  Space-time metamaterials, or materials with properties changing in space and
time, have gained a wide-spread interest due to their exotic properties. In
this Letter, we propose a novel temporal metasurface of phononic crystals in
one and two-dimensions, that combines the use of nonlocal interactions in
phononic crystals to customize dispersion relations, and the use of temporal
interfaces to transition from a local material to a nonlocal material and
vice-versa, to achieve the interesting phenomenon of \textit{wave-freezing},
where the entire propagating wave is stopped without diffusing or spreading.
The phononic crystals are modeled using spring-mass systems and we use finite
difference calculations to present our numerical results. We also demonstrate
other effects observed in such temporal metasurfaces, such as time-reversed
waves, and anomalous temporal refraction.
