Folding wrinkles of a thin stiff layer on a soft substrate

Abstract

We present the mechanics of folding surface-layer wrinkles on a soft substrate, i.e. inter-touching of neighbouring wrinkle surfaces without forming a cusp. Upon laterally compressing a stiff layer attached on a finite-elastic substrate, certain material nonlinearities trigger a number of bifurcation processes to form multi-mode wrinkle clusters. Some of these clusters eventually develop into folded wrinkles. The first bifurcation of the multi-mode wrinkles is investigated by a perturbation analysis of the surface-layer buckling on a pre-stretched neo-Hookean substrate. The post-buckling equilibrium configurations of the wrinkles are then trailed experimentally and computationally until the wrinkles are folded. The folding process is observed at various stages of wrinkling, by sectioning 20-80nm thick gold films deposited on a polydimethylsiloxane substrate at a stretch ratio of 2.1. Comparison between the experimental observation and the finite-element analysis shows that the Ogden model deformation of the substrate coupled with asymmetric bending of the film predicts the folding process closely. In contrast, if the bending stiffness of the film is symmetric or the substrate follows the neo-Hookean behaviour, then the wrinkles are hardly folded. The wrinkle folding is applicable to construction of long parallel nano/micro-channels and control of exposing functional surface areas.