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Pattern selection on axial-compressed bilayer systems with a non-zero Gauss curvature

机译：具有非零高斯曲率的轴向压缩双层系统上的图案选择

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摘要

When a soft bilayer system with curved surface is subject to uniaxial compression, surface wrinkles may appear when the compressive strain is beyond a critical value. Interestingly, diverse wrinkling patterns can occur by modulating the feature of the curved surface though the load is simple. Here we study the effect of the sign of Gauss curvature and curvature anisotropy on the wrinkling pattern selection and evolution with experiments, theoretical analysis and numerical simulations. For a system with negative Gauss curvature, our analysis reveals a critical curvature anisotropy below which the critical buckling pattern is a checkerboard mode and will evolve into a diamond-like pattern. Otherwise, the critical buckling mode is sinusoidal. In the post-buckling analysis, our analysis leads to an analytical solution to predict the critical value of the dimen-sionless curvature that dominates the wrinkling pattern transition. When the dimensionless curvature exceeds such a critical value, the system would branch into the diamond-like mode. Otherwise, the system would maintain the sinusoidal mode. Our results also show that the sign of the Gauss curvature has important influence on critical strain for the onset of wrinkling pattern transition. Negative Gauss curvature promotes the sinusoidal/diamond-like mode transition, whereas positive Gauss curvature inhibits this wrinkling pattern evaluation. Phase diagrams have been proposed which facilitate the use of the key results achieved in this paper. This study shows an example that a curved system may evolve a surface with complex patterns under simple stimuli by tuning the surface curvature.
机译：当具有弯曲表面的软双层系统受到单轴压缩的影响时，当压缩应变超出临界值时可能出现表面皱纹。有趣的是，通过调制弯曲表面的特征，可以通过调制弯曲表面的特征来发生多样化的皱纹图案。在这里，我们研究了高斯曲率和曲率各向异性的迹象对实验，理论分析和数值模拟的皱纹图案选择和演化的影响。对于具有负高斯曲率的系统，我们的分析揭示了临界曲率各向异性，下面的临界曲线是突击模式是棋盘模式，并将演变成菱形图案。否则，关键屈曲模式是正弦波。在后屈曲分析中，我们的分析导致分析解决方案来预测Dimen-Sionless曲率的临界值，该曲率占主导地位的皱纹图案过渡。当无量纲曲率超过这种临界值时，系统将分支到菱形模式中。否则，系统将保持正弦模式。我们的研究结果还表明，高斯曲率的迹象对皱纹模式转变发作的临界应变具有重要影响。负高斯曲率促进正弦/菱形模式转变，而正高斯曲率抑制这种皱纹图案评估。已经提出了相图，其中有助于使用本文实现的关键结果。该研究表明，通过调谐表面曲率，弯曲系统可以根据简单的刺激在简单的刺激下与复杂的图案演变的示例。

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  • 来源
    《Journal of the Mechanics and Physics of Solids》 |2021年第9期|104516.1-104516.12|共12页
  • 作者

    Yan Zhao; Wenjie Guo; Hanlin Zhu; Yifeng He; Chao Jiang; Yanping Cao;

  • 作者单位

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body College of Mechanical and Vehicle Engineering Hunan University Changsha 410082 P.R. China;

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body College of Mechanical and Vehicle Engineering Hunan University Changsha 410082 P.R. China;

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body College of Mechanical and Vehicle Engineering Hunan University Changsha 410082 P.R. China;

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body College of Mechanical and Vehicle Engineering Hunan University Changsha 410082 P.R. China;

    State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body College of Mechanical and Vehicle Engineering Hunan University Changsha 410082 P.R. China;

    Institute of Biomechanics and Medical Engineering AML Department of Engineering Mechanics Tsinghua University Beijing 100084 P.R. China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    wrinkling pattern selection; dimensionless curvature; curvature anisotropy; negative Gauss curvature; positive Gauss curvature;

    机译：皱纹图案选择;无量纲曲率;曲率各向异性;消极的高斯曲率;积极的高斯曲率;

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