{"title":"Frictional mechanics of knots","authors":"Ulrich Leuthäusser","doi":"10.1007/s00419-024-02566-w","DOIUrl":null,"url":null,"abstract":"<p>For some important knots, closed-form solutions are presented for the holding forces which are needed to keep a knot in equilibrium for given pulling forces. If the holding forces become zero for finite pulling forces, the knot is self-locking and is called stable. This is only possible when, first, the friction coefficient exceeds a critical value and, second, when there is additional pressure on some knot segments sandwiched by surrounding knot segments. The number of these segments depends on the topology of the knot and is characteristic for it. The other important parameter is the total curvature of the knot. In this way, the complete frictional contact inside the knot is taken into account. The presented model can explain the available experiments.</p>","PeriodicalId":477,"journal":{"name":"Archive of Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive of Applied Mechanics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1007/s00419-024-02566-w","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
For some important knots, closed-form solutions are presented for the holding forces which are needed to keep a knot in equilibrium for given pulling forces. If the holding forces become zero for finite pulling forces, the knot is self-locking and is called stable. This is only possible when, first, the friction coefficient exceeds a critical value and, second, when there is additional pressure on some knot segments sandwiched by surrounding knot segments. The number of these segments depends on the topology of the knot and is characteristic for it. The other important parameter is the total curvature of the knot. In this way, the complete frictional contact inside the knot is taken into account. The presented model can explain the available experiments.
期刊介绍:
Archive of Applied Mechanics serves as a platform to communicate original research of scholarly value in all branches of theoretical and applied mechanics, i.e., in solid and fluid mechanics, dynamics and vibrations. It focuses on continuum mechanics in general, structural mechanics, biomechanics, micro- and nano-mechanics as well as hydrodynamics. In particular, the following topics are emphasised: thermodynamics of materials, material modeling, multi-physics, mechanical properties of materials, homogenisation, phase transitions, fracture and damage mechanics, vibration, wave propagation experimental mechanics as well as machine learning techniques in the context of applied mechanics.