The mechanics of the formation and propagation of ridges on compressed stiff film/compliant substrate systems is studied theoretically and experimentally. Ridges form on bilayer systems where the elastomeric substrate is subject to a significant pre-stretch prior to attachment of the film. When the bilayer is then subject to increasing overall compressive strain, sinusoidal wrinkles first form and subsequently become unstable giving way to localized ridges with relatively large amplitudes. Two-dimensional plane strain simulations for neo-Hookean film/substrate systems reveal the transition from wrinkles to ridges under increasing compression and the reverse transition from ridges to wrinkles when the overall compression is subsequently reduced. For a significant range of pre-stretch, the two transition strains differ, and a significant hysteresis response is observed in a complete cycle of loading and unloading. The Maxwell equal-energy condition has been identified associated with co-existence of wrinkles and ridges and with the three-dimensional steady-state propagation condition for the ridges. Experiments conducted with a specially designed film/substrate loading system have been performed that confirm the essential features of ridge formation and the hysteretic behavior in loading/unloading cycles that span the two transitions.
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