Physical trefoil knots: elastic deformation and failure

ORAL

Abstract

In its open conformation, the trefoil knot sets the basis of most functional knots. Although the trefoil knot has been studied in the realm of knot theory, their physical counterparts are not investigated thus far. To understand the local geometry of this fundamental knot, we constructed both open and closed physical trefoil knots tied in an elastic rod. We evaluated the influence of elasticity of our physical knot realizations, taking existing geometric models as a reference. Specifically, a combination of X-ray tomography and finite element simulations allowed us to systematically explore the self-contact regions, curvature profiles, and contact pressure. Our findings revealed significant rod constrictions at the entrance/exit of the tight open knot, which could act as precursors for potential spots of structural weakness. Further, we study the effect of local plastic deformation in tight functional knots, including elasto-plastic material filaments. The physical insight gained from this experimental characterization will give us a better understanding of how plastic necking emerges during the tightening process of an initially loose knot with elastic filament squeezing.

*Supported by the Fonds National de la Recherche, Luxembourg 12439430

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Presenters

  • Paul Johanns

    • Flexible Structures Laboratory, Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne (EPFL), Switzerland

Authors

  • Paul Johanns

    • Flexible Structures Laboratory, Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne (EPFL), Switzerland

  • Paul Grandgeorge

    • Flexible Structures Laboratory, Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne (EPFL), Switzerland
    • Flexible Structures Laboratory, Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne

  • Tomohiko Sano

    • Ecole Polytechnique Federale de Lausanne
    • Flexible Structures Laboratory, Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne (EPFL), Switzerland
    • Flexible Structures Laboratory, Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne

  • Changyeob Baek

    • School of Engineering and Applied Sciences, Harvard University, USA
    • Department of Applied Mathematics, Harvard University

  • John H. Maddocks

    • Laboratory for Computation and Visualization in Mathematics and Mechanics, Institute of Mathematics, École Polytechnique Fédérale de Lausanne (EPFL), Switzerland

  • Pedro M Reis

    • Ecole Polytechnique Federale de Lausanne
    • Flexible Structures Laboratory, Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne
    • École polytechnique fédérale de Lausanne
    • Flexible Structures Laboratory, Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne (EPFL), Switzerland
    • Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne