Percolation transition in entangled granular networks.

Highly nonconvex granular particles, such as staples and metal shavings, can form solid-like cohesive structures through geometric entanglement (interlocking). However, the network structure formed by this entanglement remains largely unexplored. Here, we employ network science to investigate the entanglement networks of C-shaped granular particles under vibration in experiments and simulations. Analysis of key network properties reveals that these networks undergo a percolation transition as the number of links increases logarithmically over time; the entangled particles form a giant cluster when the number of links exceeds a critical threshold. We propose a continuum percolation model of rings that effectively describes this observed transition. Furthermore, we find that the particles' opening angle significantly affects mechanical bonding and, consequently, the network structure. This work demonstrates the promise of network-based approaches for studying entangled materials, with potential applications from mechanical metamaterials to entangled robot swarms.