Triply Periodic Minimal Surface (TPMS) Cellular Structures: Modeling, Manufacturing, and Application Perspectives—A Review

Triply Periodic Minimal Surfaces (TPMSs) represent a progressive class of cellular materials with high potential for high-tech applications. This review provides a comprehensive analysis of TPMS architectures, linking their mathematical underpinnings and advanced CAD modeling in PTC Creo Parametric 12 with technological aspects of additive manufacturing and macroscopic mechanical response. The work critically compares dominant topologies such as Schoen Gyroid, Schwarz Diamond, and Schwarz Primitive, focusing on the differences between uniform and functionally graded (FG-TPMS) structures. From a production perspective, this study identifies key process limitations of PBF-LB/M and SLA additive technologies, in particular the issues of unsintered powder accumulation, geometric deviations, and the negative impact of surface roughness (satellite particles) on fatigue life. Analysis of mechanical behavior confirms the superiority of sheet-based modifications in kinetic energy absorption, where specifically tailored FG-TPMS topologies exhibit stable deformation plateaus and controlled, progressive failure modes under compression. The conclusion of the work summarizes established applications in biomedical engineering for the elimination of stress shielding, as well as emerging trends in the field of 4D printing and acoustic metamaterials. This review serves as a comprehensive engineering guide for the optimization and implementation of next-generation porous structures.