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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.
Highlights
IntroductionTypical granular materials made of spherical or quasi-spherical grains require mechanical confinement to generate shear strength [1–3] or a cohesive second phase at the interface between the grains [4, 5]
Grains with more extreme geometries such as elongated rods can assemble into free standing structures with some tensile strength, because of long range interactions and multiple contact points [6–9]
In consistency with previous studies, we assumed that the extent, or density, of entanglement in a bundle is reflected by its strength, whether it is measured by stability under mechanical vibration [14], flexural tests [20], tensile tests [19] or as recently demonstrated on active entangled matter [22]
Summary
Typical granular materials made of spherical or quasi-spherical grains require mechanical confinement to generate shear strength [1–3] or a cohesive second phase at the interface between the grains [4, 5]. Grains with more extreme geometries such as elongated rods can assemble into free standing structures with some tensile strength, because of long range interactions and multiple contact points [6–9]. In turn, may be assembled into hexapods [10] or other star-like particles with entanglement or “geometric cohesion” [11], offering intriguing possibilities in terms of structural design and architecture [12, 13]. Even more extreme designs have branches with hooks and barbs, with the classical example of U-shape staple-like particles [14–17]. These particles can latch and hook onto one another, generating substantial tensile strength [15, 18, 19]. How the shapes of these particles govern entanglement, and in turn translate into strength provides a rich landscape in terms of mechanics and design.
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