An Overview of Additive Manufacturing of Triply Periodic Minimal Surface (TPMS) Structures

Triply periodic minimal surfaces (TPMS) are mathematically defined minimal surfaces that exhibit zero mean curvature and repeat periodically along all three Cartesian axes. They integrate mathematically defined geometry with extensive functional adjustability. Their smooth, non-self-intersecting topology enables systematic control over relative density and improves load transfer efficiency within the lattice. Their large surface area-to-volume ratios further enhance specific energy absorption (SEA) and enable diverse functional uses. Recent developments in additive manufacturing (AM) have made it easier to create TPMS structures. As a result, they are now considered as the architected materials that combine biological, thermal, and mechanical functions within a single framework. This study presents a comprehensive overview of the major TPMS structures. It further highlights several AM techniques used for their fabrication and provides a critical evaluation of how geometric design, relative density, and post-processing influence their mechanical and thermal performances. This work also discusses recent developments in graded and hybrid TPMS structures. It further identifies the main challenges and future research directions related to multi-material additive manufacturing and data-driven topology optimization.