Mechanical response of wrinkled structures

Wrinkling instability of compressed stiff thin films bound to soft substrates has been studied for many years and the formation and evolution of wrinkles is well understood. Recently, the wrinkling instability has been exploited to create structures with tunable drag, wetting and adhesion. While these studies successfully demonstrated the proofs of concepts, the quantitative understanding is still lacking, because we don’t know how wrinkled surfaces deform in response to interactions with environment. To address this issue, we systematically study how wrinkled structures respond to infinitesimal surface forces both in the vertical and horizontal directions. We find that the linear response diverges near the onset of wrinkling instability and then decays away from this critical threshold. The mechanical response near the critical threshold is dominated by the characteristic mode of wrinkles. In analogy with the critical phenomena in ferromagnets, we can introduce the critical exponents for the response of the characteristic mode of wrinkles, which are consistent with the Landau theory. Our theory can be further used to study the response of wrinkled structures to more complicated distributions of external forces and can thus provide insights for the above-mentioned applications.