Mode I fracture toughness maximization of low-density architected materials

This paper presents a framework for systematically optimizing the fracture toughness of periodic beam lattice materials using topology optimization. We introduce a new normalization factor for fracture toughness based on the unit cell size arguing that it offers a more consistent and unambiguous basis for comparing different lattice microstructures than the conventional beam-length-based normalization. Our analysis demonstrates that the relative performance ranking of lattice topologies is significantly affected by the choice of normalization. Notably, when evaluated using this proposed unit-cell-based normalization, classical triangular and Kagome structures consistently demonstrate remarkably high fracture toughness, outperforming a demi-regular structure that appear superior under conventional beam-length normalization. This reinforces their established efficacy as high-performance lattice designs. The proposed optimization framework is applied to design lattice structures at low ( ρ ̄ = 1 % ) and moderate ( ρ ̄ = 15 % ) relative densities. Interestingly, the framework did not yield structures that surpassed the performance of the Kagome or triangular lattices when assessed with the proposed normalization factor. However, it is remarkable that when evaluated using the conventional beam-length-based normalization from the literature, the framework is able to generate a design that significantly outperforms the triangular and Kagome lattices, as well as a tension-dominated demi-regular structure, at moderate relative densities ( 5 % < ρ ̄ < 20 % ). This work highlights the critical influence of normalization choices on performance assessment and underscores the inherent efficiency of classical lattice topologies.