Phononic crystals (PCs) have attracted plenty of attention due to their specific physical properties (such as band gap structures, negative refraction, etc.), therefore have the potential applications as wave filter, acoustic waveguide, vibration isolator, and so on.

However, the band gaps of PCs are always fixed after the design/fabrication of corresponding devices, which are related to the material contrast between matrix and inclusion, the lattice structure arrangement, the filling fraction ratio, therefore limit the application with varying requirement. It is valuable to make the PCs with tunable BGs through external stimuli, such as mechanical loading, electric fields, magnetic fields and so on.

In this work, the effects of post-buckling deformation induced by external mechanical loadings on the band gaps of soft PCs with simplified grid lattice structures are systematically studied through the commercial software ABAQUS plus own developed python script codes. It is found that the post-buckling deformation can significantly alter the configuration of a basic unit cell and result in the different band gaps, and the high order post buckling deformation is more diverse in tune the band gaps, which can be triggered by the introducing of corresponding  geometric imperfections