Dynamic Wrinkling Instability of Elastic Films on Viscoelastic Substrates

Abstract

The dynamic instability of stiff films on compliant substrates has received sustained attention due to the potential applications in flexible functional devices. Film/substrate system-based devices are increasingly utilized under dynamic conditions, including dynamic sensors, tunable optical components, anti-fouling surfaces, etc. To better design the dynamic characteristics of devices based on film/substrate systems, it is essential to establish a comprehensive dynamic model and find out the deterministic and non-deterministic instability domains of nonlinear dynamic wrinkling under time-varying biased loads. In this paper, a multi-level coupling time-varying parameter excitation dynamic model for films bonded on Kelvin viscoelastic substrates is developed. The damping effect on the nonlinear dynamic responses of wrinkled film/substrate systems under step, slope and biased sinusoidal axial time-varying excitations is analyzed. We revealed and analyzed the nonlinear dynamic behavior of film/substrate systems, which are significantly influenced by the excitation frequency and viscous coefficients of substrates. Various response forms, such as excitation-following deterministic responses, chaotic responses, and double-period resonant responses, are observed. We analyzed the parametric excitation induced dynamic bifurcation of the time-varying energy barrier that causes the nonlinear dynamic phenomenon and provided deterministic and non-deterministic dynamic response domains. Based on the theory and results, methods for generating responses of specific types are proposed, offering theoretical guidance for designing dynamic characteristics of devices based on film/substrate systems.