Buckling of a stiff thin film on a pre-strained bi-layer substrate

Controlled buckling can impart stretchable mechanics to brittle materials when integrated as thin films on soft, elastomeric substrates. Typical elastomers are permeable to fluids, however, and therefor unable to provide robust barriers to entry of water, for instance, into devices built with the supported thin films. In addition, the mechanical strength of a system dominated by a soft substrate is often unsatisfactory for realistic applications. We show that introduction of a bi-layer substrate yields a robust, high strength system that maintains stretchable characteristics, with a soft layer on top of a relatively stiff layer in the substrate. As a mechanical protection, a soft encapsulation layer can be used on top of the device and the stretchability of the encapsulated system is smaller than that of the system without encapsulation. A simple, analytic model, validated by numerical analysis and FEA, is established for stiff thin films on a bi-layer substrate, and is useful to the design of stretchable systems.