Elastic wave band gaps in a three-dimensional periodic metamaterial using the plane wave expansion method

•A periodic metamaterial is considered using spherical inclusions in a cubic lattice.•A novel Fourier series is proposed for representing this periodic configuration.•Resulting band diagrams are validated using the finite element method.•This periodic metamaterial yields low- to mid-frequency full band gaps in solids.•Geometric parameters that influence band gap formation are investigated. [Display omitted] In this work, a novel Fourier series expansion is proposed for representing periodic three-dimensional metamaterials consisting of spherical inclusions in a cubic lattice, which allows the application of the plane wave expansion (PWE) method for analyzing such media. This metamaterial may exhibit complete band gaps, thus being able to effectively attenuate elastic waves in all directions. The solutions yielded by the PWE method are rigorous at a lower computational cost when compared to the finite element (FE) method. Results are validated using the FE method, and the geometric parameters that influence the band gap formation mechanisms in this periodic medium are investigated.