Fig. 1: Phononic bandgap closing induced by uniaxial tension.

a Unit cell of the honeycomb lattice with redistributed tension (top) and the corresponding first Brillouin zone (bottom). b Phononic band structure for the unit cell shown in a under uniform tension (σ_xx = σ_yy = 0.01 N m⁻¹). For out-of-plane modes (solid lines) a clear phononic bandgap is visible (blue shaded region). The insets show the mode shape (displacement) within the unit cell at the points above and below the bandgap. c, d Phononic band structure and tension distribution in the unit cell (insets) for σ_xx/σ_yy of 1.35 and 1.7. With increasing uniaxiality in tension (σ_xx/σ_yy > 1), the phononic bands show different frequency scaling behaviour along different high symmetry lines. At σ_xx/σ_yy = 1.7, the phononic bandgap closes. e Phononic bandgap for biaxial (red) and uniaxial (blue) tension vs. total normalised tension. When the tension is increased biaxially (σ_xx = σ_yy), the bandgap centre frequency rises, and the bandgap width increases. On the contrary, uniaxial upscaling (σ_xx > σ_yy) leads to a bandgap closing.