Understanding the role of interfacial mechanics on the wrinkling behavior of compressible bilayer structures under large plane deformations

Abstract

Layered soft structures under loading may buckle in order to release energy. One commonly studied phenomenon is the wrinkling behavior of a bilayer system consisting of a stiff film on top of a compliant substrate, which has been observed ubiquitously in nature and has found several applications. While the wrinkling behavior of the incompressible bilayer system has been explored thoroughly, the large deformation behavior of a compressible bilayer system had been virtually unexplored until very recently. On the contrary, it is well established where more than one material is concerned, there always exists an interphase region between different constituents whose mechanical modeling has presented itself as a long-lasting challenge. To address these gaps in the literature, herein we first propose a theoretical, generic, large deformations framework to capture the instabilities of a compressible domain containing an interface. The general interface model is employed such that at its limits, the elastic and the cohesive interface models are recovered. The instability behavior of a compressible bilayer domain undergoing large deformations for a wide range of cohesive stiffness values, stiffness ratios, compressibilities, and film thicknesses is systematically explored. In particular, it is shown that delamination of the film can also be captured via this interface model. In addition, this generic framework is examined for a coated beam and a coated half-space too. The results of the theoretical framework are thoroughly compared to numerical results obtained via finite element method simulations enhanced with eigenvalue analysis, and an excellent agreement between the two sets of results is observed. It is found that varying substrate Poisson’s ratio has a significant effect on the bifurcation behavior for higher cohesive stiffnesses. Remarkably, while in classical bilayers the critical stretch at wrinkling is independent of the film thickness, herein we discover a significant dependence of the critical stretch to the film thickness in the presence of the interface.