Delamination of a thin sheet from a soft adhesive Winkler substrate

Abstract

A uniaxially compressed thin elastic sheet that is resting on a soft adhesive substrate can form a blister, which is a small delaminated region, if the adhesion energy is sufficiently weak. To analyze the equilibrium behavior of this system, we model the substrate as a Winkler or fluid foundation. We develop a complete set of equations for the profile of the sheet at different applied pressures. We show that at the edge of delamination, the height of the sheet is equal to sqrt[2]ℓ_{c}, where ℓ_{c} is the capillary length. We then derive an approximate solution to these equations and utilize them for two applications. First, we determine the phase diagram of the system by analyzing possible transitions from the flat and wrinkled to delaminated states of the sheet. Second, we show that our solution for a blister on a soft foundation converges to the known solution for a blister on a rigid substrate that assumed a discontinuous bending moment at the blister edges. This continuous convergence into a discontinuous state marks the formation of a boundary layer around the point of delamination. The width of this layer relative to the extent length of the blister, ℓ, scales as w/ℓ∼(ℓ_{c}/ℓ_{ec})^{1/2}, where ℓ_{ec} is the elastocapillary length scale. Notably, our findings can provide guidelines for utilizing compression to remove thin biofilms from surfaces and thereby prevent the fouling of the system.

Rucks and folds: delamination from a flat rigid substrate under uniaxial compression

“…such that the delamination threshold is now smaller than the threshold in the wet adhesion case (7).…”

“…Beyond its broad importance for numerous branches of materials industry, such as coating and stretchable electronics, the delamination of thin sheets from an adhesive substrate provides an invaluable glance into the nontrivial mechanics of slender bodies [1][2][3][4]. This viewpoint motivated several groups to consider a thin sheet under uniaxial compression as an inextensible body, and employ Euler's elastica to study its delamination from various types of adhesive substrates-a compliant solid [5], liquid bath [6,7], or a flat rigid substrate [8]. The inherent simplicity of uniaxial compression, whereby the stress field in the sheet is a scalar function (often a constant), has also been exploited to study the gravity-limited deflection of a heavy sheet from a non-adhesive floor as a model for deformation patterns in rugs [5,9], and the periodic delamination pattern from an adhesive compliant substrate [5].…”

Harnessing the interface mechanics of hard films and soft substrates for 3D assembly by controlled buckling

“…Goyal et al (46) and Mei et al (47) studied the evolution of periodic wrinkling and localized delamination of thin films on soft substrates. Through combined theoretical and experimental approaches, Vella et al (48,49), Oshri et al (50), and Zhang et al (51) developed simple analytic solutions that can predict the evolution of bucklingdriven delamination. Pan et al (52) and Boijoux et al (53) adopted cohesive models to simulate nonlinear delamination processes.…”

Elastic multi-blisters induced by geometric constraints

“…[18]. However, in our days, the elastica model is still very timely, especially for studying problems of contact [19][20][21] or its combination with other physical effects [22][23][24].…”