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Abstract Entangled matter provides intriguing perspectives in terms of deformation mechanisms, mechanical properties, assembly and disassembly. However, collective entanglement mechanisms are complex, occur over multiple length scales, and they are not fully understood to this day. In this report, we propose a simple pick-up test to measure entanglement in staple-like particles with various leg lengths, crown-leg angles, and backbone thickness. We also present a new “throw-bounce-tangle” model based on a 3D geometrical entanglement criterion between two staples, and a Monte Carlo approach to predict the probabilities of entanglement in a bundle of staples. This relatively simple model is computationally efficient, and it predicts an average density of entanglement which is consistent with the entanglement strength measured experimentally. Entanglement is very sensitive to the thickness of the backbone of the staples, even in regimes where that thickness is a small fraction (< 0.04) of the other dimensions. We finally demonstrate an interesting use for this model to optimize staple-like particles for maximum entanglement. New designs of tunable “entangled granular metamaterials” can produce attractive combinations of strength, extensibility, and toughness that may soon outperform lightweight engineering materials such as solid foams and lattices.
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This content will become publicly available on July 1, 2026
Tunable entanglement and strength with engineered staple-like particles: Experiments and discrete element models
Entangled matter displays unusual and attractive properties and mechanisms: tensile strength, capabilities for assembly and disassembly, damage tolerance. While some of the attributes and mechanisms share some traits with traditional granular materials, fewer studies have focused on entanglement and strength and there are large gaps in our understanding of the mechanics of these materials. In this report we focus on the tensile properties and mechanics of bundles made of staple-like particles, and particularly on the effect of adjusting the angle between the legs and the crown in individual staples. Our experiments, combined with discrete element models, show competing mechanisms between entanglement strength and geometric engagement between particles, giving rise to an optimum crown-leg angle that maximizes strength. We also show that tensile forces are transmitted by a small fraction of the staples, which is organized in only 1-3 force chains. The formation and breakage of these chains is highly dynamic: as force chains break, they are replaced by fresh ones which were previously mechanically invisible. Entangled matter offers interesting perspectives in terms of materials design which can lead to unusual combination of properties: simultaneous strength and toughness, controlled assembly and disassembly, re-conformability, recyclability.
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- Award ID(s):
- 2033991
- PAR ID:
- 10653682
- Publisher / Repository:
- Elsevier
- Date Published:
- Journal Name:
- Journal of the Mechanics and Physics of Solids
- Volume:
- 200
- Issue:
- C
- ISSN:
- 0022-5096
- Page Range / eLocation ID:
- 106127
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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