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To bridge the theoretical gap in cellular mechanics at relative densities exceeding 30%, this work couples continuum homogenization with blunt-crack fracture theory to predict mode-I fracture toughness across triangular and hexagonal lattices. The framework reveals that high-density lattices shift from classical beam-bending failure to nodal stress concentrations strongly governed by fillet radii, orientation, and crack-tip morphology. Validated through finite element simulations and physical tests on laser-cut PMMA, the analysis reveals that quasi-brittle lattices can achieve a 1.6x toughness gain over brittle baselines and even surpass the fracture toughness of their solid constituent material when cell size exceeds the plastic zone radius.
Architected lattices can remarkably exceed the fracture toughness of their own solid constituent material, but only when unit cell dimensions are scaled beyond the base material's intrinsic plastic zone radius.
Lattice materials have highly tunable mechanical properties that are controlled by their internal geometry and base material behavior. While fracture models for low-density lattices are well-established, the fracture of lattices at relative densities above 30% remains largely unexplored. Here, we present an analytical model that combines homogenization methods and blunt-crack fracture theory to predict the fracture toughness of triangular and hexagonal lattices over a wide range of relative densities. Finite element modeling corroborates the analytical framework and demonstrates a shift in failure mechanisms between low and high relative density regimes. At high relative densities, failure is dominated by nodal stress concentrations, which are strongly influenced by the local crack-tip geometry and the macroscopic crack path. Significant stress redistribution is observed as the relative orientation and lattice fillet radius are varied, resulting in increased fracture toughness relative to baseline geometries. Furthermore, quasi-brittle poly(methyl methacrylate) (PMMA) lattices achieve about a 1.6x enhancement in fracture toughness relative to perfectly brittle lattices as failure is delayed by localized plasticity. Notably, some quasi-brittle lattices are found to exceed the fracture toughness of their base material -- a feature only possible when the cell size is large compared to the base material's plastic radius. Experiments on lattice fracture specimens made from laser-cut PMMA validate the finite element results, but highlight the stochastic nature of failure in brittle lattice materials, especially at higher relative densities.