Mechanical Response of Fisherman's Knots during Tightening

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.