Origin of geometric cohesion in non-convex granular materials: interplay between interdigitation and rotational constraints enhancing frictional stability

TL;DR

This work addresses how non-convex, non-interlocking grains achieve mechanical stability through geometry. It uses 3D X-ray tomography of cylindrical piles of polypod particles across varied friction, concavity, and branch counts, and introduces a stability indicator $\mathcal{S}$ that blends interdigitation, rotational constraint, and friction to quantify geometrical cohesion. The results show that stability is not simply tied to crystalline order or packing fraction; instead, central locking of multiple contacts and reconformability govern robustness, with $\mathcal{S}$ tracking the observed collapse ratio $\mathcal{R}$. These findings provide concrete design rules—such as extending branch length—to maximize geometric cohesion and offer a locally computable metric for strength that could extend to a broad class of concave granular particles.

Abstract

We present a series of experiments investigating the local microstructure of cylindrical piles composed of highly concave particles. By systematically varying particle geometry -- from spheres to strongly non-convex polypods -- as well as frictional properties and the number of branches, we explore how these parameters, together with the preparation protocol, shape the internal structure of the system. Using X-ray tomography combined with a dedicated image-analysis pipeline, we accurately extract the position, orientation, and contacts of every particle in each pile. This allows us to quantify the evolution of key structural observables as a function of particle geometry and preparation method. In particular, we measure the distributions of local packing fraction, coordination number, number of neighbors, and contact locations, along with particle-particle positional and orientational correlations. More importantly, we construct a new stability indicator that correlates perfectly with the observed pile stabilities, enabling us to identify the fundamental mechanisms responsible for \textit{geometrically induced cohesion} in granular systems composed of non-interlocking particle shapes: interdigitation, rotational constraint, friction-mediated cohesion, and the ability of a pile to re-stabilize.

Figures (12)

• Figure 1: Experiment. (a) Top: High-density polyethylene (HDPE) particles with $4$ branches and concavity $\eta$, ranging from $0$ (sphere) to $0.87$ (hexapod with branch thickness of $1.5$ mm). Concavity values are given on the picture. Bottom: Polyamide 12 (PA12) particles with a fixed branch thickness of $1.5$ mm and a varying number of branches from $4$ to $20$. The number of branches is given on the picture for each particle. (b) Cylindrical pile with a diameter of $15$ cm composed of PA12 particles with $12$ branches. (c) PA12 sample with $20$ branches positioned in the X-ray microtomograph. A: X-ray CCD detector collecting the images; B: pile sample contained in a plastic bucket placed on the rotation stage; C: X-ray tube.
• Figure 2: Image post-processing. (a) Reconstructed horizontal slices of the X-ray density matrix of a hexapod pile. (b) Vertical slice of the same system, with blue points indicating the roughly measured positions of the particle centers. (c) Segmented version of the same vertical slice, where individual particles are displayed in different colors. (d) 3D iso-value rendering of the boundary-distance matrix of a single particle, with black points marking the measured extremities of its branches. All images are extracted or computed from the X-ray scan of a cylindrical pile composed of EPDM hexapods with a branch cross-section of $1.5$ mm.
• Figure 3: Pile reconstruction. Left: 3D reconstructed view of a cylindrical pile composed of EPDM hexapods with a branch cross-section of $1.5$ mm. Red spheres indicate interparticle contacts. Right: Close-up view of the central region of the pile.
• Figure 4: Probability density functions (PDFs) of the local packing fraction, $\phi_l$, around a given particle are presented. Panel (a) shows the PDFs for particles with $n_b=6$ branches and varying concavities, $\eta$, while panel (b) illustrates the PDFs for particles with a concavity $\eta=0.87$ and a variable number of branches, $n_b$. In panel (b), solid lines represent the PDFs considering all particles, whereas dashed lines correspond to PDFs excluding particles near the pile boundaries. The insets display the evolution of the packing fraction, $\phi$ (calculated as average of $\phi_l$), as a function of particle concavity, $\eta$ (a), and the number of branches, $n_b$ (b). In the insets, $95~\%$ confidence intervals are shown where discernible.
• Figure 5: Evolution of the average radial distribution, $g$, as a function of the scaled distance to the particle center, $r/l_b$, is presented. Panel (a) illustrates $g(r/l_b)$ for piles composed of particles with $n_b=6$ branches and varying concavities, $\eta$, while panel (b) displays it for particles with a concavity $\eta=0.87$ and a variable number of branches, $n_b$. For $\eta = 0.79$ and $0.58$ (panel (a)) and $n_b = 6$ and $20$ (panel (b)) a pair of randomly chosen particles corresponding with the configuration at the pick are given