School of Civil Engineering and Institute of Mechanics and Technology, Xi'an University of Architecture and Technology, Xi'an, 710055, China.
Sci Rep. 2022 Mar 8;12(1):4074. doi: 10.1038/s41598-022-08136-w.
Surface buckling behaviors of thin-film soft-substrate bilayers have important research value. Recent research has focused on bilayers with infinite-thickness substrates. However, bilayers with finite-thickness substrates widely exist. To study this problem more comprehensively, we extended the stability theory of a beam on an elastic foundation to bilayers and then established a finite element method of bilayers using the neo-Hookean hyperelastic constitutive model. A self-contact analysis method was coupled to the finite element method so that the further buckling evolution of the film surface after folding could be simulated. Based on our analysis of various modulus ratios and thickness ratios, the evolution of the buckling path was significantly influenced by the thickness ratio. Without considering the situation of a prestressed substrate, four new buckling paths were found. Thus, we extended the single buckling path (under infinite thickness substrate) to five types. Our study also found that for path four, the substrate with a certain thickness exhibited a special final stable surface morphology. That is, regardless of the friction, a new periodic morphology after film folding appeared due to the contact slip of the film surface. Finally, further analysis showed that these five buckling paths were all dependent on different modulus ratios and thickness ratios.
薄膜软基底双层结构的表面屈曲行为具有重要的研究价值。最近的研究集中在具有无限厚度基底的双层结构上。然而，具有有限厚度基底的双层结构广泛存在。为了更全面地研究这个问题，我们将弹性地基上梁的稳定性理论扩展到双层结构中，然后使用新的胡克弹性本构模型建立了双层结构的有限元方法。将自接触分析方法与有限元方法相结合，以便模拟薄膜表面折叠后的进一步屈曲演化。通过对各种模量比和厚度比的分析，发现屈曲路径的演化受到厚度比的显著影响。在不考虑预应力基底的情况下，发现了四种新的屈曲路径。因此，我们将单一的屈曲路径（在无限厚度基底下）扩展到了五种类型。我们的研究还发现，对于路径四，具有一定厚度的基底表现出一种特殊的最终稳定表面形貌。也就是说，无论摩擦如何，由于薄膜表面的接触滑移，薄膜折叠后会出现一种新的周期性形貌。最后，进一步的分析表明，这五种屈曲路径都依赖于不同的模量比和厚度比。
