Friction-controlled reentrant aging and fluidization in granular materials

Abstract

Granular materials densify under repeated mechanical perturbations, a nonequilibrium dynamics that underlies many natural and industrial processes. Because granular relaxation is governed by frictional contacts and energy dissipation, this aging behavior fundamentally differs from that of thermal glasses despite their apparent similarities. Here, we uncover how friction controls the compaction dynamics of granular packings subjected to cyclic shear. Using discrete element simulations, we construct a dynamic state diagram as a function of strain amplitude and friction, revealing a rich interplay between jamming marginality, stabilization, and fluidization. We identify a friction-dependent crossover strain that separates aging and fluidized regimes, showing reentrant, non-monotonic behavior: Increasing friction first suppresses fluidization, then promotes it through smooth, creep-like rearrangements. This transition is marked by a shift from intermittent, avalanche-like rearrangements to continuous, diffusive motion. Our findings demonstrate that friction exerts a dual role in granular aging -- both stabilizing and fluidizing -- thereby uncovering the fundamental nonequilibrium mechanisms that govern compaction, rheology, and aging in athermal disordered systems. More broadly, our results reveal a general principle for how friction governs metastability and flow in athermal matter -- from granular and frictional colloids to soils and seismic faults -- linking microscopic contact mechanics to macroscopic dynamics.

Figures (14)

• Figure 1: (a) Packing fraction ($\phi_0$) and coordination number ($Z$) as functions of the friction coefficient ($\mu$) obtained from a quasistatic compression protocol. The trends remains consistent under an imposed dimensionless pressure of $P = 0.004$ (solid symbols) compared to a much lower pressure of $P = 2 \times 10^{-4}$ (open symbols), approaching the hard-particle limit. (b) Simple shear setup: Side boundaries (blue) tilt to induce shear, while the top and bottom layers (red) shift (i) along the shear direction and (ii) adaptively perpendicular to maintain imposed pressure $P$. (c-e) Packing fraction $\phi(t_w)$ during compaction for $\mu = 0$, $0.1$, and $1$, for various shear amplitudes $\Gamma$. Solid lines indicate a solid-like aging regime, while dashed lines denote a fluidized regime (see main text for definition). (f) Final packing fraction $\phi_{\rm f}$ vs. $\Gamma$ and $\mu$. Data for $\mu = 0 - 0.2$ are shifted upwards by 0.03, 0.025, 0.02, ..., 0.005 for clarity. Open symbols: Systems that are not yet in the steady state. Left shaded region: Elastic regime. Right shaded region: No compaction for $\Gamma > \Gamma_{\rm nc}(\mu)$; short lines mark $\Gamma_{\rm nc}(\mu)$. Dotted curves: Aging--fluidized boundary.
• Figure 2: Friction and shear amplitude dependence of aging, memory, and relaxation dynamics. See the color codes in $\Gamma$ on the left. (a) Van Hove function $G_s$ at $t=1$, showing the distribution of normalized $x$-directional displacements $d_x = |\delta x_i| / \sqrt{\langle\delta x^2_i\rangle}$ averaged over 300--1000 cycles, excluding the initial transient $t_w\Gamma = 20$. Gray dotted curves represent Gaussian distributions. Bold gray lines represent exponential functions that characterize the decay of $G_s$ in the crossover regime. (b) Mean squared displacements $\Delta r^2(t)$ for $t_w\Gamma = 20$. Solid curves indicate the solid-like aging regime with sub-diffusive motion, while dashed curves denote the fluidized regime showing normal diffusion. The solid gray line for $\mu = 1$ marks an intermediate sub-diffusive (creep-like) regime. (c) One-cycle displacement $\Delta x^2(1) = \langle\delta x_i^2(t_w, 1)\rangle$ for $\mu = 0$, $0.1$, and $1$, smoothed using a filter of size 15 in $t_w$. We mark $\Gamma_{\rm opt}$ for $\mu = 0$ and $0.1$. (d) Memory function corresponding to the data of panel (c), filtered with window sizes of 15 for $t_w \leq 100$ and 50 for $t_w > 100$. All results, except for panel (b), are averaged over 5--10 realizations.
• Figure 3: $\Gamma-\mu$ state diagram and dynamic intermittency. See Methods for definitions of local events, normalization, and clustering detection. (a) Dynamic state diagram showing the clustering level of the fastest 5% of particles, averaged over large $t_w$. Clustering level is determined by the ratio of the largest cluster size to the number of selected fast particles. Crosses mark the crossover strain $\Gamma_{\rm C}(\mu)$, identified from the Van Hove function in Fig. \ref{['Figure2']}(a). Dashed line shows $\Gamma_{\rm opt}(\mu)$ for $\mu \leq 0.2$ from compaction curves. Dash-dotted line shows the limit strain $\Gamma_{\rm nc}(\mu)$ above which compaction is absent, while the dotted line marks the elastic regime boundary, which is defined via the caged mean squared displacement. (b--d) Spatio-temporal maps of normalized particle displacements for selected $\mu$ and $\Gamma$ (marked by gray symbols in (A)). The horizontal axis spans 500 shear cycles, and the vertical axis corresponds to 40 spatial bins along the $x$-direction. (e) Packing fraction evolution for $\Gamma = 0.02$ and $\mu = 0$ and 1.0 from $t_w = 1000$ to $3000$. The two arrows indicate the configurations presented in panels (g) and (h). (f) Corresponding mean squared displacements $\Delta r^2(t_w = 1000, t)$. (g)(h) Correlation between local packing fraction changes (left) and normalized particle displacements (right) for $\mu = 0$ at $t_w = 1288$ and $1500$, respectively. $t_w = 1288$ marks a large avalanche event in (e). (i) Similar correlations for $\mu = 1$ at $t_w = 1100$. Panels (g-i) share the same color scale (bottom).
• Figure 4: (a--c) Average non-affine motion $D^2_{\rm min}$ over a complete strain loop ($\gamma = 0 \rightarrow \Gamma \rightarrow -\Gamma \rightarrow 0^*$) for three friction coefficients $\mu$ and various shear amplitudes $\Gamma$. See the color code for $\Gamma$ on the left. (d) Comparison of $D^2_{\rm min}$ at maximal strain $\gamma = \Gamma$ ($\blacksquare$, +, x) and after strain reversal $\gamma = 0^*$ ($\square$, $\bigcirc$, $\triangle$) for $\mu=0, 0.1$, and 1, respectively. The dashed line shows the scaling relation of $\Gamma^2$. Arrows mark the crossover strains $\Gamma_{\rm C} = 0.045$ for $\mu=0$ and $\Gamma_{\rm C}= 0.11$ for $\mu=0.1$, above which irreversible motion becomes dominant, as well as the elastic-aging boundary $\Gamma \approx 0.05$ for $\mu = 0.1$.
• Figure S1: Time evolution of packing fraction for varying friction coefficients and strain amplitudes. Temporal evolution of the packing fraction, $\phi(t_w)$, for five representative friction coefficients, $\mu$, under various strain amplitudes, $\Gamma$ (color-coded as indicated in the bottom right). Complementing Figs. 1(c--e) in the main text, the optimal strain amplitude for compaction, $\Gamma_{\rm opt}$, increases with $\mu$ for $\mu \lesssim 0.2$, but becomes less well-defined at higher $\mu$. In contrast, the threshold strain above which compaction is no longer effective, $\Gamma_{\rm nc}$, increases monotonically with $\mu$.