A fast evaluation method for surface area, volume fraction, and hydraulic diameter of TPMS with different geometric characteristics

The utilization of triply periodic minimal surface (TPMS) structures, fabricated through additive manufacturing techniques, in engineering applications has garnered considerable attention. However, existing studies have largely overlooked the intricate relationship between design parameters and key geometric indices such as surface area, volume fraction, and hydraulic diameters, along with their distribution patterns. This study aims to fill this gap by conducting a comprehensive investigation to unveil the correlations between design parameters and performance indices for various TPMS types. A newly developed parallelogram patch method for area calculation is introduced and compared with the conventional triangular patch method. Regression equations are synthesized to derive geometric indices based on design parameters, facilitating the final performance prediction. Notably, Fischer Koch S, Schoen I-WP, and Schwarz Primitive emerge as the leading performers, achieving the largest surface area of 21.523 m², volume fraction of 0.8732, and hydraulic diameter of 0.7856 m, respectively, within the feasible range. Conversely, Schoen Gyroid, Schwarz Primitive, and Fischer Koch S exhibit the lowest surface area of 3.5668 m², volume fraction of 0.0752, and hydraulic diameter of 0.0745 m. The regression equations and the parallelogram patch area calculating method, demonstrate commendable accuracy, with less than a 2.5% relative error, making them suitable for practical calculations. These summarized regression equations can serve as a valuable guide for the preliminary design of TPMS lattices.