Nonlinear wave propagation in one-dimensional polycatenated ring chains
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.
