Critical behaviors of jamming in cyclically sheared frictional hard granular particles

TL;DR

This study reveals that frictional granular particles under cyclic shear self-organize near a critical jamming state, exhibiting scale-free velocity fluctuations and diverging length scales, advancing understanding of granular jamming.

Contribution

It demonstrates the critical jamming behavior of frictional granular packings under cyclic shear, supported by quantitative agreement with effective medium theory.

Findings

Scale-free velocity fluctuations with power spectra $E(k) \,\propto\, k^{-\alpha}$, $\alpha \approx 2.0$

Nearly flat spectra $E(\omega) \propto \text{const}$ in frequency domain

Identification of two diverging length scales associated with modes

Abstract

In stark contrast to the jamming of frictionless hard-sphere (hard-disk if in two dimensions) packings, the critical jamming of frictional packings is much more elusive and still under intense debate. Here we show that frictional hard-disk packings self-organize near a critical jamming state when subjected to quasi-static steady-state cyclic shear, displaying scale-free fluctuations in particle velocity fields as characterized by the power spectra $E(k)\propto k^{-\alpha}$ for both longitudinal and transverse modes in wavevector space, with $\alpha\approx2.0\pm0.15$, and the nearly flat spectra $E(\omega)\propto const.$ in angular frequency domain. Our findings agree quantitatively with the predictions of the Langevin-type effective medium theory of S. Henkes and coworkers with two diverging length scales associated respectively with the longitudinal and transverse modes, showing a hallmark of critical behaviors of jamming. Moreover, our findings are consistent with the conceptual framework of general isostaticity but with a key difference that the system self-organizes to a critical jamming state through a strong coupling of mechanical structure and dynamics. Our findings are important in providing microscopic mechanism in understanding the nonlocal rheologies and guide principles in developing constitutive relations of real granular materials.