Numerical Analysis on the Wrinkling Instability of a Stiff Film Adhering to an Elastic Substrate with a Graded Coating

Abstract

The wrinkling instability of a stiff film adhering to a pre-strained inhomogeneous bi-layer substrate consisting of a homogeneous substrate and a graded coating is investigated in the present paper. The critical strain, wavelength and amplitude of the film/inhomogeneous substrate system are calculated numerically and analyzed comprehensively. Compared with the numerical result, a theoretical model is introduced to approximately predict the wrinkling responses of the system. The influence of various geometric and material parameters on the wrinkling behavior is mainly focused. The wrinkling responses are found to be highly related to the graded laws and the thickness of the inhomogeneous coating as well as the Poisson’s ratio. What is more, a proper choice of graded properties of a substrate can improve the wrinkling response of a film/substrate system. The present finding should be very meaningful to guide the design of various stretchable and flexible electronics.