Buckling of a stiff thin film on a bi-layer compliant substrate of finite thickness

The buckling of a stiff thin film on a compliant substrate has been widely studied over the past decade due to its wide applications such as stretchable electronics, micro- and nano-metrology, and surface engineering. Instead of a single-layer compliant substrate, a bi-layer compliant substrate is usually encountered in practical applications. In this paper, the buckling of a stiff thin film on a bi-layer compliant substrate of finite thickness is studied theoretically, numerically and experimentally. The theoretical models based on the small-deformation theory and the simple finite-deformation theory accounting for the geometry change by using the energy method are both developed and presented. The good agreement among theoretical predictions, finite element analysis and experimental measurements of the buckling behavior validates the theoretical model. The influences of finite thickness of the bi-layer substrate and substrate modulus ratio on the buckling wavelength and critical buckling strain are systematically investigated. The buckling configurations at various applied strains are also measured to further validate the theoretical model. These results shed light on the influence of finite substrate thickness on buckling of the bi-layer substrate-supported thin films and are helpful to provide design guidelines in practical applications.