Nonlinear Wave Propagation in 1D Polycatenated Ring Chains

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 pretensioned by gravity, we observe and explain nonlinear waves characterized by a compact leading wavefront followed by persistent trailing oscillations, which arise from energy partitioning into the rings' internal bending modes. 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.