Adhesion of elastic membranes. Part I: a generalized Tabor parameter

For elastic slabs, adhesive behaviour is often described by continuum theories such as Johnson–Kendall–Roberts (JKR) for compliant systems and by atomistic force-based models such as Derjaguin–Muller–Toporov (DMT) for rigid systems, with the transition between them typically characterized by the Tabor parameter. In contrast, the adhesion mechanics of thin elastic membranes remain less understood. Particularly, although recent studies have applied the JKR framework to membranes, the corresponding transition towards the rigid limit has not been fully established. A central difficulty lies in the fact that the effective rigidity of a membrane is influenced not only by its intrinsic Young’s modulus but also by in-plane residual tension and out-of-plane loading such as pressure. Here, we address this issue by introducing a membrane-specific Tabor parameter that incorporates all of these factors. This parameter is validated through numerical calculations and previous experimental measurements, providing a consistent framework to classify membrane adhesion across diverse systems, from biological membranes to microelectromechanical devices.