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, w_ad, 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, Ι_ec=(B/w_ad)^1/2, where B is the bending modulus, the former is continuous and depends, in addition to Ι_ec, on the capillary length-scale, Ι_c=(w_ad/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.