Adhesion evaluation for a stratified system in JKR geometry

The JKR test, which consists of investigating the contact between an elasti c lens and a rigid substrate, is a local and precise adhesion test. However , in the classical JKR mechanical analysis, the dimensions of the system mu st be large compared to the size of the contact area; we consider here a ri gid substrate coated with a thin layer of a softer material. We show that t his case cannot be analysed using the JKR theory. We propose a simple mecha nical approach, modeling the layer as an elastic mattress, which accounts f or the experimentally observed phenomena.