Delamination of open cylindrical shells from soft and adhesive Winkler's foundation

We investigate the equilibrium configuration of an open cylindrical shell with natural curvature κ and bending modulus B, that is adhered to a soft and adhesive foundation with stiffness K. We derive an analytical model that predicts the critical conditions for delamination. While in the case of a rigid foundation, K→∞, our model recovers the known, two states, solution, at which the shell either remains completely attached to the substrate or completely detaches from it, on a soft foundation our model predicts the emergence of a new branch of solutions. This branch corresponds to partially adhered shells, where the contact zone between the shell and the substrate is finite and scales as (B/K)^1/4. In addition, we find that the criterion for delamination depends on the total length of the shell along the curved direction, L. While relatively short shells, L∽(B/K)^1/4, transform continuously between adhered and delaminated solutions, long shells, L»(B/K)^1/4, transform discontinuously.