Abstract This paper presents a numerical study on the self-assembly of mono-size granular spheres with periodic boundary conditions under uniform and non-uniform 3D vibration. For uniform 3D vibration, the vibration conditions for self-assembly are similar to those under 1D vertical vibration. For non-uniform 3D vibration, slight horizontal vibration added to 1D vertical vibration can significantly promote or depress self-assembly. Moreover, under 1D or uniform 3D vibration, self-assembly results in a RHCP (random hexagonal close packed) structure, while under certain non-uniform vibration, a packing can self-assemble into a nearly pure FCC (face centered cubic) or HCP (hexagonal close packed) crystal structure. The microscopical analyses on the local structures, dynamics and forces provide rich insight into the different self-assembly processes under different vibration modes. These results can help understand the self-assembly of granular materials under vibration and guide how to control the structure of packed beds.

中文翻译：

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振动模式对三维振动下颗粒球自组装的影响

摘要 本文对均匀和非均匀3D 振动下具有周期性边界条件的单尺寸颗粒球的自组装进行了数值研究。对于均匀的 3D 振动，自组装的振动条件类似于 1D 垂直振动下的振动条件。对于非均匀 3D 振动，在 1D 垂直振动基础上添加轻微的水平振动可以显着促进或抑制自组装。此外，在一维或均匀的 3D 振动下，自组装导致 RHCP（随机六边形密堆积）结构，而在某些非均匀振动下，填料可以自组装成接近纯 FCC（面心立方）或 HCP （六方密堆积）晶体结构。局部结构的微观分析，动力学和力提供了对不同振动模式下不同自组装过程的深入了解。这些结果有助于了解颗粒材料在振动作用下的自组装，并指导如何控制填充床的结构。