Snap-through instability of graphene on corrugated substrates

We discuss atomic force microscopy measurements of the interplay between interfacial bonding energy and strain energy in few-layer-graphene (FLG) placed on micro-scale corrugated metallic substrates. For fixed corrugation amplitude and wavelength, the theoretical strain energy of conformed FLG scales with the third power of its thickness. We present evidence of a so-called ``snap-through instability,'' where the behavior of the FLG abruptly changes, as a function of thickness, from fully conformed, to completely detached. The large FLG thickness, and by implication strain energy, at the snap-through point implies that the FLG-substrate bonding is larger than expected for van der Waals forces.