Abstract:

With the rapidly increasing demand for strongly coupled multifunctional materials in engineering applications such as high-performance sensors, defect problems in piezoelectric quasicrystals (PQCs) have attracted growing attention. This study investigates the mechanical behavior of a two-dimensional (2D) PQC containing an elliptical inclusion subjected to uniform loading at infinity and a concentrated force applied in the matrix. Based on the Stroh formalism, combined with conformal mapping and analytic continuation techniques, the analytical solutions for the in-plane displacements and stresses are derived. Meanwhile, the correctness of the model is verified through a comparison between the degenerated infinite-plane numerical results and classical reference solutions. Numerical examples are further conducted to systematically analyze the influence of the inclusion geometry and the loading position on the multi-field coupling responses. The results show that the elliptical inclusion significantly alters the spatial distributions of the mechanical and electrical fields, producing strong disturbances near the inclusion boundary. In particular, decreasing the ellipse aspect ratio b/a markedly enhances the local coupling and stress concentration, whereas the circular inclusion exhibits the weakest anisotropy, resulting in relatively smooth field distributions and low stress concentration. These findings indicate that properly utilizing geometric defects can serve as an effective means of tuning multi-field coupling behavior, and this strategy should be fully considered in engineering design.

Key words: piezoelectric quasicrystal (PQC), Stroh formalism, elliptical inclusion, analytical solution, multi-field coupling