Growth-induced delamination of an elastic film adhered to a cylinder

We study the delamination induced by the growth of a thin adhesive sheet from a cylindrical, rigid substrate. Neglecting the deformations along the axis of the cylinder, we treat the sheet as a one-dimensional flexible and compressible ring, which adheres to the substrate by capillary adhesion. Using the calculus of variations, we obtain the equilibrium equations and in particular arrive at a transversality condition involving in a non-trivial way the curvature of the substrate, the extensibility of the ring and capillary adhesion. By numerically solving the equilibrium equations, we show that delamination by growth occurs through a discontinuous transition from the fully adherent solution to the partially delaminated one. The shape of the delaminated part can take the form either of a ruck, with a small slope, or a fold, with a large slope. Furthermore, in the weak adhesion regime, complete delamination may occur. We construct the phase diagram between the different solutions in the parameter space. In the quasi-incompressible limit, numerical results are also supported by asymptotic calculations both in the strong and weak adhesion regimes.