Elastic metamaterials and effective medium theory

The unusual properties of a metamaterial are induced by the resonance in its building blocks. We derived an effective medium theory for elastic metamaterials in two dimensions, which is capable of predicting the wave propagation behavior inside the metamaterial near resonances of the building-block. It reveals the connection between resonances and negativities in effective medium parameters. Based on the EMT, we design two types of elastic metamaterials consisting of different resonance structures in their building blocks that can exhibit multiple negative dispersion bands with special characteristics. One is able to produce negative shear modulus and negative mass density simultaneously over a frequency regime, and the other is super-anisotropic. All of these unusual properties are demonstrated by multiple-scattering theory or finite element simulations.