该研究团队构建了一个模型系统，在该系统中，张拉整体元素被随机地添加到规则的骨干结构中。通过运用有向图理论进行解析求解，研究人员成功揭示了一个推广的麦克斯韦力学临界点的存在。研究显示，即便只是增加了少数类电缆元素，也会对这个过渡点的性质产生根本性的改变，进而影响后续向完全刚性结构的过渡过程。此外，研究还发现张拉整体网络表现出了集体雪崩行为，即单个电缆的增加会导致多个软盘模式的消除，这一现象在过渡点处尤为显著。这些现象对于具有非线性机械约束的各种系统都有重要影响，包括生物聚合物网络、软体机器人、堵塞的填料以及折纸片等。
据悉，在工程和生物界中，一种特殊的功能结构将刚性元素（如骨骼和柱子）与柔性元素（如电缆、纤维和膜）结合在一起。由于这些类电缆元素仅支持拉伸张力，表现出高度非线性的特性，因此这类结构被称为张拉整体。特别值得一提的是，微刚性系统因结构约束的数量而能够允许柔性变形并支撑外部负载，这一特性引起了人们极大的兴趣。
附：英文原文
Title: Rigidity percolation in a random tensegrity via analytic graph theory
Author: Stephenson, William, Sudhakar, Vishal, McInerney, James, Czajkowski, Michael, Rocklin, D. Zeb
Issue&Volume: 2023-11-21
Abstract: Functional structures from across the engineered and biological world combine rigid elements such as bones and columns with flexible ones such as cables, fibers, and membranes. These structures are known loosely as tensegrities, since these cable-like elements have the highly nonlinear property of supporting only extensile tension. Marginally rigid systems are of particular interest because the number of structural constraints permits both flexible deformation and the support of external loads. We present a model system in which tensegrity elements are added at random to a regular backbone. This system can be solved analytically via a directed graph theory, revealing a mechanical critical point generalizing that of Maxwell. We show that even the addition of a few cable-like elements fundamentally modifies the nature of this transition point, as well as the later transition to a fully rigid structure. Moreover, the tensegrity network displays a collective avalanche behavior, in which the addition of a single cable leads to the elimination of multiple floppy modes, a phenomenon that becomes dominant at the transition point. These phenomena have implications for systems with nonlinear mechanical constraints, from biopolymer networks to soft robots to jammed packings to origami sheets.
DOI: 10.1073/pnas.2302536120
Source: https://www.pnas.org/doi/abs/10.1073/pnas.2302536120