC plane subjected to far-field loadings, Gao et al (2014) derived the analytical expressions for both the entire fields and the asymptotic fields near the crack tip, adopting the weight functions and the Stroh formalism. It is noted that a comprehensive review on the crack problem, in the context of planar elasticity of QCs, is far beyond the scope of the present study, and http://dx.doi.org/10.1016/j.ijsolstr.2015.04.013 0020-7683/Ó 2015 Elsevier Ltd. All rights reserved.…”