论文标题
无序弹性网络中临界应变膨胀的缩放理论
Scaling theory of critical strain-stiffening in disordered elastic networks
论文作者
论文摘要
无序的弹性网络为描述各种物理系统提供了一个框架，从无定形固体到聚合纤维纤维材料到汇合细胞组织。在许多情况下，此类网络具有两个广泛分开的刚度尺度，几乎是软盘，但是当驱动到足够大的菌株时，它们会发生急剧的僵硬过渡。我们介绍了临界应变稳定状态的完整缩放理论，该理论是刚度尺度之间的小比例，该比例在奇异扰动理论的框架中概念化。临界状态具有四分之一的非谐度，从中得出了一组非线性缩放关系。也得出了宏观弹性模量对临界状态之外的缩放预测，从而揭示了先前未识别的特征应变量表。与生物聚合物网络模型的广泛可用数值数据相比，这些预测是定量的，讨论了未来的研究问题。
Disordered elastic networks provide a framework for describing a wide variety of physical systems, ranging from amorphous solids, through polymeric fibrous materials to confluent cell tissues. In many cases, such networks feature two widely separated rigidity scales and are nearly floppy, yet they undergo a dramatic stiffening transition when driven to sufficiently large strains. We present a complete scaling theory of the critical strain-stiffened state in terms of the small ratio between the rigidity scales, which is conceptualized in the framework of a singular perturbation theory. The critical state features quartic anharmonicity, from which a set of nonlinear scaling relations is derived. Scaling predictions for the macroscopic elastic modulus beyond the critical state are derived as well, revealing a previously unidentified characteristic strain scale. The predictions are quantitatively compared to a broad range of available numerical data on biopolymer network models and future research questions are discussed.
