PSI - Issue 80

Thi Ngoc Diep Tran et al. / Procedia Structural Integrity 80 (2026) 378–391 Thi Ngoc Diep Tran/ Structural Integrity Procedia 00 (2019) 000–000 shown in Fig. 4c. To ensure accurate path reconstruction, two points ( ��� , ��� ) and ( ��� , ��� ) were added to the corners as illustrated by an X mark in Fig. 4d. Note that these incorporated points have no impact on altering the inherent geometry of the other cross-section types as shown in Fig. 4e and Fig. 4f. Since the desired cross-sectional segment constitutes a 2D polygon shape, its area can be calculated using the polyarea function in MATLAB. The surface area calculation for other TPMS types follows the same algorithm as Primitive structure. 383 6

Fig. 4 a) Incorrect path without points arrangement; b) Area generated by nearest-neighbour algorithm, considering a quarter of cross-section to prevent geometrical problems; c) Incorrect path caused by missing corner points; d) Correct path by adding two corner points; e) and f) No geometric impact of added corner points on different cross-sections. 3.2. Calculating inclination angle Constraints in manufacturability limit the geometries that can be reliably fabricated, potentially leading to imperfections in the final structure. Yan et al. (2013) reported that overhanging surfaces with inclination angles less than 30 ° are susceptible to geometric distortion during fabrication. Building on this, the present study explores whether surface inclination angle can influence the crack propagation behavior. Inclination angle of a face index is defined as the angle between the normal vector � of this face and its vertical component �� (Jones et al. (2021b)): � = arccos �| �� | | � |�,0° ≤ � ≤90°. (12) This calculation was implemented in MATLAB and visualized by the colour-encoded distribution of inclination angle ranging from red ( 0 ° ) to blue ( 90 ° ). As defined, the surface is locally horizontally oriented by 0 ° and vertically oriented by 90 ° . Fig. 5a shows the coloured distribution of inclination angles in different TPMS unit cells. The corresponding relative frequency of these occurrence angles in each structure are presented as histograms in the same scaling in Fig. 5b. It can be seen that in Primitive, Gyroid, and Neovius, inclination angles tend to cluster around 55°, while in IWP they are primarily concentrated at 75°. High angles (>75°) are more frequent in Neovius and IWP. The very steep angles (>80°) occur most often in Neovius.