Investigation of torsional and fatigue resistance properties based on triply periodic minimal surfaces (TPMS)

Abstract Triply periodic minimal surfaces (TPMS) are algebraic surfaces found in nature, defined by implicit functions, and exhibit exceptional properties in various fields such as mechanics, computer graphics, and tissue engineering. This study focuses on four common minimal surface structures: Gyroid, Diamond, I-WP, and Schwarz P structures, and presents two methods for converting these surfaces into TPMS cells. These four surface structures are converted into TPMS cells, which are then organized into TPMS cylindrical units for finite element analysis. Through a comparison of the torsional mechanical properties of different minimal surfaces using the finite element method, the stress-strain curves of TPMS were generated. The findings suggest that the Schwarz P cylindrical structure remains within the elastic deformation stage under the same load, with a stress-load curve exhibiting a smaller slope, indicating superior torsional resistance. Additionally, a fatigue strength analysis of various minimal surface structures revealed that, under equivalent load conditions, the fatigue life of the Schwarz P cylindrical structure tends towards infinity.