Stress Isotropization in Weakly Jammed Granular Packings

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 the increase in relative stress. 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 remain 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.