Quantifying the intrinsic mechanical properties of one-dimensional nanostructures such as nanotubes and nanowires is technically challenging due to their extremely small sizes and large aspect ratios. In comparison with direct tensile measurements, displacement responses of an end-clamped rod under transverse loads are more significant and more feasible for experimental characterization. However, the displacement–force relationship could be non-trivial due to the presence of geometrical nonlinearity and contributions from both stretching and bending. Choosing a simple but reliable model to extract the mechanical parameters from experimental data is thus important for the design of tests. Starting from the fully nonlinear, extensible Kirchhoff rod theory, we explore the application scope of several simplifications by referring to recent experimental studies on carbon nanotubes. The horizontal displacement is shown to be crucial information for strain analysis in the stretching-dominated regime, and the constant-tension assumption fails at large loading amplitudes. The capability of several simplified models is assessed through the Euclidean distance between deflection curves, as well as the error in estimating the strain distribution. Practical issues such as boundary slippage and dynamical effects are also discussed. This study offers a theoretical groundwork to understand the mechanical responses of one-dimensional nanostructures in typical experimental setups and provides a standard or guideline for the experimental design.

中文翻译：

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横向载荷作用下一维纳米结构力学测试的弹性杆模型

量化一维纳米结构（如纳米管和纳米线）的固有机械性能在技术上具有挑战性，因为它们具有极小的尺寸和大的纵横比。与直接拉伸测量相比，端部夹紧杆在横向载荷下的位移响应更显着，更适用于实验表征。然而，由于存在几何非线性以及拉伸和弯曲的贡献，位移-力的关系可能并不重要。因此，选择一个简单但可靠的模型来从实验数据中提取力学参数对于测试设计非常重要。从完全非线性、可扩展的基尔霍夫杆理论出发，我们通过参考最近对碳纳米管的实验研究探索了几种简化的应用范围。水平位移被证明是拉伸主导状态下应变分析的关键信息，并且恒张力假设在大载荷振幅下失败。几个简化模型的能力是通过挠度曲线之间的欧几里得距离以及估计应变分布的误差来评估的。还讨论了诸如边界滑移和动力学效应等实际问题。这项研究为理解典型实验设置中一维纳米结构的机械响应提供了理论基础，并为实验设计提供了标准或指南。水平位移被证明是拉伸主导状态下应变分析的关键信息，并且恒张力假设在大载荷振幅下失败。几个简化模型的能力是通过挠度曲线之间的欧几里得距离以及估计应变分布的误差来评估的。还讨论了诸如边界滑移和动力学效应等实际问题。这项研究为理解典型实验设置中一维纳米结构的机械响应提供了理论基础，并为实验设计提供了标准或指南。水平位移被证明是拉伸主导状态下应变分析的关键信息，并且恒张力假设在大载荷振幅下失败。几个简化模型的能力是通过挠度曲线之间的欧几里得距离以及估计应变分布的误差来评估的。还讨论了诸如边界滑移和动力学效应等实际问题。这项研究为理解典型实验设置中一维纳米结构的机械响应提供了理论基础，并为实验设计提供了标准或指南。几个简化模型的能力是通过挠度曲线之间的欧几里得距离以及估计应变分布的误差来评估的。还讨论了诸如边界滑移和动力学效应等实际问题。这项研究为理解典型实验设置中一维纳米结构的机械响应提供了理论基础，并为实验设计提供了标准或指南。几个简化模型的能力是通过挠度曲线之间的欧几里得距离以及估计应变分布的误差来评估的。还讨论了诸如边界滑移和动力学效应等实际问题。这项研究为理解典型实验设置中一维纳米结构的机械响应提供了理论基础，并为实验设计提供了标准或指南。