Finite Element Modeling of Tight Elastic Knots

Changyeob Baek, Paul Johanns, Tomohiko G. Sano, Paul Grandgeorge, Pedro M. Reis

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


We present a methodology to simulate the mechanics of knots in elastic rods using geometrically nonlinear, full three-dimensional (3D) finite element analysis. We focus on the mechanical behavior of knots in tight configurations, for which the full 3D deformation must be taken into account. To setup the topology of our knotted structures, we apply a sequence of prescribed displacement steps to the centerline of an initially straight rod that is meshed with 3D solid elements. Self-contact is enforced with a normal penalty force combined with Coulomb friction. As test cases, we investigate both overhand and figure-of-eight knots. Our simulations are validated with precision model experiments, combining rod fabrication and X-ray tomography. Even if the focus is given to the methods, our results reveal that 3D deformation of tight elastic knots is central to their mechanical response. These findings contrast to a previous analysis of loose knots, for which 1D centerline-based rod theories sufficed for a predictive understanding. Our method serves as a robust framework to access complex mechanical behavior of tightly knotted structures that are not readily available through experiments nor existing reduced-order theories.

Original languageEnglish
Article number1090536
JournalJournal of Applied Mechanics, Transactions ASME
Issue number2
Publication statusPublished - 2021 Feb 1
Externally publishedYes

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


Dive into the research topics of 'Finite Element Modeling of Tight Elastic Knots'. Together they form a unique fingerprint.

Cite this