We present a full acoustic band structure calculation for periodic elastomeric solids at different levels of deformation. We demonstrate the ability to use deformation to transform phononic band gaps. Periodic elastomeric structures are subjected to axial compression and are found to undergo a transformation in their patterned structure upon reaching a critical value of applied load. During the initial linear regime of the nominal stress-strain behavior, the band gaps evolve in an affine and marginal manner. Upon reaching the critical load, the pattern transformation is found to strongly affect the in-plane phononic band gaps, resulting in the closure of existing band gaps and in the opening of new ones. The elastomeric nature of the material makes the transformation in both structural pattern and phononic band gap a reversible and repeatable process, creating a phononic band gap switch.

• Received 9 January 2008

DOI:https://doi.org/10.1103/PhysRevB.77.052105