An isogeometric approach for analysis of phononic crystals and elastic metamaterials with complex geometries

An isogeometric analysis (IGA) framework is presented to construct and solve dispersion relations for generating the band structure of periodic materials with complicated geometries representing phononic crystals and elastic metamaterials. As the dispersive properties depend on the microstructural geometry, an accurate representation of microstructural geometrical features is paramount. To this end, the ability of isogeometric analysis to exactly model complex curved geometries is exploited, and wave propagation in infinitely periodic solids is combined with isogeometric analysis. The benefits of IGA are demonstrated by comparing the results to those obtained using standard finite element analysis (FEA). It is shown that the IGA solutions can reach the same level of accuracy as FEA while using significantly fewer degrees of freedom. IGA is applied to phononic crystals and elastic metamaterials and the band structure for a variety of unit cells with complex microstructural geometries is investigated to illustrate the desirable dispersive effects in these metamaterials.