Electro-mechanical frictionless contact behavior of a functionally graded piezoelectric layered half-plane under a rigid punch

The frictionless contact problem of a functionally graded piezoelectric layered half-plane in-plane strain state under the action of a rigid flat or cylindrical punch is investigated in this paper. It is assumed that the punch is a perfect electrical conductor with a constant potential. The electro-elastic properties of the functionally graded piezoelectric materials (FGPMs) vary exponentially along the thickness direction. The problem is reduced to a pair of coupled Cauchy singular integral equations by using the Fourier integral transform technique and then is numerically solved to determine the contact pressure, surface electric charge distribution, normal stress and electric displacement fields. For a flat punch, the normal stress intensity factor and electric displacement intensity factor are also given to quantitatively characterize the singularity behavior at the punch ends. Numerical results show that both material property gradient of the FGPM layer and punch geometry have a significant influence on the contact performance of the FGPM layered half-plane.