Abstract
An analysis for the prediction of the electromechanical field in composite piezoelectric half-planes with attached surface electrode is presented. The composite half-planes are composed of distinct constituents and may include internal defects in various locations. The solution is carried out in a sufficiently large rectangular region, the boundary conditions of which are obtained from the corresponding solution of a homogeneous piezoelectric half-plane. This is followed by the application of the discrete Fourier transform at the domain of which a boundary-value problem is formulated. The solution of this boundary-value problem, followed by the inversion of the Fourier transform, provides, in conjunction with an iterative procedure, the electromechanical field at any point of the rectangular region. Applications are given for a piezoelectric half-plane with defects in the form of a cavity and of short and semi-infinite cracks as well as of a periodically bilayered composite with a crack in one of its layers.
Highlights
Piezoelectric materials which are subjected to an applied electric voltage generate mechanical deformations and vice versa
The present analysis is based on the idea that the application of the jumps (Equation (14)) of the field variables generated in a homogeneous piezoelectric half-plane with a surface electrode at the boundaries of the rectangular region −D ≤ x1 ≤ D, −L ≤ x3 ≤ L, should generate the correct solution after its discretization into several cells (K1, K3), the application of the discrete Fourier transform (Equation (21)), solving the resulting boundary-value problem (Equations (24)–(26)) in the transform domain, followed by its inversion (Equation (28))
The composite half-planes are composed of distinct constituents, and their behavior is determined in conjunction with the closed-form expressions of the corresponding homogenized piezoelectric half-plane in which the electromechanical constants are determined by a micromechanical analysis
Summary
Piezoelectric materials which are subjected to an applied electric voltage generate mechanical deformations and vice versa. In order to utilize the above analytical solutions for analyzing half-plane and layered piezoelectric composites with incorporated electrodes, it would be necessary to homogenize the composite by an appropriate micromechanical model and to employ the predicted effective material constants in the relevant analytical expressions. By following this approach the microstructural and architectural properties of the composite are lost since it is merely considered as a homogeneous piezoelectric material.
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