Stress Isotropization in Weakly Jammed Granular Packings

TL;DR

This study investigates how nonlinear stress responses near the unjamming transition in granular media lead to isotropic stress propagation, challenging traditional quadrupolar models and impacting the understanding of yielding in amorphous materials.

Contribution

It demonstrates through simulations that nonlinearities cause stress isotropization near the unjamming transition, supported by a continuum elastic model, offering new insights into plasticity in granular media.

Findings

Stress propagation becomes isotropic near unjamming.

Nonlinear effects dominate as confining pressure vanishes.

Supports continuum elastic model with simulation results.

Abstract

When sheared, granular media experience localized plastic events known as shear transformations which generate anisotropic internal stresses. Under strong confining pressure, the response of granular media to local force multipoles is essentially linear, resulting in quadrupolar propagated stresses. This can lead to additional plastic events along the direction of relative stress increase. Closer to the unjamming transition however, as the confining pressure and the shear modulus vanish, nonlinearities become relevant. Yet, the consequences of these nonlinearities on the stress response to plastic events remains poorly understood. We show with granular dynamics simulations that this brings about an isotropization of the propagated stresses, in agreement with a previously developed continuum elastic model. This could significantly modify the yielding transition of weakly-jammed amorphous media, which has been conceptualized as an avalanche of such plastic events.