Mechanics of two filaments in tight orthogonal contact

Paul Grandgeorge, Changyeob Baek, Harmeet Singh, Paul Johanns, Tomohiko G. Sano, Alastair Flynn, John H. Maddocks, Pedro M. Reis

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


Networks of flexible filaments often involve regions of tight contact. Predictively understanding the equilibrium configurations of these systems is challenging due to intricate couplings between topology, geometry, large nonlinear deformations, and friction. Here, we perform an in-depth study of a simple, yet canonical, problem that captures the essence of contact between filaments. In the orthogonal clasp, two filaments are brought into contact, with each centerline lying in one of a pair of orthogonal planes. Our data from X-ray tomography (µCT) and mechanical testing experiments are in excellent agreement with finite element method (FEM) simulations. Despite the apparent simplicity of the physical system, the data exhibit strikingly unintuitive behavior, even when the contact is frictionless. Specifically, we observe a curvilinear diamond-shaped ridge in the contact-pressure field between the two filaments, sometimes with an inner gap. When a relative displacement is imposed between the filaments, friction is activated, and a highly asymmetric pressure field develops. These findings contrast to the classic capstan analysis of a single filament wrapped around a rigid body. Both the µCT and FEM data indicate that the cross-sections of the filaments can deform significantly. Nonetheless, an idealized geometrical theory assuming undeformable tube cross-sections and neglecting elasticity rationalizes our observations qualitatively and highlights the central role of the small, but nonzero, tube radius of the filaments. We believe that our orthogonal clasp analysis provides a building block for future modeling efforts in frictional contact mechanics of more complex filamentary structures.

Original languageEnglish
Article numbere2021684118
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number15
Publication statusPublished - 2021 Apr 13
Externally publishedYes


  • Capstan equation
  • Contact mechanics
  • Elastic structures
  • Kirchhoff rods
  • Knots

ASJC Scopus subject areas

  • General


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