Bifurcation analysis of pressure-induced detachment of a rod adhered to a plate

We study the lift of an elastica adhering to a flat rigid surface induced by a pressure difference. Adhesion is modelled by a cohesive force that decreases linearly with separation. Using a nonlinear local analysis, we determine the bifurcation diagram that governs the peeling process under quasi-static conditions. We show that the delamination emerges through a discontinuous transition: a normal form of the bifurcation diagram allows us to draw in a simple way the main physical mechanism, elucidating the local validity of the theory at the transition. We predict that the pressure, as a function of the detachment length, undergoes an initial drop followed by an approximately constant behaviour, while the detachment length at the transition is always finite and is roughly proportional to the elasto-adhesion length. This analysis can be the starting point to understand more complex-related problems that arise in fracture mechanics or in biology, such as testing of adhesives in a flowfield and the arterial dissection.