On the delamination of thin elastic sheet from soft adhesive substrate

Thin elastic sheet that is resting on soft adhesive substrate and uniaxially compressed from the boundaries forms a delamination blister when the adhesion energy, wad, is small enough. In the present study we derive an approximate solution to the problem, yet nonlinear, and compare it to the known solution of a blister on a rigid substrate. While the latter presents discontinuity at the threshold of delamination and depends solely on the elasto-capillary length-scale, Iec=(B/wad)1/2, where B is the bending modulus, the former is continuous and depends, in addition to Iec, on the capillary length-scale, Ic=(wad/K)1/2, where K is the substrate stiffness. Nevertheless, the two solutions converge for large confinement up to a narrow boundary layer that forms around the take-off point. Across this layer the bending moment rapidly decays to zero. In addition, we utilize our solution to derive the details of the flat-to-blister and the wrinkles-to-blister instabilities and to construct the "phase-diagram" of the system.