Surface instabilities include a variety of different modes such as wrinkles, folds, and creases. Such surface instabilities have been used in numerous contexts including changing the wetting, optical, and mechanical properties of different material surfaces for applications in flexible electronics, tissue engineering and biosensors. Interesting surface morphologies can arise due to differences in pre-strain, stiffness, and thickness between the film and substrate; however, the effects of these differences are not well understood. We have developed an experimental system, complemented by finite element simulations, to systematically vary the pre-stretch of the substrate, modulus contrast and thickness contrast to study the transitions of surface instabilities in compressed bi-layers as strain is increased. We find that for systems with large modulus contrast, but varying degrees of substrate pre-stretch, the pre-stretched substrates not only substantially shift the critical strain for post-wrinkling bifurcations, but also qualitatively change the post-wrinkling modes observed.
Understanding that pre-stretching the substrate affects post-wrinkling behaviors, the remaining experiments were conducted with no substrate pre-stretch. Examining the effect of modulus contrast, we report that below a film to substrate elastic modulus ratio of approximately 2, the flat state transitions directly to the creased state. For slightly larger contrasts, wrinkling occurs first but there are two distinct types of post-wrinkling behaviors: (1) wrinkles that transition into creases without period-doubling; and (2) wrinkles to creases preceded by period doubling. Finally, considering the effect of thickness contrast between the film and substrate, we discover that the critical strain for post-wrinkling behavior increases as thickness contrast decreases leading to wrinkles with aspect ratios (defined as amplitude normalized by wavelength) as high as 0.6. Further increases in aspect ratio can be achieved by increasing the modulus contrast, leading first to the formation of localized ridges, and then uniform, high aspect ratio wrinkles. Understanding surface instabilities in such non-ideal bi-layer systems provides important insight into the behavior of natural and synthetic systems with varying substrate pre-strain and modulus and thickness contrast
