TPMS porous architectures offer a way of designing porous and surface-rich light-weight materials based on mathematics, allowing additive manufacturing of the designed materials. The importance of TPMS from a scientific perspective can be found in a core issue of material design, in which the same internal geometry determines fluid access, heat exchange, stiffness, powder removal, fidelity of wall thickness, coatings and environmental stability. In this context, the main question addressed by this study is what should be the choice of TPMS unit topology when mechanical support, permeability, thermal transport and access to the service are taken into account as related design criteria. The approach adopted in the work is to analyze the available literature on TPMS using implicit geometric descriptors, ten design figures and relevant quantified findings reported on TPMS research. Among the data used for the analysis are gyroid superior performance with respect to heat transfer compared to commercial open-cell foam by the factor of 1.07 and ability to dissipate more heat almost twice at the same temperature difference, F-RD structure having 103\% higher thermal conductivity and 488\% higher stiffness in comparison with stochastic foam at identical porosity, porosity-graded TPMS architectures with reduction of pressure drop by 27.6\% while not exceeding 15.7\% in heat transfer loss, radial permeability being approximately half the longitudinal one for cylindrical scaffolds, permeability models with prediction differences lower than 5\%, and microfabrication processes allowing \SI{5}{\micro\meter} thickness layers or micrometer-size features. The results of the analysis revealed that TPMS choice cannot be limited to porosity or relative density only. It was demonstrated that primitive and gyroid geometries have advantages in case of continuous access and moderate tortuosity, diamond geometries are beneficial in cases with predominance of stiffness and split-merge flow paths, while I-WP or F-RD geometries gain importance in case of internal surface density and heat-conduction pathways.

triply periodic minimal surface,porous architecture,additive manufacturing,thermal transport,permeability,lattice materials,service exposure,materials design