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Nonlinear wave propagation in one-dimensional polycatenated ring chains

Xiaoxiao Xiong1,*, Reo Yanagi2,*, Tingtao Zhou2, and Chiara Daraio2,†

  • *These authors contributed equally to this work.
  • †Contact author: daraio@caltech.edu
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Phys. Rev. E 114, 044209 – Published 13 October, 2026

DOI: https://doi.org/10.1103/3z2t-368x

Abstract

We study the nonlinear wave dynamics of one-dimensional chains of polycatenated rings. These interlocked structures support amplitude-dependent nonlinear wave propagation driven by tensile activation and internal structural flexibility, unlike traditional granular crystals. Through dynamic impact experiments, finite-element modeling, and discrete-particle simulations of vertical chains, we observe and model a distinctive nonlinear wave morphology. It results from energy partitioning between the chain's two deformation channels: nonlinear indentation of the inter-ring contacts, which carries a compact leading wave front, and bending of the individual rings, which trails it as a persistent oscillatory train. Further, we demonstrate that the system's nonlinearity is not a fixed material constant. By altering the rings' geometric aspect ratio and contact angles, we can tune the effective contact exponent and the amplitude scaling of the wave speed. This work builds upon nonlinear wave propagation in classical granular crystals and establishes polycatenated systems as a highly tunable and designable platform to study and control nonlinear dynamics.

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Phys. Rev. E 114, 044209– Published 13 October, 2026
  • Received 19 May 2026
  • Accepted 24 September 2026
Article part of CHORUS
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