Rigidity Percolation in Disordered 3D Rod Systems
Rigidity Percolation in Disordered 3D Rod Systems
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DOI：
10.1137/21m1401206
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发表时间：
2021-03
期刊：
影响因子：
--
通讯作者：
Samuel Heroy;D. Taylor;F. Shi;M. Forest;P. Mucha
中科院分区：
文献类型：
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作者：
Samuel Heroy;D. Taylor;F. Shi;M. Forest;P. Mucha
在由软的聚合物基体和硬的高纵横比颗粒组成的复合材料中，当内含物相超过临界密度时，复合材料经历机械强度的转变。这种现象（流变学或机械逾渗）是众所周知的，发生在许多复合材料中的临界密度超过电导率逾渗阈值。导电性渗透是由于接触渗透而发生的，接触渗透是指导电颗粒形成跨越复合材料的连接组分。然而，流变逾渗却没有一个完整的理论解释和预测描述。一个自然的假设是，流变渗流出现由于刚性渗流，从而夹杂物的刚性组件跨越复合材料。我们将复合材料建模为软芯棒的随机各向同性分散体，并研究了这种系统中的刚性渗流。在二维系统先前结果的基础上，我们开发了一种近似算法，通过迭代识别和压缩可证明的刚性基序来识别跨越的刚性组件--等效地，将巨大的刚性组件分解为依次较小的刚性组件的刚性组件。我们将此算法应用于随机杆系统，以估计刚性渗流阈值，并探讨其对杆的纵横比的依赖。我们发现，这个过渡点，像接触渗滤过渡点，比例成反比的平均（纵横比依赖）棒排除体积。然而，与接触渗滤缩放不同，刚性渗滤阈值的缩放对于相对低的纵横比是有效的。此外，临界杆接触数是恒定的纵横比高于一些相对较低的值，并低于预测从麦克斯韦的均衡条件。
In composite materials composed of soft polymer matrix and stiff, high-aspect-ratio particles, the composite undergoes a transition in mechanical strength when the inclusion phase surpasses a critical density. This phenomenon (rheological or mechanical percolation) is well-known to occur in many composites at a critical density that exceeds the conductivity percolation threshold. Conductivity percolation occurs as a consequence of contact percolation, which refers to the conducting particles' formation of a connected component that spans the composite. Rheological percolation, however, has evaded a complete theoretical explanation and predictive description. A natural hypothesis is that rheological percolation arises due to rigidity percolation, whereby a rigid component of inclusions spans the composite. We model composites as random isotropic dispersions of soft-core rods, and study rigidity percolation in such systems. Building on previous results for two-dimensional systems, we develop an approximate algorithm that identifies spanning rigid components through iteratively identifying and compressing provably rigid motifs -- equivalently, decomposing giant rigid components into rigid assemblies of successively smaller rigid components. We apply this algorithm to random rod systems to estimate a rigidity percolation threshold and explore its dependence on rod aspect ratio. We show that this transition point, like the contact percolation transition point, scales inversely with the average (aspect ratio-dependent) rod excluded volume. However, the scaling of the rigidity percolation threshold, unlike the contact percolation scaling, is valid for relatively low aspect ratio. Moreover, the critical rod contact number is constant for aspect ratio above some relatively low value; and lies below the prediction from Maxwell's isostatic condition.