Bloch wave propagation in finitely stretched soft lattice

Abstract

In this study, the in-plane Bloch wave propagation in a finitely stretched square lattice is investigated numerically and theoretically. Precisely, the elastic band diagram is calculated for an infinite periodic structure with a cruciform hyperelastic unit cell under uniaxial or biaxial tension. Meanwhile, an elastodynamic tight-binding model is proposed to investigate the formation and evolution of the band structure. In said lattice, the finite stretch was found to not only tune the symmetry of the band structure but also purify the elastic waves into easy modes. The uniaxial stretch exhibits the opposite impacts on the evolution of two easy modes, while the effect of the biaxial stretch is equated with the superposition of the uniaxial stretches in the two tessellation directions. The mentioned effects on the band structure could be attributed to the competition between the effective shear moduli and lengths for different beam components. As a result, the finite stretch could tune the directional elastic wave bandgap of the soft lattice, and the broadest bandgap could be anticipated in an equi-biaxial stretch. This study may shed some light on the design and implementation of elastic wave control devices with weight efficiency and tunability. It also reveals that the theoretically predicted flat bands did not exist in the numerical calculations, a difference between the physical system and the corresponding simplified theoretical model.