Hierarchical sheet triply periodic minimal surface lattices: design, geometric and mechanical performance

Lattices with hierarchical architectures exhibit unique geometric and mechanical properties compared with single scale ones. While numerous research efforts have focused on hierarchical strut lattices, hierarchical sheet lattices have yet to be studied in detail. This paper proposes a systemic framework including geometric design, finite element modelling, additive manufacturing, and mechanical testing for hierarchical sheet triply periodic minimal surface (TPMS) lattices such that the lattice walls comprise successively smaller scale TPMS architectures. Geometric properties including relative densities and volume-specific surface areas of hierarchical lattices are analytically calculated and verified via numerical calculations. The compressive properties of 2-order sheet Gyroid lattices are investigated with finite element simulations and experimentally validated using micro-selective laser melting fabricated stainless-steel specimens. Geometric analysis shows that hierarchical sheet lattices have great potential to achieve a wide range of controllable geometric properties including hierarchical porosities, ultralow densities, and significantly enlarged surface areas. Simulation results indicate that 2-order lattices have superior buckling strength over single scale lattices at ultralow densities. At moderate densities, 2-order lattices exhibit reduced modulus and strength, but more stable failure behaviour. With these unique combinations of geometric and mechanical properties, hierarchical sheet TPMS designs are shown to be desirable structural configurations for biomedical scaffolds.