Theory of adhesive contact on multi-ferroic composite materials: Spherical indenter

Abstract This article is devoted to studying the adhesive contact problem for a spherical indenter on a half-space of the transversely isotropic multi-ferroic composite materials in a systematic manner. In view of magneto-electric properties of the spherical punch, four sets of mixed boundary value problems are taken into account. By virtue of the generalized potential theory method, the physical quantities on the contact surface, corresponding to the Johnson-Kendall-Roberts (JKR) and Maugis-Dugdale (MD) models, are explicitly obtained in the closed form. The expressions of indentation force and penetration depth associated with the Derjaguin-Muller-Toporov (DMT) model, which is the limiting case of the MD model, are derived through a limiting procedure. In particular, the analytical solutions to an external circular crack problem, which is new to literature, are presented as an auxiliary. Energy release rates pertinent to the JKR and MD models are derived and the corresponding equilibrium relations are established according to the Griffith energy balance. The adhesive contact behaviors including the pull-out force especially for three classical models are elaborated. The adjustment and control mechanism by the magnetic and electric means on adhesive contact behaviors is revealed. Numerical calculations are performed to present the obtained analytical results, compare the adhesive models and analyze the effect of magneto-electric properties on adhesive models. The obtained solutions are expected to be crucial to the forthcoming experiments on characterization of properties of multi-ferroic composite media, especially on the micro/nonoscopic scale.