Super-thin films follow the exact same 'universal law' to stop a bullet, even if they’re made of totally different stuff.
March 24, 2026
Original Paper
Universal inverse-cube thickness scaling of projectile penetration energy in ultrathin films
arXiv · 2603.22207
The Takeaway
Whether it is graphene, graphene oxide, or a simple plastic film, the energy required to shoot through them at high speed scales by the same inverse-cube law regardless of the material's chemistry. This discovery suggests that at the nanoscale, the resistance of a solid isn't about what it's made of, but a fundamental geometric property of how it's confined.
From the abstract
Ultrathin films of widely different materials exhibit a dramatic enhancement of projectile penetration resistance under high--velocity impact. Despite extensive simulations and experiments, a unifying physical explanation has remained elusive. Here we show that the thickness dependence of the specific penetration energy obeys a universal law, $E_p^*(h)=E_{p,\infty}^*+B h^{-3}$, independent of chemical composition and degree of disorder. The inverse--cube scaling is traced back to a finite--size