Band Gaps in Bravais Lattices Inspired Periodic Cellular Materials and the Effect of Relative Density and Strain Fields

Abstract

Periodic cellular (lattice) materials, by virtue of their periodic structures and associated geometric impedance mismatch, exhibit wave dispersion, frequency dependent transmissibility, and directional characteristics that are inherently dependent on their constituent material and mesoscale microstructural features. These characteristics render lattice materials as potential candidates to perform as low frequency phononic crystals and metamaterials for radar, sonar, wave guiding, wave modulation and isolation applications. Accelerating the wide-spread implementation of lattice materials as phononic crystals hinges on establishing the ability to engineer them to exhibit application-tailored properties and tunable behavior (e.g. to activate/deactivate band gaps). Achieving tunability and application-oriented tailorablity requires, first, establishing an understating of phononic, acoustic, wave dispersion and directional properties of the lattices and how they are affected by lattices’ inherent features. Accordingly, using Bloch’s theorem in conjunction with finite element analysis, this work investigates the relationships between inherent microstructural features (such as lattice symmetry, relative density (i.e. volume fraction) and constituent material) and the acoustic properties (such as wave dispersion, band gaps, and acoustic anisotropy) of architectured lattice materials. The coupling between microstructural features and band gaps is investigated in a hexagonal lattice geometry which is inspired by the two dimensional Bravais family of lattices. Results illustrate that band structure and phononic properties are highly sensitive to relative density and can scale non-uniformly with it as eigenmodes are associated with relative density dependent deformation mechanisms. Moreover, results show that band gaps can potentially be activated and deactivated using macroscopic strain fields. The latter opens horizons for realizing cellular based phononic crystals with tunable properties.