Budday Silvia, Andres Sebastian, Walter Bastian, Steinmann Paul, Kuhl Ellen
Department of Applied Mechanics, University of Erlangen-Nuremberg, 91058 Erlangen, Germany.
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
Philos Trans A Math Phys Eng Sci. 2017 May 13;375(2093). doi: 10.1098/rsta.2016.0163.
Wrinkling phenomena control the surface morphology of many technical and biological systems. While primary wrinkling has been extensively studied, experimentally, analytically and computationally, higher-order instabilities remain insufficiently understood, especially in systems with stiffness contrasts well below 100. Here, we use the model system of an elastomeric bilayer to experimentally characterize primary and secondary wrinkling at moderate stiffness contrasts. We systematically vary the film thickness and substrate prestretch to explore which parameters modulate the emergence of secondary instabilities, including period-doubling, period-tripling and wrinkle-to-fold transitions. Our experiments suggest that period-doubling is the favourable secondary instability mode and that period-tripling can emerge under disturbed boundary conditions. High substrate prestretch can suppress period-doubling and primary wrinkles immediately transform into folds. We combine analytical models with computational simulations to predict the onset of primary wrinkling, the post-buckling behaviour, secondary bifurcations and the wrinkle-to-fold transition. Understanding the mechanisms of pattern selection and identifying the critical control parameters of wrinkling will allow us to fabricate smart surfaces with tunable properties and to control undesired surface patterns like in the asthmatic airway.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'
皱纹现象控制着许多技术和生物系统的表面形态。虽然初级皱纹已经在实验、分析和计算方面得到了广泛研究，但高阶不稳定性仍未得到充分理解，尤其是在刚度对比度远低于100的系统中。在此，我们使用弹性体双层的模型系统，在中等刚度对比度下对初级和次级皱纹进行实验表征。我们系统地改变薄膜厚度和基底预拉伸，以探索哪些参数调节次级不稳定性的出现，包括倍周期、三倍周期和皱纹到褶皱的转变。我们的实验表明，倍周期是有利的次级不稳定性模式，三倍周期可以在受干扰的边界条件下出现。高基底预拉伸可以抑制倍周期，初级皱纹会立即转变为褶皱。我们将分析模型与计算模拟相结合，以预测初级皱纹的起始、屈曲后行为、次级分岔以及皱纹到褶皱的转变。理解图案选择机制并确定皱纹的关键控制参数，将使我们能够制造具有可调特性的智能表面，并控制哮喘气道中出现的不良表面图案。本文是主题为“通过复杂介质中的不稳定性进行图案化：理论与应用”的特刊的一部分。
