Strut-Buckling Transformation Enabling Anomalous Density-Scaling Toughening Law in Ultralight Lattice Metamaterials

Lightweight lattice metamaterials attract considerable attention due to their exceptional and tunable mechanical properties. However, their practical application is ultimately limited by their tolerance to inevitable manufacturing defects. Traditional fracture mechanics of lattice metamaterials are confined to localized tensile failure of a crack-tip strut, overlooking the toughening effect of buckling instability in discrete struts around the crack front. Here, via a combination of additive manufacturing, numerical simulation, and theoretical analysis, this work identifies an anomalous power scaling law of specific fracture energy with relative density, where the scaling exponent shifts to negative values below a critical relative density. This anomalous toughening law stems from crack-tip blunting triggered by delocalized strut-buckling transformation at ultralow densities, which is universal across various lattice metamaterials with varying length scales, crack orientations, node connectivity, and component properties. By strategically harnessing strut buckling mechanisms, exceptionally high specific fracture toughness can be achieved at extremely low relative density, thereby addressing gaps in the material property design space. These findings not only provide physical insights into discrete lattice fracture but also offer design motifs for ultralight, ultra-tough lattice metamaterials.