Penetration of a spherical conductive punch into a piezoelectric half-space with a functionally graded coating

Contact problem on indentation of an electroelastic piezoelectric half-space by a rigid spherical conductive punch is considered. The half-space consists of a functionally graded layer (coating) with arbitrary variation of electromechanical properties in depth and a homogeneous semi-infinite substrate. Both, coating and substrate materials are assumed to be transversely isotropic. The punch is assumed to be an ideal electric conductor. Normal centrally applied force and electric charge are applied to the punch, leading to electroelastic deformation of the half-space. The problem was described mathematically in terms of the linear theory of electroelasticity and reduced to the solution of a system of integral equations. A generalization of the bilateral asymptotic method was used to construct an approximated solution of that system. Analytical expressions for contact stresses, electric induction and expressions connecting indentation force, electric charge, electric potential and indentation depth are provided. The results obtained are asymptotically exact both for thin and thick coatings and of high accuracy for coating of intermediate thickness. (C) 2019 Elsevier Ltd. All rights reserved.