A receding contact problem between a graded piezoelectric layer and a piezoelectric substrate

The receding contact problem between a graded piezoelectric layer and a homogeneous piezoelectric substrate is considered in this paper. It is assumed that the gradation of the elastic piezoelectric graded layer is of exponential type through its thickness. Using standard Fourier transform, the contact problem is converted to a system of two singular integral equations in which the contact pressures and the electric charge displacement in addition to the contact dimensions are the unknowns. The integral equations are then solved numerically using Gauss-Jacobi integration formula. The primary objective of this paper is to investigate the effect of material gradation on the contact pressure, electric charge distribution and on the length of the receding contact. The main findings of the paper are that the inhomogeneity parameter has a strong effect on the contact pressure and the electric charge distribution at the receding contact interface. It is concluded that a softer FGPM in +z direction results in lower contact pressure and electric displacement.