The roles of the viscoelastic layer on controlling evolution of wrinkles in a tri-layer structure with finite thickness

Stretchable electronics are typically of a structure of a stiff film on a compliant substrate and have various applications in engineering. The substrate usually displays time-dependent material behaviour due to its viscoelasticity, which can significantly affect the deformation pattern of the film/substrate structure. In this paper, the evolution of wrinkles on a film on viscoelastic-layerelastic-substrate structure of finite thickness is investigated. In order to derive the equilibrium equation of this tri-layer structure, the normal and shear stresses between the film and the viscoelastic middle layer, and between the middle viscoelastic layer and the elastic substrate are obtained at first. Using Laplace transform, the analytical expression of the deformation of this structure is also obtained. Through numerical simulations, the influence of the viscoelasticity on the evolution of wrinkles in this structure is analysed. The proposed formation can well predict the wrinkling regimes, and the evolutionary paths for the kinetic single-layer and bi-layer wrinkling patterns are provided. In addition, the wrinkling pattern of this tri-layer structure would evolve from the kinetic bi-layer wrinkling to the single-layer wrinkling over time, and the viscoelasticity serves to increase this evolution time. The theoretical results reported in this paper provide a useful theoretical basis for the design of tri-layer type stretchable electronics.