Long-range retarded elastic metamaterials: wave-stopping, negative, and hypersonic or superluminal group velocity

This paper investigates new phenomena in elastic wave propagation in metamaterials, characterised by long-range interactions. The kind of waves borne in this context unveil wave-stopping, negative group velocity, instability and hypersonic or superluminal effects, both for instantaneous and for nonlocal retarded actions. Closed form results are presented and a universal propagation map synthesizes the expected properties of these materials. Perspectives in physics, engineering and social dynamics are discussed.