论文标题
在各向同性应变下僵硬的春季网络的僵硬
Stiffening of under-constrained spring networks under isotropic strain
论文作者
论文摘要
无序的春季网络是检查无定形材料的宏观机械性能的有用范式。在这里，我们研究了不受约束的春季网络的弹性行为，即比弹簧更自由度的网络。尽管这种网络通常是软盘，但可以通过应用外部应变来稳定它们。最近，已经开发了一种分析形式主义，以预测接近这种刚度过渡的机械网络特性。在这里，我们从数字上表明，这些预测适用于许多不同类别的春季网络，包括幻影三角，Delaunay，Voronoi和Honeycomb网络。分析预测进一步表明，剪切模量$ g $与各向同性应力$ t $ ta $接近刚度过渡的缩放；但是，这似乎与最近的数值研究不符，表明$ g $和$ t $的指数小于某些网络类别的指数。使用增加的数值精度和剪切稳定，我们在这里证明了靠近过渡线性缩放的$ g \ sim t $独立于网络类。最后，我们表明，根据网络类别，我们的结果并没有或仅受到有限尺寸效果的影响。
Disordered spring networks are a useful paradigm to examine macroscopic mechanical properties of amorphous materials. Here, we study the elastic behavior of under-constrained spring networks, i.e.\ networks with more degrees of freedom than springs. While such networks are usually floppy, they can be rigidified by applying external strain. Recently, an analytical formalism has been developed to predict the mechanical network properties close to this rigidity transition. Here we numerically show that these predictions apply to many different classes of spring networks, including phantom triangular, Delaunay, Voronoi, and honeycomb networks. The analytical predictions further imply that the shear modulus $G$ scales linearly with isotropic stress $T$ close to the rigidity transition; however, this seems to be at odds with recent numerical studies suggesting an exponent between $G$ and $T$ that is smaller than one for some network classes. Using increased numerical precision and shear stabilization, we demonstrate here that close to the transition linear scaling, $G\sim T$, holds independent of the network class. Finally, we show that our results are not or only weakly affected by finite-size effects, depending on the network class.
