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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. [ABSTRACT FROM AUTHOR]

We examine the plane strain deformations of a bimaterial system consisting of a line edge dislocation interacting with a flat interface between two dissimilar isotropic half-planes in which the additional effects of interface elasticity are incorporated into the model of deformation. The entire system is assumed to be free of any external loading. Despite the fact that it is generally accepted that the separate interface modulus describing interface elasticity is permitted to take negative values, we show that simple closed-form solutions for the dislocation-induced stress field and the image force acting on the dislocation are available only when the interface modulus is assumed to be positive; the corresponding system admits no valid solutions when the interface modulus is negative. We present several numerical examples to illustrate our solutions. Additionally, we show that the influence of interface elasticity on the dislocation-induced interfacial stress field decays with increasing hardness of the adjoining half-plane (free of the dislocation). Moreover, we find that for a given (positive) in-plane interface modulus, the corresponding interface effects on the image force (acting on the dislocation) can reach maximum or minimum values when the Burgers vector of the dislocation is either parallel or perpendicular to the interface. [ABSTRACT FROM AUTHOR]

We study the anti-plane deformations of a linearly elastic bimaterial. One phase of the bimaterial is weakened by a finite crack with surface elasticity perpendicular to the interface and is also subjected to a screw dislocation. The surface elasticity is incorporated by using a version of the continuum-based surface/interface model of Gurtin and Murdoch. By considering a distribution of screw dislocations and line forces on the crack, the interaction problem is reduced to two decoupled first-order Cauchy singular integro-differential equations, which can be numerically solved by means of the Chebyshev polynomials and the collocation method. The associated problem of a mode III Zener-Stroh crack perpendicular to a bimaterial interface is also solved. [ABSTRACT FROM AUTHOR]

A representation theorem is obtained for an arbitrarily loaded elastic bimaterial solid consisting of an infinite plane containing a circular inhomogeneity. The elastic image method is used for the analysis. The theorem expresses the Airy stress functions that generate the elastic fields for the composite solid explicitly in terms of the Airy stress function for the corresponding homogeneous infinite solid. It shows that if the solution for the homogeneous infinite solid is available, then the solutions for the corresponding bimaterial solid can be deduced by the process of differentiation and integration. The result could provide the important advantage of economy of effort in the determination of the elastic fields for composite planes with circular interfaces. [ABSTRACT FROM AUTHOR]

The elastostatic bending of an arbitrarily loaded bimaterial plate with a circular interface is analysed. It is shown that the deflections in the composite solid are directly related to the deflection in the corresponding homogeneous material by integral and differential operators. It is further shown that, by a simple transformation of elastic constants, the Airy stress function induced in the composite by a stretching singularity can be deduced from the deflection induced by a bending singularity. This result is significant for reduction of mathematical labour and for systematic construction of solutions for more complex structures with circular geometry. [ABSTRACT FROM AUTHOR]