Analysis of Sinusoidal Interfacial Wrinkling of an Anisotropic Film Sandwiched Between Two Compliant Layers

Abstract

When a stiff film is bonded to a compliant layer and meanwhile encapsulated by another compliant layer on top, the film may form wrinkles under applied compressive stress. Inspired by the recent development of foldable circuit sealed in an encapsulating layer to improve bendability, unlike the wide study of surface wrinkling in a bilayer system, this paper presents a study of possible sinusoidal interfacial wrinkling in such sandwich system. The film is assumed to be anisotropic with arbitrary orientation of elastic axis while both layers are isotropic. A linear perturbation analysis is performed to predict critical membrane stress, wave number and equilibrium amplitude for the onset of interfacial wrinkles. The effect of parameters such as elastic axis orientation of the film and moduli, thicknesses, and Poisson's ratios of the layers on the wrinkling is evaluated in detail. The results show that compared to two compliant layers, the stiffer and thinner the film is, the smaller the values of both the critical stress and wave number for wrinkling will be. Especially, we illustrate three limiting cases: two layers both reach thicklayer limit, two layers both reach thinlayer limit and one layer reaches thicklayer limit while the other layer reaches thinlayer limit. Analytical solutions are obtained for first two cases and numerical solutions are plotted for the third case. It is found that as long as the thinlayer is near incompressible, the interfacial wrinkles can be suppressed. In addition, the equilibrium wave modes for the three limiting cases are also given. The resulting solutions for the sandwich system can be reduced to the classic solutions for a bilayer system.