Emergent Rigidity and Shape in Entangled Ribbon Network

Shredded paper fragments form clumps, and bird nests take on three-dimensional structures. These are classic examples of randomly curved, elongated elements packed disorderly through temporary frictional contact. Although the dynamics of packed solid particles are well studied, how flexible, elongated elements form stable networks at low volume fractions remains largely unexplored. This study experimentally investigates the shape and overall mechanical properties formed by random network structures composed of slender elements. In the experiments, ribbon-shaped paper strips were placed in a cylindrical container at specific volume fractions and subjected to compression tests. Compression randomly introduced folds into the ribbons, and subsequent vibration operations enabled the realization of stable entanglement structures. By systematically varying the relevant parameters such as strip length and volume fraction, we find a variety of the scaling regimes. In particular, the linear elasticity and self-supporting structures emerge above a critical strip length that scales linearly with the cylinder radius. In this regime, the effective Young's modulus of the network is insensitive to the strip length but scales with the square of the volume fraction. We also argue a strong connection between the degree of crumpling of individual strips and the network elasticity.