Singularities of Three-Dimensional Cubic Piezoelectric Quasicrystal Composite Wedges and Spaces

In this paper, the planar problems of three-dimensional (3D) cubic piezoelectric quasicrystal composite wedges and spaces are investigated. The study focuses on the singular behaviors of interface corner and interface crack of composite wedges and spaces. To research the stress singularities, the stress function is assumed to have the exponential form. Based on the Stroh formalism and Barnett-Lothe matrices, we derive a crucial matrix concerned with material properties and wedge angle and obtain the transcendental equation determining the singular orders by simple multiplication of the crucial matrix. Numerical examples of the singular orders are given for some general cases including single, bi-material, and tri-material wedges and spaces under different boundary conditions. The correctness of numerical results is verified by comparison with the existing results of piezoelectric material. Numerical results show that the phonon field, phason field, electric field, material properties, and boundary conditions have great influences on singularities.