Elastic cloaking for a periodic distribution of parallel finite cracks

We achieve elastic cloaking for a periodic distribution of an infinite number of parallel finite mode III cracks by means of the complex variable method and the theory of Cauchy singular integral equations. The cloaking bimaterial structure is composed of an undisturbed uniformly stressed left half-plane perfectly bonded via a wavy interface to the right half-plane which contains periodic cracks. The original design of the wavy interface and the positions of the periodic cracks are ultimately reduced to the solution of a Cauchy singular integral equation which can be solved numerically.

The Antiplane Shearing Problem of Circular Holes with 4k Periodic Cracks in One-Dimensional Hexagonal Quasicrystals

Using the method of complex analysis and by constructing conformal mapping, the study investigated the antiplane shearing problem of circular holes with 4k periodic cracks in one-dimensional hexagonal quasicrystals. Wherefrom we simulated the problem of antiplane shearing in circular holes of cross-cracks, symmetrical four-cracks, as well as symmetrical eight-cracks, and provided an analytic solution to the crack tip stress intensity factor (SIF).