  Topological acoustic and elastic waves have recently emerged as an exciting
interdisciplinary field which is still mainly focused on low-dimensional
structures and model systems. Here we demonstrate numerically an elastic-wave
analogue of topological node-lines in three-dimensional mechanical metacrystals
with ribbon- or drumhead-like surface states. These two-dimensional topological
surface states offer unprecedented, robust subwavelength confinement of elastic
waves. Design principles for topological mechanical metamaterials, from both
material and symmetry aspects, are unveiled and connected to fundamental
conservation laws and nonsymmorphic space group. Our study paves the way toward
the synergy between three-dimensional mechanical metamaterials and topological
wave dynamics.
