Elastic Wave Propagation and Bandgaps in Finitely Stretched Soft Lattice Material

Abstract

In this study, the in-plane Bloch wave propagation and bandgaps in a finitely stretched square lattice were investigated numerically and theoretically. To be specific, the elastic band diagram was calculated for an infinite periodic structure with a cruciform hyperelastic unit cell under uniaxial or biaxial tension. In addition, an elastodynamic "tight binding" model was proposed to investigate the formation and evolution of the band structure. The elastic waves were found to propagate largely under "easy" modes in the pre-stretched soft lattice, and finite stretch tuned the symmetry of the band structure, but also "purify" the propagation modes. Moreover, the uniaxial stretch exhibits the opposite impacts on the two "easy" modes. The effect of the biaxial stretch was equated with the superposition of the uniaxial stretches in the 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. Next, the finite stretch could tune the directional bandgap of the soft lattice, and the broadest elastic wave bandgaps could be anticipated in an equi-biaxial stretch. In this study, an avenue was opened to design and implement elastic wave control devices with weight efficiency and tunability. Furthermore, the differences between the physical system and the corresponding simplified theoretical model (e.g., the theoretically predicted flat bands) did not exist in the numerical calculations.