Dynamic Resonance in Stochastically Entangled Soft Filament Networks

Entangled filamentary networks are ubiquitous in everyday life, manifesting as bowls of soft spaghetti, structurally resilient hanging bird nests, and even tangles of headphones. Yet, their dynamic properties influenced by entanglement remain underexplored. In this study, we investigate the impact of contact topology and filament entanglement on the dynamic resonant behavior of tangled soft materials through benchtop experiments. We focus on extracting a single soft filament from a tangled assembly under vertical agitation. Utilizing a mechanical test bed and conducting experiments with stochastically generated tangles of varying packing densities, we identify an optimal frequency that enhances the extraction rate. Simplified experiments with soft meshes reveal the critical roles of entanglement and contact cohesiveness in the speed of fiber extraction. By employing coils of threads as soft elastic materials, we demonstrate that these topological tangles act as effective springs with stiffness dependent on contact density. Our findings contribute to establishing a potential framework for categorizing various types of topologically entangled filaments based on their stiffness per unit mass and contact cohesiveness. By identifying and tuning the resonant normal modes in these "stochastically entangled metamaterials", we hope to advance nonlinear spring applications and airless tire design.