Dynamic Homogenization of Metamaterials: Nonlocal Effects and Additional Constitutive Parameters

We present a dynamical homogenization method for acoustic and elastic metamaterials based on periodic arrangements of inclusions. The method allows for the calculation of the frequency-dependent effective parameters. It is shown that they are also spatially dispersive (nonlocal). Additionally, new constitutive parameters, which can also be accurately computed in the framework of the present theory, are found in the homogenization process. Several propagation regimes concerning these nonlocal effects are studied and some examples are given