Elastic
The elastic metamaterials use different parameters to achieve a negative refract index that are not electromagnetic. "a new design for elastic metamaterials that can behave either as liquids or solids over a limited frequency range may enable new applications based on the control of acoustic, elastic and seismic waves." \cite{Page_2011}
Acoustic
When sound enters into a kind of medium, like light, refraction and reflection both exist.When it comes to Acoustic metamaterials, by control different forms of sound, as with like electromagnetic waves, sonic waves can exhibit negative refraction. \cite{Guenneau_2007}