Herringbone buckling patterns of compressed thin films on compliant substrates

A thin metal film vapor deposited on thick elastomer substrate develops an equi-biaxial compressive stress state when the system is cooled due to the large thermal expansion mismatch between the elastomer and the metal. At a critical stress, the film undergoes buckling into a family of modes with short wavelengths characteristic of a thin plate on a compliant elastic foundation. As the system is further cooled, a highly ordered herring-bone pattern has been observed to develop. Here it is shown that the herringbone mode constitutes a minimum energy configuration among a limited set of competing modes.