Robustly Tuning Bandgaps in Two-Dimensional Soft Phononic Crystals with Criss-Crossed Elliptical Holes

Tuning band gaps in soft materials by post-buckling deformation is becoming an appealing means to manipulate elastic waves. As one of the most favorable topologies, two-dimensional soft structures with circular holes have been extensively studied. Based on the contrarian thinking, this paper starts from the two-dimensional soft structures with criss-crossed elliptical holes, which is close to the post-buckling configuration of soft structures with circular holes, and then proposes to tune the band gaps through elongating or stretching rather than compressing. Influences of the loading magnitude and loading pattern (i.e., uniaxial and biaxial elongations) on the band gaps are studied via the nonlinear finite element simulations. Effects of the geometric parameters (the major-to-minor half-axis ratio and the porosity of the structure) are also discussed. It is shown that, compared with the traditional circular hole case, the band gaps of the unloaded structure with criss-crossed elliptical holes are much richer, and they could be reversely and continuously tuned by tensile loadings. In particular, the deformation is very robust and is insensitive to small geometric imperfections, which is always necessary for triggering the post-buckling deformations. The present work provides a useful reference to the manipulation of elastic waves in periodic structures as well as the design of soft phononic crystals/acoustic devices.