摘要翻译：
研究了赫兹球的四种数值随机各向同性填料的弹性模量。四个样品是用不同的制备程序组装的，其中两个旨在通过振动和润滑再现实验压实。样品的力学性能随制备历史的变化而变化，且与配位数的关系比密度的关系要大得多。其次，分析了平均应变引起的质点位移的波动，并分析了它们对宏观行为的影响。研究发现，在宏观尺度上，只有这些波动引起的相对位移的平均取向接触才是相关的。这个平均值取决于配位数、接触网络的平均几何形状和平均接触刚度。就质点位移和转动的独立贡献而言，前者抵消了沿接触法线的平均应变，而后者则抵消了切向平面的平均应变。相反，中心位移的切向分量主要是为了加强局部平衡而产生的，在宏观尺度上具有较小的、普遍的加劲效应。最后，对文献中两种方法所产生的波动和剪切模量进行了数值估算。这两种方法都是基于一个小型代表大会的平衡。对平均应变假设的改进表明，与宏观行为相关的涨落发生在短的相关长度下。
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英文标题：
《On the elastic moduli of three-dimensional assemblies of spheres:
  characterization and modeling of fluctuations in the particle displacement
  and rotation》
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作者：
I. Agnolin, J.-N. Roux
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Materials Science        材料科学
分类描述：Techniques, synthesis, characterization, structure.  Structural phase transitions, mechanical properties, phonons. Defects, adsorbates, interfaces
技术，合成，表征，结构。结构相变，力学性质，声子。缺陷，吸附质，界面
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一级分类：Physics        物理学
二级分类：Disordered Systems and Neural Networks        无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
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一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  The elastic moduli of four numerical random isotropic packings of Hertzian spheres are studied. The four samples are assembled with different preparation procedures, two of which aim to reproduce experimental compaction by vibration and lubrication. The mechanical properties of the samples are found to change with the preparation history, and to depend much more on coordination number than on density.   Secondly, the fluctuations in the particle displacements from the average strain are analysed, and the way they affect the macroscopic behavior analyzed. It is found that only the average over equally oriented contacts of the relative displacement these fluctuations induce is relevant at the macroscopic scale. This average depends on coordination number, average geometry of the contact network and average contact stiffness. As far as the separate contributions from particle displacements and rotations are concerned, the former is found to counteract the average strain along the contact normal, while the latter do in the tangential plane. Conversely, the tangential components of the center displacements mainly arise to enforce local equilibrium, and have a small, and generally stiffening effect at the macro-scale.   Finally, the fluctuations and the shear modulus that result from two approaches available in the literature are estimated numerically. These approaches are both based on the equilibrium of a small-sized representative assembly. The improvement of these estimate with respect to the average strain assumption indicates that the fluctuations relevant to the macroscopic behavior occur with short correlation length.
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PDF链接：
https://arxiv.org/pdf/707.18