  A material's response to small but finite deformations can reveal the roots
of its response to much larger deformations. Here, we identify commonalities in
the responses of 2D soft jammed solids with different amounts of disorder. We
cyclically shear the materials while tracking their constituent particles, in
experiments that feature a stable population of repeated structural
relaxations. Using bidisperse particle sizes creates a more amorphous material,
while monodisperse sizes yield a more polycrystalline one. We find that the
materials' responses are very similar, both at the macroscopic, mechanical
level and in the microscopic motions of individual particles. However, both
locally and in bulk, crystalline arrangements of particles are stiffer (greater
elastic modulus) and less likely to rearrange. Our work supports the idea of a
common description for the responses of a wide array of materials.
