# Percolation transition in entangled granular networks

## TL;DR

This study investigates how entangled granular particles form networks that undergo a percolation transition, revealing the critical link threshold and the influence of particle geometry on network formation.

## Contribution

It introduces a network science approach to analyze entanglement networks and proposes a continuum percolation model for rings that captures the transition.

## Key findings

- Networks undergo a percolation transition with a critical link threshold.
- Particle opening angle influences network structure and mechanical bonding.
- A continuum percolation model effectively describes the transition.

## Abstract

Highly nonconvex granular particles, such as staples and metal shavings, can form solid-like cohesive structures through geometric entanglement (interlocking). The network structure formed by this entanglement, however, remains largely unexplored. Here we utilize network science to investigate the entanglement networks of C-shaped granular particles under vibration through experiments and simulations. By analyzing key network properties, we demonstrate 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 the observed transition. Additionally, we find that particle's opening angle significantly affects mechanical bonding and, consequently, the network structure. This work highlights the potential of network-based approaches to study entangled materials, paving the way for advancements in applications ranging from mechanical metamaterials to entangled robot swarms.