The Role of Nonlinear Substrate Elasticity in the Wrinkling of Thin Films

Abstract

The role of substrate nonlinearity on the stability of wrinkling of thin films bonded to compliant substrates is investigated within the initial post-bifurcation range when wrinkling first emerges. A fully nonlinear neo-Hookean bilayer composed of a thin film on a deep substrate is analyzed for a wide range of the film/substrate stiffness ratio, from films that are very stiff compared to the substrate to those only slightly stiffer. Substrate pre-stretch prior to film attachment is shown to have a significant effect on the nonlinearity relevant to wrinkling. Two dimensionless parameters are identified which control the stability and mode shape evolution of the bilayer: one specifying arbitrary uniform substrate pre-stretch and the other a stretch- modified modulus ratio. For systems with film stiffness greater than about five times that of the substrate the wrinkling bifurcation is stable, while for systems with smaller relative film stiffness bifurcation can be unstable, especially if substrate pre-stretch is not tensile.