New mountain ridge modes in a film/substrate bilayer
New mountain ridge modes in a film/substrate bilayer
复制标题
DOI：
10.1177/10812865231208414
复制
发表时间：
2023-11
影响因子：
2.6
通讯作者：
Yuxin Fu;Yuesheng Wang;Yibin Fu
中科院分区：
文献类型：
--
作者：
Yuxin Fu;Yuesheng Wang;Yibin Fu
本文研究了薄膜-基底双层材料在平面应变状态下沿自由表面受沿着单轴压缩时的屈曲问题。以前的数值模拟表明，在这样的双层预拉伸衬底可能会导致形成的山脊模式作为二次分叉。我们提出了一个方案，在这种本地化模式也可能作为第一分叉。首先通过线性分叉分析示出，通过对基底施加预压缩，拉伸λ与波数k的关系除了当膜比基底更硬时在不存在预压缩的情况下已经存在的局部最大值之外，还可以形成局部最小值。因此，如果预压缩超过阈值，则k = 0处的λ可能变得大于局部最大值，并且因此成为分叉的临界拉伸。本文考虑了这种情况，通过弱非线性分析表明，多个长波长模式可能从一致解亚临界分叉，并迅速以山脊的形式局部化。这样找到的解可能是不稳定的，但形成了理解全局分叉行为的重要组成部分。希望我们的分析结果将指导未来的数值模拟和实验研究。
This article is concerned with the buckling of a film-substrate bilayer in a state of plane strain when it is subjected to a uni-axial compression along its free surface. Previous numerical simulations have indicated that pre-stretching the substrate in such a bilayer may lead to the formation of a mountain ridge mode as a secondary bifurcation. We present a scenario in which such a localized mode is also possible as a first bifurcation. It is first shown through a linear bifurcation analysis that by applying a pre-compression to the substrate, the stretch λ versus wavenumber k may develop a local minimum in addition to the local maximum that already exists in the absence of a pre-compression when the film is stiffer than the substrate. As a result, the λ at k = 0 may become larger than the local maximum if the pre-compression exceeds a threshold value, and hence becomes the critical stretch for bifurcation. This case is considered in this article, and it is shown through a weakly nonlinear analysis that multiple long wavelength modes may bifurcate subcritically from the uniform solution and quickly localize in the form of a mountain ridge. The solutions thus found are probably unstable, but form an essential part in the understanding of the global bifurcation behavior. It is hoped that our analytical results will guide future numerical simulations and experimental studies.