Sheared amorphous solids, pure and simple

Disordered materials, such as jammed packings of soft spheres, will become unstable and rearrange when strained past their elastic limit. A great deal of work has been focused on predicting where and when these rearrangements will occur, yet much remains unexplored about the instabilities themselves. Here, we probe particle rearrangements in a simulation with periodic boundary conditions. We continuously control the direction of the applied shear strain, θ, by combining pure and simple shear with different amplitudes. This gives rise to a two-dimensional parameter space with, for example, θ and shear amplitude, γ, as the two axes. We find that some instabilities persist over a surprisingly large variation of the shear direction with a characteristic shape γ(θ). We use this new technique to map out pairs of instabilities that pass through each other and to measure the persistence of paired rearrangements that are elementary units of hysteretic behavior in the packing.