  We propose a 3D-printed graded lattice made of hollow elliptical cylinders
(HECs) as a new way to design impact mitigation systems. We observe asymmetric
dynamics in the graded HEC chains with increasing and decreasing stiffness.
Specifically, the increasing stiffness chain shows an acceleration of the
propagating waves, while the decreasing stiffness chain shows the opposite.
From the standpoint of impact mitigation, the decreasing stiffness chain
combined with the strain-softening behavior of HECs results in an
order-of-magnitude improvement in force attenuation compared to the increasing
stiffness chain. We extend this finding to the graded 2D arrays and demonstrate
a similar trend of wave transmission efficiency contrast between the increasing
and decreasing stiffness lattices. The 3D-printed HEC lattices shown in this
study can lead to the development of a new type of impact mitigating and shock
absorbing structures.
