Contact instability of a soft elastic film bonded to a patterned substrate

Abstract

A linear stability analysis is presented for the contact instability of a soft thin elastic film which is rigidly bonded to a physically patterned substrate, and is in adhesive contact with a smooth rigid contactor. Increasing roughness by enhancing the substrate-amplitude produces increasingly smaller instability length-scales. The smallest wavelengths obtainable are 0.3^*h, an order of magnitude smaller than that observed with films on flat substrates (3^*h). Instability length-scales are found to be largely independent of substrate length-scales. For van der Waals interaction, increase in substrate roughness increases the energy penalty and, consequently, requires smaller gap distances (< 1nm for stiff films) to engender instabilities. When an externally controllable long-range electric field is employed instead, instabilities can be initiated at very low critical voltages (˜32 V) even in relatively stiff films, making it a more suitable route to produce miniaturized instability patterns.