On self-contact and non-interpenetration of elastic rods

Chiara Lonati; Alfredo Marzocchi

doi:10.1177/10812865231226311

On self-contact and non-interpenetration of elastic rods

Chiara Lonati
, Alfredo Marzocchi^*

^*Corresponding author

Research output: Contribution to journal › Article › peer-review

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

Original language	English
Pages (from-to)	1-20
Number of pages	20
Journal	Mathematics and Mechanics of Solids
DOIs	https://doi.org/10.1177/10812865231226311
Publication status	Published - 2024

Keywords

Self-contact, injectivity, elastic rods, knots, non-interpenetration of matter

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10.1177/10812865231226311

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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",

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AB - 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

KW - Self-contact, injectivity, elastic rods, knots, non-interpenetration of matter

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On self-contact and non-interpenetration of elastic rods

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Keywords

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