Directional stretching effects on frequency bandgaps of 2D periodic lattices

Abstract

This study investigates the potential for modulating and tuning the frequency bandgaps of 2D lattice materials using uniform strain fields to provide a path for realizing continuous and predictable tuning over a range of strains. Accordingly, it analyzes the effect of multiple levels of in-plane uniform strain fields on the frequency bandgaps in the range of 0 to 1000 kHz of three lattices comprising hexagonal, Kagome, and anti-chiral topologies. Two strain directions and three levels are considered. A finite element framework is used to evaluate the bandgap behavior of each lattice at relative densities ranging from 5% to 30%. The results show that lattices exhibit a distinct response to stretching. In hexagonal honeycombs, stretching generally increases wave transmissibility by narrowing or eliminating existing bandgaps, particularly in the higher frequency range. Kagome lattices exhibit more complex and strain-directional behavior, where large lateral strains increase the number of bandgaps in a non-monotonic manner, while axial strains significantly reduce the number of bandgaps. The anti-chiral lattices retain a rich bandgap structure under all conditions. Across all lattices, the applied strains switched bandgaps on and off, induced bandgap shifts up to 50% (honeycomb), and narrowed bandgaps widths by as much as 60% (Kagome). Strain-induced activation/deactivation, shifting, and narrowing exhibited a complex and strong dependence on relative density. Overall, the results demonstrate that lattice topology, strain mode, and relative density can be used collectively to tailor and modulate frequency bandgaps, offering a practical path for designing programmable and reconfigurable metamaterials.