Revisiting the wrinkling of elastic bilayers II: Post-bifurcation analysis
Revisiting the wrinkling of elastic bilayers II: Post-bifurcation analysis
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DOI：
10.1016/j.jmps.2020.104053
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发表时间：
2020-10-01
影响因子：
5.3
通讯作者：
Goriely, Alain
中科院分区：
文献类型：
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作者：
Alawiye, Hamza;Farrell, Patrick E.;Goriely, Alain
我们研究的问题的弹性薄膜粘结到一个弹性基板，并受到压缩应力（引起的薄膜或横向压缩的整个系统的增长）。继先前进行的线性分析，以确定所需的临界增长/压缩比，以诱导在膜中，我们进行了弱非线性分析，推导出一个振幅方程，描述了超越分叉点的扭曲振幅的演变。我们进行了一个全面的数值分岔分析的问题，使用有限元方法和弱非线性分析和数值实验之间表现出良好的协议。我们也能够直接解决我们的离散化系统中的分叉点，并表征实施细节的影响，如观察到的分叉点上的计算域的纵横比。最后，我们探讨的振幅方程的解决方案的情况下，允许在长的空间和/或时间尺度上变化的振幅。(C)2020爱思唯尔有限公司保留所有权利。
We examine the problem of an elastic film bonded to an elastic substrate and subjected to compressive stress (induced by growth of the film or lateral compression of the whole system). Following the linear analysis previously carried out to determine the critical growth/compression ratio required to induce wrinkling in the film, we carry out a weakly-nonlinear analysis to derive an amplitude equation that describes the evolution of the wrinkling amplitude beyond the bifurcation point. We carry out a comprehensive numerical bifurcation analysis of the problem using the finite element method and show excellent agreements between the weakly-nonlinear analysis and the numerical experiments. We are also able to solve directly for the bifurcation point in our discretized system and characterize the effect of implementation details such as the aspect ratio of the computational domain on the observed bifurcation point. Finally, we explore solutions of the amplitude equation in the case that the wrinkling amplitude is allowed to vary over long spatial and/or temporal scales. (C) 2020 Elsevier Ltd. All rights reserved.