A universal scaling law of grain chain elasticity under pressure revealed by a simple force vibration method.
A universal scaling law of grain chain elasticity under pressure revealed by a simple force vibration method.
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DOI：
10.1039/c4sm00727a
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发表时间：
2014-08
期刊：
影响因子：
3.4
通讯作者：
Lichen Chai;Xuebang Wu;C. S. Liu
中科院分区：
文献类型：
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作者：
Lichen Chai;Xuebang Wu;C. S. Liu
颗粒接触力是决定颗粒材料力学性能的关键因素，它取决于颗粒的弹性模量和变形量。然而，我们的知识在三维颗粒介质中的关系是有限的，主要是由于难以实现直接的实验研究。利用一种简单的力振动技术，我们测量了三种不同弹性模量的颗粒在不同压力（以改变颗粒变形）下的耗散谱（频率响应）。耗散谱呈现多个共振峰，表明不同长度的晶粒链发生了共振。这使我们能够定量表征晶粒链的弹性行为。对于具有不同材料性质（杨氏模量E、密度ρ和泊松系数ν）的所有颗粒系统，观察到颗粒链的共振频率（f）与变形的普遍相关性：f（2）<$δ（1/2）E/ρ（1 - ν）。在压力下的晶粒链的变形遵循p（2/3）压力依赖性。这一普遍行为表明，压力引起的变形的晶粒链在低频弱剪切振动是压倒了非线性赫兹接触弹性。
The grain contact force, the key player in determining the mechanical properties of grain materials, depends on the elastic modulus and deformation (δ) of grains. However, our knowledge on their relationship in a three-dimensional granular medium is limited mainly owing to the difficulty of realizing direct experimental investigation. Using a simple force vibration technique, we measure the dissipation spectra (the frequency response) of three kinds of grains with different elastic moduli under different pressures (to change the grain deformation). The dissipation spectra exhibit multiple resonant peaks, indicative of the resonance of grain chains with different lengths. This allows us to quantitatively characterize the elastic behaviors of grain chains. A universal correlation of the resonant frequency (f) of a grain chain with deformation is observed for all granular systems with different material properties (Young's modulus E, density ρ and Poisson's coefficient ν): f(2) ∝ δ(1/2)E/ρ(1 - ν). The deformation of the grain chain under pressure follows a p(2/3) pressure dependence. This general behavior suggests that the pressure-induced deformation of the grain chain under low-frequency weak shear vibration is overwhelmed by the nonlinear Hertzian contact elasticity.