  The question of how a disordered material's microstructure translates into
macroscopic mechanical response is central to understanding and designing
materials like pastes, foams and metallic glasses. Here, we examine a 2D soft
jammed material under cyclic shear, imaging the structure of ~50,000 particles.
Below a certain strain amplitude, the structure becomes conserved at long
times, while above, it continually rearranges. We identify the boundary between
these regimes as a yield strain, defined without rheological measurement. Its
value is consistent with a simultaneous but independent measurement of yielding
by stress-controlled bulk rheometry. While there are virtually no irreversible
rearrangements in the steady state below yielding, we find a largely stable
population of plastic rearrangements that are reversed with each cycle. These
results point to a microscopic view of mechanical properties under cyclic
deformation.
