An analytical analysis of receding contact between a compressible elastic thin film and a rigid substrate due to spherical indentation

A simple analytical method based on the Kerr-type model is proposed to study the spherical indentation of a compressible elastic thin film resting on a rigid flat substrate. The interface between the film and the substrate is either frictionless or infinitely rough. Due to indentation, the outer part of the film's lower surface loses contact with the substrate, and the contact zone along the film-substrate interface shrinks to a circular area. The radius of the contact zone is then derived and several asymptotic explicit relations between the indentation force, the indentation depth and the indentation radius are obtained, with the aid of an energy method. The present analytical method is remarkably simpler than existing numerical methods. Reasonable agreement with finite element analysis results shows that the present method has the capability to capture the main contact behaviors of a compressible elastic thin film resting on a rigid substrate.