The fracture toughness of demi-regular lattices

Abstract

The properties of lattices are strongly influenced by their nodal connectivity; yet, previous studies have focused mainly on topologies with a single vertex configuration. This work investigates the potential of demi-regular lattices, with two vertex configurations, to outperform existing topologies, such as triangular and kagome lattices. We used finite element simulations to predict the fracture toughness of three elastic-brittle demi-regular lattices under modes I, II, and mixed-mode loading. The fracture toughness of two demi-regular lattices scales linearly with relative density ρ, and outperforms a triangular lattice by 15% under mode I and 30% under mode II. The third demi-regular lattice has a fracture toughness 𝐾 𝐼𝑐 that scales with √ ρ and matches the remarkable toughness of a kagome lattice. Finally, a kinematic matrix analysis revealed that topologies with 𝐾 𝐼𝑐 ∝ √ ρ have periodic mechanisms and this may be a key feature explaining their high fracture toughness.