Edge-buckling in stretched thin films under in-plane bending (Q885805)

Using the singular perturbation theory, the author investigates localized wrinkling instabilities in a stretched thin solid film under in-plane bending described by a linearized Donnell-von Kármán bifurcation equation for thin plates. The main goal is to assess the dependence of the critical wrinkling load on the bending stiffness of the film, which is achieved with the help of WKB analysis in conjunction with a careful examination of the determinantal equation. This approach reveals that several features of the wrinkling process can be described accurately by a simplified second-order eigenvalue problem which takes into account bending effects. Additionally, the author shows the presence of a turning point in this reduced model.