Analytical and computational methods for a laterally graded surface loaded by a bonded piezoelectric thin film

Analytical and computational techniques are developed to carry out stress analyses for an advanced material system comprising a piezoelectric thin film bonded to a laterally graded half-plane. The piezoelectric thin film is assumed to be under electric field loading. Governing partial differential equations are derived in terms of an inhomogeneity parameter in accordance with the theory of elasticity. Applying the Fourier transformation technique and enforcing strain compatibility between the thin film and the laterally graded surface, the problem is reduced to a singular integral equation. A scheme based on the expansion-collocation approach is applied to generate the numerical results. The computational technique is developed by utilizing the finite element method and implemented by means of the general purpose software ANSYS. Comparisons of various stress components indicate a high level of accuracy and reliability in the proposed analytical and computational methods. Parametric analyses illustrate the influences of inhomogeneity, geometry, and elasticity parameters upon interfacial shear stress, thin film normal stress, and lateral normal stress at the bounding surface of the laterally graded medium. In the previous work on thin film loading of functionally graded surfaces, the shear modulus is assumed to be a function of the thickness coordinate. The main novelty in the present study is therefore the development of analytical and computational methods for surfaces possessing the shear modulus variation in the lateral direction. The methods presented could particularly be useful in design, analysis, and optimization studies involving piezoelectric thin films bonded to laterally graded surfaces.