Sliding frictional and adhesive coupling contact analysis of FGPM layered half-space under an insulating indenter

•The analysis model for the sliding frictional and adhesive coupling contact problem between the FGPM layered half-space and an insulating indenter was proposed by using the Maugis type of adhesion theory and extended Amonton’s law of friction.•The numerical solutions of the integral equations for present adhesive contact problem were given by using new algorithm.•The effect of the gradient index, friction coefficient and adhesion parameters on the surface electro-mechanical response of FGPM layered half-space was carried out systemically.•Based on our model, for given values of parameters R, w, βh and μ, when value of σ0 decreases from infinity to zero there is a continuous transition from the JKR approximation to the DMT approximation. This paper proposes an analysis model for the sliding frictional and adhesive coupling contact problem in the plane strain state between the FGPM layered half-space and an insulating indenter. The electro-mechanical properties of FGPM layer vary exponentially along the thickness direction. By applying the Fourier integral transformation and superposition principle to the governing boundary value problem, the general solution for the sliding frictional and adhesive coupling contact problem can be derived by using the Maugis type of adhesion theory and extended Amonton’s law of friction. A Cauchy singular integral equation is further derived for present problem which is then numerically solved. The primary aim of this paper is to provide insight into the likely behavior for the effect of the gradient index, friction coefficient and adhesion parameters on the surface electro-mechanical response of FGPM layered half-space. For given values of parameters R, w, βh and μ, when value of σ0 decreases from infinity to zero there is a continuous transition from the JKR approximation to the DMT approximation. The research not only helps to further understand the frictional and adhesive damage mechanisms of MEMS devices composed of FGPM, but also provides reference basis for FGPM layer experimental analysis and intelligent structure design.