The role of substrate pre-stretch in post-wrinkling bifurcations

Abstract

When a stiff film on a soft substrate is compressed, the surface of the film forms wrinkles, with tunable wavelengths and amplitudes that enable a variety of applications. As the compressive strain increases, the film undergoes post-wrinkling bifurcations, leading to period doubling and eventually to formation of localized folds or ridges. Here we study the post-wrinkling bifurcations in films on pre-stretched substrates. Through a combination of experiments and simulations, we demonstrate that pre-stretched substrates not only show substantial shifts in the critical strain for the onset of post-wrinkling bifurcations, but also exhibit qualitatively different post-wrinkled states. In particular, we report on the stabilization of wrinkles in films on pre-tensioned substrates and the emergence of 'chaotic' morphologies in films on pre-compressed substrates.

From period-doubling to folding in stiff film/soft substrate system: The role of substrate nonlinearity

“…(16) indicates that ε PD is a linear function of the pre-stretch; moreover, the variation of the modulus ratio makes no difference to the proportion, which further corroborates that the effect of the modulus ratio can be neglected. These trends are in accordance with the experiment and simulation carried by Auguste et al [36]. If the substrate is not pre-stretched (λ 0 1 ¼ 1), it can be seen from Eq.…”

“…Given that the maximum strain in this study is as large as $ 0.3, both the film and the substrate are modeled as a hyperelastic solid. The incompressible neo-Hookean constitutive model provides a good description of the hyperelastic materials within the range of strain considered here [25,36]. The hybrid plane strain quadrilateral element (CPE8RH) is adopted and the meshes near the film/substrate interface are refined.…”

Post-wrinkle bifurcations in elastic bilayers with modest contrast in modulus

“…Such elastomeric materials with strains under 0.5 are commonly described by the neo-Hookean model, which has led to good agreement with experiments in previous work [37,39,41,46], thus we model both the film and substrate as incompressible neo-Hookean materials, with perfect bonding between the layers. We set the total thickness of the bilayer to be 50 times the film thickness so that the substrate is effectively infinite.…”

“…However, their simulations could not continue past the onset of creases. In addition, both studies reported by Wang, et al [28,41], and Tallinen, et al [42], involve differential pre-stretch of the substrate compared to the film, which is known to have important effects on post-wrinkling behavior [37,44,45].…”

“…If the substrate is not highly pre-stretched, period doubling-wherein the amplitude of every other wrinkle peak grows while its neighbors shrink-is the next mode to appear, [33][34][35][36][37] followed by period quadrupling and eventually folding.…”