Mechanism of Coupling Twist Angle and Projectile Radius on Ballistic Impact Performance of Bilayer Phosphorene Membranes

This study employs coarse-grained molecular dynamics simulations to investigate the synergistic coupling between interlayer twist angle (0°–90°) and projectile radius (2–10 nm) on the ballistic impact performance of bilayer phosphorene membranes (radius: 48 nm). For projectiles ≤6 nm, twist angle minimally influences impact forces, velocity attenuation, or ballistic limit velocity, as failure remains localized near the impact site. However, cone wavefront morphology evolves significantly with twist—progressing from elliptical (axial ratio 1.44 at 0°) to circular (ratio 1.0 at 90°) while rotating counterclockwise. Crucially, for projectiles ≥8 nm, twist angle critically modulates mechanical response: maximum impact force fluctuates negligibly below 60° but surges by 38% and 82% at 90° for 8 and 10 nm, respectively, triggering global membrane failure through amplified reflection and interference of cone waves. This stems from twist-dependent geometric mismatch between wavefront shape and membrane boundaries, which governs wave reflection intensity. Minimal mismatch at 90° twist maximizes force amplification, reducing ballistic limit by 28% (e.g., from 610 m/s at 0° to 440 m/s for projectiles = 10 nm). Our findings establish projectile radius as a threshold parameter that activates twist angle’s influence on impact resistance: below 6 nm, failure is local and twist-insensitive; above 8 nm, global failure emerges and is dominated by twist-mediated wave-boundary interactions, with 90° configurations exhibiting peak vulnerability. These results provide actionable guidelines for designing phosphorene-based nano-armor, emphasizing optimization of twist angle relative to anticipated projectile scales to maximize impact protection.