Frictionless contact analysis of a functionally graded piezoelectric layered half-plane

This paper investigates the frictionless contact problem of a layered half-plane made of functionally graded piezoelectric material (FGPM) in the plane strain state under the action of a rigid punch whose shape may be flat, triangular or cylindrical. It is assumed that the punch is a perfect electrical insulator with zero electric charge distribution. The electroelastic properties of the FGPM layer vary exponentially along the thickness direction. By using the Fourier integral transform technique, the problem is reduced to a Cauchy singular integral equation which is then numerically solved to determine the contact pressure, contact region, maximum indentation depth, normal stress, electrical potential and electric displacement fields. The stress intensity factor is also given to quantitatively characterize the singularity behavior of the contact pressure at the ends of a flat and triangular punch. Numerical results show that both the material property gradient of the FGPM layer and the punch geometry have a significant influence on the contact performance of the FGPM layered half-plane.