Correlation between the structural geometry and damage localization of Triply periodic minimal surface-based ceramic unit cells

Inspired by porous structures in nature, artificial porous materials are manufactured for a wide range of applications. Compared with other porous structures, Triply periodic minimal surfaces (TPMS) have the following significant features: the geometries can be completely expressed via mathematical functions; TPMS are periodic in three directions; the mean curvature of TPMS is zero, providing highly interconnected architecture, and TPMS can be easily printed as construction elements after microstructure optimization for prescribed loading. In the presented studies, the compression failure of four typical TPMS structures with the same volume fraction was investigated using Finite element (FE) analysis. They are Primitive, Gyroid, Neovius, and IWP. Considering the critical influence of structural geometry on failure behavior, a computational approach was developed to analyze the surface inclination angle and estimate the cross-sectional area within each TPMS structure. After that, the distributions of cross-sectional area, inclination angle, and damage localization were compared to assess their interrelated effects within each TPMS. The stress concentration along the cross-sections and throughout the inclined surface was also studied to understand the influence of local geometry on crack development. Finally, the crack propagation observed in this study was compared with experimental results to evaluate the geometric effect of unit cells on periodic structures.