Cross-property relations for triply periodic minimal surface (TPMS) structures

Triply periodic minimal surface (TPMS) structures are distinguished by their potential for multifunctional applications. Establishing cross-property relations within these microstructures enables rapid estimation of multiple physical properties and simplifies multi-objective optimization. In this study, the relation between elastic modulus and thermal conductivity in TPMS structures is explored through homogenization with voxel models and finite element method. All analyses are compared with the theoretical Voigt-Reuss bounds and Hashin-Shtrikman bounds to ensure accuracy. Gradient TPMS structures and random TPMS structures are generated for six common types of TPMS structures. The results indicate that within a error of 10%, the cross-property relations of each TPMS structure exhibit universality. Additionally, the cross-property relations of composite TPMS structures and interpenetrating phase composite structures are investigated, and the results suggest that they may possess superior properties of 5% compared to single TPMS structures. • Cross-property relations are constructed for triply periodic minimal surface (TPMS) structures. • For gradient and random TPMS structures, the variations in cross-property relations are relatively minor. • Composite TPMS structures may exhibit superior properties compared to single TPMS structures. • The influence of the interpenetrating phase composite TPMS structures is primarily reflected in the distribution range of properties.