Categorization of congruent TPMS by geometric features using manifold learning and clustering

Recent advances in additive manufacturing technology have enabled the use of architected porous materials in several fields of science and engineering. Triply periodic minimal surface (TPMS) structures garner particular interest due to their smooth and regular features that lead to advantageous effective properties for many applications. In this study, five geometric features (tortuosity of the structure, tortuosity of the flow channels, surface area, solid thickness, and channel width) are calculated for 14 congruent TPMS types (Gyroid, D, P, Neovius, C(Y), S, F, C(D), C(S), Y, ±Y, C(±Y), W, C(G)) over 9 porosities. The geometric features of each TPMS type are fit as functions of solid volume fraction. The Uniform Manifold Approximation and Projection (UMAP) algorithm is applied to reduce the dimensionality of the set of best-fit parameters, and then K-Means clustering is used to divide the projection into clusters. This analysis reveals four categories that are reasonable and physically meaningful, which demonstrates the promise of manifold learning approximations paired with clustering for design exploration tasks. Interpretations and recommendations are presented for each of the resulting categories in an attempt to ease the selection process of congruent TPMS types. Specifically, a category consisting of C(Y), C(±Y), D, Gyroid, and S is broadly recommended as the first option for most applications when advanced manufacturing techniques such as additive manufacturing are available. Additionally, the F and W types permit no flow and are topologically quite simple, allowing for possible manufacture without use of advanced manufacturing techniques.