Topological constraints suppress shear localization in granular chain ensembles

TL;DR

This work addresses how geometric connectivity constraints in granular chains alter shear localization and plastic flow. Using direct shear tests and DEM simulations across a range of chain lengths $N$, the authors show a transition from shear softening at $N=1$ to pronounced shear hardening and sustained dilation for longer chains, with the hardening onset occurring between $N\approx 8$ and $N\approx 10$. Micromechanically, tensile forces emerge from local jamming, correlated with a high non-covalent coordination number $Z_{nc}$, and tensile link forces peak near the deformation initiation region while the force network remains system-spanning; longer chains exhibit more diffuse deformation and asymmetric particle rotations. These findings establish granular chains as a minimal, connectivity-controlled model for geometric cohesion, with implications for granular metamaterials, earthquake-resistant geostructures, and 3D printing, by mapping how chain topology governs rigidity and flow.

Abstract

Entangled granular systems exhibit mechanical rigidity and resistance to deformation, reminiscent of cohesive materials, due to their reduced degrees of freedom and contact friction. A quantitative understanding of how classical granular phenomena, such as shear localization and plastic flow, appear in such geometrically cohesive systems remains unknown. Here, we investigate this using granular chain ensembles subjected to direct shear tests. Our experiments reveal that chains longer than four beads exhibit pronounced shear hardening, which is nearly independent of the applied normal stress and is accompanied by the complete suppression of shear localization. The volume dilation of the long chain ensembles also does not vanish in the steady state. We complement this phenomenology, which is distinct from that of typical frictional granular ensembles, with DEM simulations. The simulations reveal that tensile forces are generated due to particles being locally jammed, characterized by a high non-covalent coordination number. Consequently, this leads to a deformation that shows a very diffuse region of localization and enhanced shear hardening. Overall, our study highlights that granular chains provide a systematic route to map how connectivity constraints impact flow properties and mechanical rigidity.

Figures (8)

• Figure 1: a) Schematic of the chain geometry. b) The smallest possible loop of a granular chain comprised of 9 beads, each bead of diameter $b_d = 2~mm$, highlighting the flexibility and spacing constraints (scale bar, $5~mm$). c) Schematic of the experimental setup for direct shear testing. d) Simulation setup at the final state of the direct shear test simulation. The "deformation region" is indicated by the black-dashed rectangle and is defined as a zone of thickness equal to six bead diameters. $L_0$ denotes the total length of the deformation region.
• Figure 2: Stress ratio-Shear strain curves from experiments and DEM simulations for different chain lengths: a) $N=1$, b) $N=4$, c) $N=12$, d) $N=24$, b.inset) $N=8$, and c.inset) $N=10$. Symbols represent experimental data, while data from DEM simulations are shown as dashed lines. The shaded region is the standard deviation in stress ratio.
• Figure 3: Stress–Dilatancy relationship from experiments and DEM simulations for different chain lengths: a) $N=1$, b) $N=4$, c) $N=12$, d) $N=24$, b.inset) $N=8$, and c.inset) $N=10$, under various normal stresses, highlighting how the mechanical response changes with chain length and applied stress. Symbols represent experimental data, while data from DEM simulations are shown as dashed lines. The shaded region is the standard deviation in stress ratio.
• Figure 4: Time-averaged representation of the shear zone for different chain lengths and applied normal stresses ($\sigma_n$) over a steady state window from $13$ to $26$ minutes. The chain length increases upwards, and $\sigma_n$ increases to the right. The color-coded regions illustrate the extent of the shear zone at different percentages of the maximum Vertical gradient of $V_x$: red - $30\%$, green - $50\%$, light blue - $70\%$, blue - $90\%$. The resulting field of dominant ZELs is overlaid over the contours of shear zone (ZEL magnitude scaled up by a factor of 6 for visibility). $L$/$b_d$ is the length along the centerline of the shear box normalized by the bead diameter.
• Figure 5: Comparison of experimental (solid lines) and numerical (dashed lines) normalized velocity profile along the height of the sample under a normal stress of $100~kPa$. The velocities are averaged in the middle one-third width of the sample from the shear strain interval ($\gamma$) of $0.15$ to $0.16$.