Atomically thin sheets, such as graphene, are widely used in nanotechnology. Recently they have also been used in applications including kirigami and self-folding origami, where it becomes important to understand how they respond to external loads. Motivated by this, we investigate how isotropic sheets respond to uniaxial tension by employing the self-consistent screening analysis method and molecular dynamics simulations. Previously, it was shown that for freely suspended sheets thermal fluctuations effectively renormalize elastic constants, which become scale-dependent beyond a characteristic thermal length scale (a few nanometers for graphene at room temperature), beyond which the bending rigidity increases, while the in-plane elastic constants reduce with universal power law exponents. For sheets under uniaxial tension, $\sigma_{11}$, we find that beyond a stress-dependent length scale, the effective in-plane elastic constants become strongly anisotropic and scale differently along the axis of uni-axial stress and orthogonal to it. The bending rigidities on the other hand will not exhibit any anomalous behavior beyond this stress-dependent length scale. In addition, for moderate tensions we find a universal non-linear stress-strain relation. For large uni-axial tensions, the Young's modulus of the bare elastic material is recovered.

中文翻译：

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单轴张力下脉动弹性膜的力学性能

原子薄片，例如石墨烯，广泛用于纳米技术。最近，它们还被用于剪纸和自折叠折纸等应用中，在这些应用中，了解它们如何响应外部负载变得很重要。受此启发，我们通过采用自洽筛选分析方法和分子动力学模拟来研究各向同性片材如何响应单轴张力。此前，研究表明，对于自由悬浮的片材，热波动有效地重新调整了弹性常数，超出了特征热长度尺度（室温下石墨烯为几纳米），弹性常数变得依赖于尺度，超过该尺度，弯曲刚度增加，而 in-平面弹性常数随通用幂律指数而减小。对于单轴张力下的片材，$\sigma_{11}$，我们发现，在与应力相关的长度尺度之外，有效的面内弹性常数变得强烈各向异性，并且沿单轴应力轴并与其正交。另一方面，弯曲刚度将不会表现出超出该应力相关长度尺度的任何异常行为。此外，对于中等张力，我们发现了普遍的非线性应力-应变关系。对于大的单轴张力，裸弹性材料的杨氏模量得到恢复。对于中等张力，我们发现了一个普遍的非线性应力-应变关系。对于大的单轴张力，裸弹性材料的杨氏模量得到恢复。对于中等张力，我们发现了一个普遍的非线性应力-应变关系。对于大的单轴张力，裸弹性材料的杨氏模量得到恢复。