Fragility and hysteretic creep in frictional granular jamming

TL;DR

This study investigates the fragile and hysteretic behavior of frictional granular packs during jamming, revealing how friction controls the fragile state, influences hysteresis, and causes creep towards stable configurations under repeated compression.

Contribution

It introduces the concept of fragility in the first compression cycle, linking it to a percolation mechanism and demonstrating how friction controls the fragile state and hysteretic creep.

Findings

Fragile state exists between two packing fractions with exponential pressure and displacement changes.

Friction coefficient influences the onset and slope of the fragile state.

Repeated compression causes hysteresis and slow increase in jamming threshold, indicating creep.

Abstract

The granular jamming transition is experimentally investigated in a two-dimensional system of frictional, bi-dispersed disks subject to quasi-static, uniaxial compression at zero granular temperature. Currently accepted results show the jamming transition occurs at a critical packing fraction $\phi_c$. In contrast, we observe the first compression cycle exhibits {\it fragility} - metastable configuration with simultaneous jammed and un-jammed clusters - over a small interval in packing fraction ($\phi_1 < \phi < \phi_2$). The fragile state separates the two conditions that define $\phi_c$ with an exponential rise in pressure starting at $\phi_1$ and an exponential fall in disk displacements ending at $\phi_2$. The results are explained through a percolation mechanism of stressed contacts where cluster growth exhibits strong spatial correlation with disk displacements. Measurements with several disk materials of varying elastic moduli $E$ and friction coefficients $\mu$, show friction directly controls the start of the fragile state, but indirectly controls the exponential slope. Additionally, we experimentally confirm recent predictions relating the dependence of $\phi_c$ on $\mu$. Under repetitive loading (compression), the system exhibits hysteresis in pressure, and the onset $\phi_c$ increases slowly with repetition number. This friction induced hysteretic creep is interpreted as the granular pack's evolution from a metastable to an eventual structurally stable configuration. It is shown to depend upon the quasi-static step size $\Delta \phi$ which provides the only perturbative mechanism in the experimental protocol, and the friction coefficient $\mu$ which acts to stabilize the pack.