{"title":"On self-contact and non-interpenetration of elastic rods","authors":"Chiara Lonati, Alfredo Marzocchi","doi":"10.1177/10812865231226311","DOIUrl":null,"url":null,"abstract":"In this review, we discuss some conditions for achieving non-interpenetration and self-contact of solids, in particular for regular, inextensible, and closed elastic rods. We establish some equivalences between conditions that were stated sometimes independently, underlying their local or global character. We then examine three conditions related to virtual displacements and to topological characters of knots, that can be generalized to filaments, considering the midline of the loop as an inextensible regular knot.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"48 1","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics and Mechanics of Solids","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1177/10812865231226311","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATERIALS SCIENCE, MULTIDISCIPLINARY","Score":null,"Total":0}
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Abstract
In this review, we discuss some conditions for achieving non-interpenetration and self-contact of solids, in particular for regular, inextensible, and closed elastic rods. We establish some equivalences between conditions that were stated sometimes independently, underlying their local or global character. We then examine three conditions related to virtual displacements and to topological characters of knots, that can be generalized to filaments, considering the midline of the loop as an inextensible regular knot.
期刊介绍：
Mathematics and Mechanics of Solids is an international peer-reviewed journal that publishes the highest quality original innovative research in solid mechanics and materials science.
The central aim of MMS is to publish original, well-written and self-contained research that elucidates the mechanical behaviour of solids with particular emphasis on mathematical principles. This journal is a member of the Committee on Publication Ethics (COPE).
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