Wrinkling behavior of thin films encapsulated between two identically pre-stretched soft substrates

Engineered surface patterns, such as wrinkling and serpentine geometries, enable stretchable electrodes to achieve both high stretchability and compact packaging. Traditionally, wrinkled thin films are fabricated by depositing a film onto a pre-stretched substrate and subsequently releasing the tension. However, in bi-layer systems where a thin stiff film is placed on a soft thick substrate, specific conditions are required for localized wrinkling without global bending: (1) a low pre-stretching ratio and (2) a substrate significantly thicker than the film. In this study, we investigate the wrinkling mechanics of a tri-layer design, where the wrinkled film is encapsulated between two equally pre-stretched substrates. This configuration facilitates uniform localized wrinkling, even with thinner substrates and higher pre-stretch ratios. Our results demonstrate that in the tri-layer system, the substrate-to-film thickness ratio needed for localized wrinkling is below 10, compared to the bi-layer system, which requires a ratio exceeding 100. This approach reduces overall thickness, enhancing packaging density. Numerical simulations were used to analyze the evolution of amplitude and wavelength based on thickness and modulus ratios, with experimental validation supporting the theoretical findings.