ArticleProceedings of the National Academy of Sciences of the United States of America2026
General inverse-cube thickness scaling of projectile penetration energy in ultrathin films.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2026. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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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 specific penetration energy follows a general inverse-cube scaling law, [Formula: see text], across chemically and structurally distinct systems. The inverse-cube scaling is traced to a finite-size correction to the effective shear modulus caused by suppression of long-wavelength nonaffine modes. The scaling describes impact data for multilayer graphene, graphene oxide, and polymer thin films, revealing a common elastic contribution to nanoscale impact resistance.
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