Mechanical Response of Fisherman’s Knots During Tightening

Author:

Tong Dezhong1,Ibrahim Khalil Md2,Justin Silva Matthew1,Wang Guanjin1,Khoda Bashir2,Khalid Jawed Mohammad1

Affiliation:

1. University of California Department of Mechanical and Aerospace Engineering, , Los Angeles, CA 90095

2. University of Maine Department of Mechanical Engineering, , Orono, ME 04473

Abstract

Abstract The fisherman’s knot, renowned for its strength and reliability, finds applications in engineering and medicine. However, a comprehensive understanding of its mechanics remains limited in scientific literature. In this paper, we present a systematic study of the tightening behavior of the fisherman’s knot through a combined approach of tabletop experiments and discrete elastic rods simulations. Our experimental setup involves gradually applying tension to the two ends of the fisherman’s knot until it fractures. We observed a correlation between the knot’s material properties and its behavior during tightening, leading up to fracture. The tightening process of the fisherman’s knot exhibits distinct “sliding” or “stretching” motions, influenced by factors such as friction and elastic stiffness. Furthermore, the failure modes of the knot (material fracture and topological failure) are determined by an interplay between elastic stiffness, friction, and initial conditions. This study sheds light on the underlying mechanics of the fisherman’s knot and provides insight into its behavior during the tightening process, contributing to the broader understanding of the mechanics of knots in practical applications.

Funder

National Science Foundation

Publisher

ASME International

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

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4. Dna Knotting Caused by Head-On Collision of Transcription and Replication;Olavarrieta;J. Mol. Biol.,2002

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