Generation of buckling and wrinkling in elastic films: The effect of initial imperfection

The symmetry breaking that is induced by initial imperfection (e.g., geometry or material inhomogeneity and out-of-plane disturbance) is a necessary condition for film buckling. However, the effect of initial imperfection on the buckling behavior is still not clear cut. Herein, given an elastic substrate-free circular film subjected to in-plane compressive stress and arbitrary initial imperfection, evolution of the deflection morphology is numerically studied and theoretically analyzed. Specifically, a two-dimensional spatial spectrum analysis is adopted to acquire the deflection morphology's dominant wavelength, which is combined with the maximum absolute deflection to characterize the deflection patterns. Before the so-called critical instability, the film under compression is found to go through a transition stage. Overall, the deflection increment in this stage is negligible except approaching the critical state. However, the dominant wavelength is found to be continuously growing (or decreasing) rather than suddenly appears upon reaching the so-called critical state, and, interestingly, such growth is found to be independent of the intensity and pattern of the initial imperfection if the same initial dominant wavelength is guaranteed. In the discussion, for both the transition and buckling stages, evolution laws of the deflection amplitude and wavelength are established analytically and found to agree well with the numerical results. This research clearly presents the actual evolution process of wrinkling morphology from linear in-plane deformation with small stable deflection to out-of-plane instability with large deflection, which deepens the cognition of instability behavior of films and provides a basis for related applications such as high-precision mechanical characterization.