Nonlinear dynamic instability of wrinkled film-substrate structure under axial load

To avoid structural failure, the issue of the dynamic reliability of a wrinkled-film-substrate structure has become one of the most key problems for the design of the film-substrate-type flexible electronics. In this paper, an improved theoretical model of such a structure with finite deformation is established, which takes the shear stress at the interface between the film and substrate into account. Post-buckling mode would take place when that structure is subjected to further repeated stretches and compression in the longitudinal (axial) direction. Based on the Lagrangian principle, the governing equation of the post-buckled structure is derived and solved by the symplectic Runge–Kutta method. Through numerical examples, the effects of the soft substrate’s Young’s modulus and axially applied harmonic strain on the dynamic behaviours of the post-buckled structure are analysed. The results of this paper reveal that: the softer the substrate, the larger the dynamic safe region, and the stronger the dynamic reliability of the buckled structure. At the same time, the shorter the applied strain’s period, the larger dynamic maximum peak strain, and the film-substrate-type flexible electronics easily lead to structural failure. The findings of this paper would provide a dynamic insight for the design of this type of flexible electronics.