Universal inverse-cube thickness scaling of projectile penetration energy in ultrathin films

TL;DR

This study uncovers a universal inverse-cube law governing projectile penetration energy in ultrathin films, linking nanoscale impact resistance to elastic properties across diverse materials.

Contribution

It reveals a universal inverse-cube scaling law for penetration energy and explains it through a finite-size correction to shear modulus, applicable to various ultrathin materials.

Findings

Penetration energy follows a universal law: $E_p^*(h)=E_{p, ext{infinity}}^*+B h^{-3}$.

Scaling applies to multilayer graphene, graphene oxide, and polymer films.

Elastic origin of nanoscale impact resistance is demonstrated.

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 correction to the effective shear modulus arising from the suppression of long--wavelength nonaffine deformation modes in confined solids. The scaling quantitatively describes impact data for multilayer graphene, graphene oxide, and polymer thin films, revealing a common elastic origin for nanoscale impact resistance.