Recently, we have established that, when loaded in compression, edge-on, atomic layers in layered solid can fail by buckling. The resulting structure is termed a ripplocation. When more than one layer buckles, they outline standing waves with boundaries that we labeled ripplocation boundaries that are nearly fully recoverable. In this paper, we examine buckling of layers at the centimeter level to explore continuum buckling theory and its applicability to atomic layers. Specifically, we examine buckling by confining and cyclically loading thin steel sheets, edge-on, determining that increasing confining pressure, sheet thickness, and/or decreasing the number of layers increases the buckling load. Concomitantly, the resulting wavelengths and amplitudes are reduced. A nonlinear, folding mechanics model, which accounts for frictional bending and foundation energies, is adapted and verified on our experimental results. We also demonstrate that Coulombic friction between the layers can account for the energy dissipated per cycle. The predicted values of buckling nucleation loads and number of modes from the model are in good agreement—at low levels of confinement—with continuum and atomistic scale results. The wavelength estimates from the model correlate surprisingly well with the continuum buckling results; however, likely due to the complex mechanics at the lower length scales and limiting theoretical assumptions in the derivation, the accuracy decreases at the atomistic scale and at higher confining pressures.

中文翻译：

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薄板中的受限屈曲及其与波纹的相关性：层状固体中的变形机制

最近，我们已经确定，当压缩加载时，层状固体中的侧向原子层可能会因屈曲而失效。由此产生的结构称为ripplocation。当不止一层弯曲时，它们勾勒出带有边界的驻波，我们将这些边界标记为几乎完全可恢复的ripplocation边界。在本文中，我们研究了厘米级层的屈曲，以探索连续屈曲理论及其对原子层的适用性。具体来说，我们通过限制和循环加载薄钢板，边上来检查屈曲，确定增加围压、板材厚度和/或减少层数会增加屈曲载荷。伴随而来的是，由此产生的波长和振幅会减少。非线性折叠力学模型，考虑了摩擦弯曲和基础能量，根据我们的实验结果进行了调整和验证。我们还证明了层之间的库仑摩擦可以解释每个循环耗散的能量。模型中屈曲成核载荷和模态数量的预测值与连续介质和原子尺度结果非常吻合（在低限制水平下）。模型的波长估计与连续屈曲结果的相关性出奇地好；然而，可能由于较低长度尺度上的复杂力学和推导中的理论假设有限，原子尺度和较高围压下的精度会降低。我们还证明了层之间的库仑摩擦可以解释每个循环耗散的能量。模型中屈曲成核载荷和模态数量的预测值与连续介质和原子尺度结果非常吻合（在低限制水平下）。模型的波长估计与连续屈曲结果的相关性出奇地好；然而，可能由于较低长度尺度上的复杂力学和推导中的理论假设有限，原子尺度和较高围压下的精度会降低。我们还证明了层之间的库仑摩擦可以解释每个循环耗散的能量。模型中屈曲成核载荷和模态数量的预测值与连续介质和原子尺度结果非常吻合（在低限制水平下）。模型的波长估计与连续屈曲结果的相关性出奇地好；然而，可能由于较低长度尺度上的复杂力学和推导中的理论假设有限，原子尺度和较高围压下的精度会降低。模型的波长估计与连续屈曲结果的相关性出奇地好；然而，可能由于较低长度尺度上的复杂力学和推导中的理论假设有限，原子尺度和较高围压下的精度会降低。模型的波长估计与连续屈曲结果的相关性出奇地好；然而，可能由于较低长度尺度上的复杂力学和推导中的理论假设有限，原子尺度和较高围压下的精度会降低。