Tuning geometry in staple-like and barbed entangled particles: “pick-up” experiments and Monte Carlo simulations

Entangled granular matter offers new insights into deformation, mechanical properties, assembly and disassembly. However, the entanglement mechanisms, occurring across multiple length scales, remain incompletely understood. We propose a simple pick-up experiment to measure entanglement in staple-like particles with varying leg lengths, crown-leg angles, and backbone thicknesses. Additionally, we introduce a “throw-bounce-tangle” model based on a 3D geometrical entanglement criterion between two staples, along with a Monte Carlo simulation to predict entanglement probabilities in staple bundles. This computationally efficient model predicts an average entanglement density consistent with experimental measurements. An interesting use for this simulation model is to optimize the geometry of the particles to maximize entanglement. We also apply the model to more complex barbed particles, showing how the number of branches and barb geometry can be tuned to control particle accessibility to entanglement and the number of particles that can entangle with a given particle. These effects create design trade-offs and determine the optimal number of branches, resulting in entanglement strengths several times greater than simple staples. These new designs for tunable "entangled granular metamaterials" offer a unique combination of strength, extensibility, and toughness that may soon outperform lightweight engineering materials like solid foams and lattices.