Green’s functions of two-dimensional piezoelectric quasicrystal in half-space and bimaterials

doi:10.1007/s10483-023-2955-9

摘要/Abstract

摘要： In this paper, we obtain Green’s functions of two-dimensional (2D) piezoelectric quasicrystal (PQC) in half-space and bimaterials. Based on the elastic theory of QCs, the Stroh formalism is used to derive the general solutions of displacements and stresses. Then, we obtain the analytical solutions of half-space and bimaterial Green’s functions. Besides, the interfacial Green’s function for bimaterials is also obtained in the analytical form. Before numerical studies, a comparative study is carried out to validate the present solutions. Typical numerical examples are performed to investigate the effects of multi-physics loadings such as the line force, the line dislocation, the line charge, and the phason line force. As a result, the coupling effect among the phonon field, the phason field, and the electric field is prominent, and the butterfly-shaped contours are characteristic in 2D PQCs. In addition, the changes of material parameters cause variations in physical quantities to a certain degree.

关键词: Green's function, two-dimensional (2D) piezoelectric quasicrystal (PQC), Stroh formalism, half-space, bimaterial

Abstract: In this paper, we obtain Green’s functions of two-dimensional (2D) piezoelectric quasicrystal (PQC) in half-space and bimaterials. Based on the elastic theory of QCs, the Stroh formalism is used to derive the general solutions of displacements and stresses. Then, we obtain the analytical solutions of half-space and bimaterial Green’s functions. Besides, the interfacial Green’s function for bimaterials is also obtained in the analytical form. Before numerical studies, a comparative study is carried out to validate the present solutions. Typical numerical examples are performed to investigate the effects of multi-physics loadings such as the line force, the line dislocation, the line charge, and the phason line force. As a result, the coupling effect among the phonon field, the phason field, and the electric field is prominent, and the butterfly-shaped contours are characteristic in 2D PQCs. In addition, the changes of material parameters cause variations in physical quantities to a certain degree.

Key words: Green's function, two-dimensional (2D) piezoelectric quasicrystal (PQC), Stroh formalism, half-space, bimaterial

中图分类号:

74B05

Xiaoyu FU, Xiang MU, Jinming ZHANG, Liangliang ZHANG, Yang GAO. Green’s functions of two-dimensional piezoelectric quasicrystal in half-space and bimaterials[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(2): 237-254.

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