Programmable materials hold great potential for many applications such as deployable structures, soft robotics, and wave control; however, the presence of instability and disorder might hinder their utilization. Through a combination of analytical, numerical, and experimental analyses, we harness the interplay between instabilities, geometric frustration, and mechanical deformations to control the propagation of sound waves within self-assembled soft materials. We consider levitated magnetic disks confined by a magnetic boundary in-plane. The assemblies can be either ordered or disordered depending on the intrinsic disk symmetry. By applying an external load to the assembly, we observe the nucleation and propagation of different topological defects within the lattices. In the presence of instabilities, the defect propagation gives rise to time-independent localized transition waves. Surprisingly, in the presence of frustration, the applied load briefly introduces deformation-induced order to the material. By further deforming the lattices, new patterns emerge across all disk symmetries. We utilize these patterns to tune sound propagation through the material. Our findings could open new possibilities for designing exotic materials with potential applications ranging from sound control to soft robotics.

• Received 12 March 2021
• Revised 20 September 2021
• Accepted 4 October 2021

DOI:https://doi.org/10.1103/PhysRevB.104.L140101