Interplay between rearrangements, strain, and softness and during avalanche propagation*

Disordered solids yield at a common shear strain of about 3%, but the behavior beyond yield is different for different systems and for systems with different histories. Foams can deform indefinitely without fracturing, many systems exhibit crackling noise or avalanche behavior, and still others exhibit shear banding and brittle fracture. Here we study an athermal, jammed packing of Hertzian particles that is sheared quasistatically. We identify the stress drops associated with rearrangements and then use steepest descent dynamics to study the evolution of the avalanches. We find that the avalanches consist of localized events that appear sequentially in well-separated locations of the sample. To understand this behavior, we study the interplay between rearrangements, strain, and softness, a machine-learned structural descriptor that predicts the propensity of a particle to rearrange. We find that each rearrangement gives rise to a shear strain field that can immediately trigger other rearrangements, while also causing an isotropic strain field that changes the softness of other particles; this may affect subsequent rearrangements over a much longer time scale. We compare our results to elasto-plastic and mean-field models of avalanches.