Generation of buckling and wrinkling in elastic films: The effect of initial imperfection,Physical Review E

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Generation of buckling and wrinkling in elastic films: The effect of initial imperfection
Physical Review E ( IF 2.2 ) Pub Date : 2021-11-09 , DOI: 10.1103/physreve.104.055002
Yidu Zhang ₁ , Langquan Shui ₂ , Yongshou Liu ₁ , Ze Liu ₂

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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.

中文翻译：

弹性薄膜中屈曲和起皱的产生：初始缺陷的影响

由初始缺陷（例如，几何形状或材料不均匀性和平面外扰动）引起的对称破坏是薄膜屈曲的必要条件。然而，初始缺陷对屈曲行为的影响仍不清楚。在此，给定承受面内压缩应力和任意初始缺陷的弹性无基材圆形薄膜，对偏转形态的演变进行了数值研究和理论分析。具体而言，采用二维空间谱分析获取偏转形态的主波长，结合最大绝对偏转来表征偏转模式。在所谓的临界不稳定性之前，发现受压薄膜经历了一个过渡阶段。全面的，除了接近临界状态外，该阶段的挠度增量可以忽略不计。然而，发现主波长持续增长（或减少）而不是在达到所谓的临界状态时突然出现，而且有趣的是，发现这种增长与初始缺陷的强度和模式无关，如果保证相同的初始主波长。在讨论中，对于过渡阶段和屈曲阶段，分析建立了挠度幅度和波长的演变规律，发现与数值结果非常吻合。本研究清楚地呈现了起皱形态从具有小稳定挠度的线性面内变形到具有大挠度的面外不稳定的实际演变过程，

更新日期：2021-11-10

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