Transition between partially and fully delaminated configurations of glued thin films

The insurgence of delamination phenomena of glued slender devices represents a diffuse drawback in numerous technological applications and it is diffusely observed in several biomechanical systems. Starting from the classical Euler elastica, we study the delamination of an inextensible elastic rod, with an end–end confinement, adhered to a rigid flat substrate. This system represents also a prototypical scheme mimicking decohesion induced by differential growth. Using energetic considerations, we draw a phase diagram between two classes of solutions: partially adhered and fully detached equilibrium states. We highlight a discontinuous transition between these two configurations, triggered by the confinement ɛ and regulated by the ratio between the elastocapillary length ℓec and the length of the rod L. Eventually, we provide the approximate formula ɛcr≈L2/(27π2ℓec2), in very good agreement with the numerical results.