  We report an experimental and numerical demonstration of dispersive
rarefaction shocks (DRS) in a 3D-printed soft chain of hollow elliptical
cylinders. We find that, in contrast to conventional nonlinear waves, these DRS
have their lower amplitude components travel faster, while the higher amplitude
ones propagate slower. This results in the backward-tilted shape of the front
of the wave (the rarefaction segment) and the breakage of wave tails into a
modulated waveform (the dispersive shock segment). Examining the DRS under
various impact conditions, we find the counter-intuitive feature that the
higher striker velocity causes the slower propagation of the DRS. These unique
features can be useful for mitigating impact controllably and efficiently
without relying on material damping or plasticity effects.
