Buckling controls Wave Propagation in Elastic Phononic Crystals

Elastic Phononic Crystals (EPC) are soft deformable metamaterials that have periodic modulations in material properties such as shear modulus, bulk modulus, and density, whose microstructure is characterized by a repeatable region called the unit cell. The dispersion relation, described by band diagrams, of waves propagating through phononic crystals is affected not only by material properties but also by symmetry properties of the crystal. It has previously been shown that buckling of compressed EPCs can tune wave propagation properties – for example, by decreasing the number of intersections (degeneracies) in the band diagram, potentially leading to the opening of band gaps. Since buckling also changes the symmetries of the EPC, we have previously used a group representation theory (GRT)-based framework to explain the effect of primitive unit cell symmetries on degeneracies in the band diagram for undeformed EPCs. However, the periodic unit cell of buckled EPCs can also span several primitive unit cells of the reference undeformed EPC. Thus, we extended our GRT framework to include the effect of buckling-induced symmetry-breaking in larger unit cells on band diagrams of deformed EPCs. By understanding the interplay between elastic instability and symmetry of EPCs at different length scales and its impact on wave propagation properties, we can potentially formulate rational design rules for deformation-tunable EPCs.