変形可能なシステムの力学:ケーブル状構造の数学的謎を解く研究(The Dynamics of Deformable Systems: Study Unravels Mathematical Mystery of Cable-like Structures)

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2024-02-08 ジョージア工科大学

The research team's main object of study, shown here, is structures that consist of large numbers of pores — arranged in columns and rows with cables and rods added at random.

ジョージア工科大学の物理学部助教であるゼブ・ロクリン氏は、新しい論文で、現実世界における固体と液体の境界線の曖昧さをモデル化しています。彼の研究は、柔軟性と耐久性の組み合わせを提供する変形可能な固体の可能性を示し、生物学から工学、ナノテクノロジーに至るまでの分野に影響を与える可能性があります。特に、ケーブル構造を利用したモデルは、構造物の設計やナノテクノロジーにおける応用に革新をもたらす可能性があります

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解析的グラフ理論によるランダムテンセグリティの剛性浸透 Rigidity percolation in a random tensegrity via analytic graph theory

William Stephenson, Vishal Sudhakar, James McInerney, +1, and D. Zeb Rocklin
Proceedings of the National Academy of Sciences  Published:November 21, 2023
DOI:https://doi.org/10.1073/pnas.2302536120

Significance

Mechanical structures combining rigid elements, like rods and bone, with flexible ones, like cables and membranes, are ubiquitous across a wide range of scales in natural and engineered systems. We examine how rigidity emerges as rigid and flexible elements are randomly assembled by introducing an analytic method. We find that nonlinear interactions between elements lead to the abrupt emergence of rigidity, allowing the system to support loads as it maintains flexibility. Flexible elements fundamentally modify the equilibrium and nonequilibrium behavior of the systems, including by allowing a single element to eliminate multiple deformation modes. This sheds light on how biological structures balance robustness, strength, and flexibility and how this can be emulated via engineering techniques.

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.

1700応用理学一般
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