Abstract
Complete phononic band gaps–frequency intervals that exclude elastic waves of every polarization–have so far been realized only in periodic phononic crystals, whose band structures are direction-dependent and defect-sensitive. Disordered stealthy hyperuniform composites have produced complete and isotropic photonic band gaps, but analogous elastic designs have so far fallen short. Here we show that pushing such composites to the ultradense inclusion packing fractions recently shown to be achievable–using stiff, high-mass-density disk inclusions embedded in a compliant, low-mass-density matrix–breaks this barrier. As inclusion packing fraction
ϕ
2
increases, the in-plane and out-of-plane polarization band gaps widen until they overlap, yielding the first complete and isotropic phononic band gap, which persists for systems as large as
N
=
4
,
000
disks. Full-wave finite-element calculations and Rayleigh quotient analysis show that conventional, lower-packing-fraction stealthy hyperuniform composites never achieve this overlap because nearly contacting inclusion pairs and large matrix pore regions keep the two polarization gaps apart. Our analysis further reveals a general microstructural requirement for complete phononic–but not photonic–band gaps: a high-volume-fraction, disconnected stiff phase embedded in a connected compliant matrix. These results establish a route to disordered media with large, direction-independent phononic band gaps for shielding, filtering, and guiding elastic waves across length scales, with potential applications ranging from thermal-phonon management in microdevices to sound, vibration, and seismic-wave insulation.