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We propose a type of elastic metamaterial comprising fluid-solid compositeinclusions which can possess negative shear modulus and negative mass densityover a large frequency region. Such a solid metamaterial has a unique elasticproperty that only transverse waves can propagate with a negative dispersionwhile longitudinal waves are forbidden. This leads to many interestingphenomena such as negative refraction, which is demonstrated by using a wedgesample, and a significant amount of mode conversion from transverse waves tolongitudinal waves that cannot occur on the interface of two natural solids.

Elastic metamaterials with simultaneously negative effective shear modulus and mass density