Stiffness and strength enhancement of hierarchical TPMS-based shell lattices via inter-level conformal design

Hierarchical structures in nature provide a blueprint design principle for engineering advanced lattice structures with enhanced mechanical properties and multifunctional performance. However, traditional Boolean-operation-based hierarchical lattices with incomplete second-level lattice structures at the boundaries, often suffer from localized deformation and stress concentration, limiting their stiffness and strength. Here, we introduce an inter-level conformal design for constructing hierarchical shell lattices that exhibit superior mechanical properties. By integrating a parameterized Monge patch model with iso-parametric transformation techniques, we achieve geometric conformity across multiple hierarchical levels. Numerical simulations with experimental validation reveal that inter-level conformal hierarchical triply periodic minimal surface (TPMS) shell lattices outperform their non-conformal Boolean-operation-based counterparts in stiffness, strength, and specific energy absorption by 28.4 %, 47.3 %, and 48.1 %, respectively. Such performance enhancement stems from the inter-level conformal design, which eliminates structural discontinuities and geometric truncations, prevent degrading the mechanical performance and introducing deadweight. Additionally, inter-level conformal architectures mitigate anisotropy, resulting in lower anisotropic Zener and Poisson's ratios. A statistical analysis of deformation mechanisms in hierarchical TPMS-based lattices reveals that both inter-level conformal and non-conformal designs exhibit a Weibull distribution of deformation behaviors. Notably, inter-level conformal designs are effective to reduce the stress localization, resulting in higher mechanical performance. These findings highlight the potential of inter-level conformal hierarchical design in enhancing the stiffness and strength of lattice structures, offering new opportunities for the design of high-performance lattice metamaterials across diverse engineering applications.