  The nature of yield in amorphous materials under stress has yet to be fully
elucidated. In particular, understanding how microscopic rearrangement gives
rise to macroscopic structural and rheological signatures in disordered systems
is vital for the prediction and characterization of yield and for the study of
how memory is stored in disordered materials. Here, we investigate the
evolution of local structural homogeneity on an individual particle level in
amorphous jammed two-dimensional systems under oscillatory shear, and relate
this evolution to rearrangement, memory, and macroscale rheological
measurements. We identify a new structural metric, crystalline shielding, that
is predictive of rearrangement propensity and the structural volatility of
individual particles under shear. We use this metric to identify localized
regions of the system in which the material's memory of its preparation is
preserved. Our results contribute to a growing understanding of how local
structure relates to dynamic response and memory in disordered systems.
