PSI - Issue 80

7

Thi Ngoc Diep Tran et al. / Procedia Structural Integrity 80 (2026) 378–391 Thi Ngoc Diep Tran/ Structural Integrity Procedia 00 (2019) 000–000

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Fig. 5 a) Visualization of inclination angle regions; b) Histograms of inclination angle.

4. Results 4.1. Cross-sectional area analysis

By cutting the entire structure into a series of parallel cross-sections, the summation of these discretized volumes should yield the whole volume fraction. Four investigated unit cells have the same volume fraction of 0.22. Table 2 shows the volume fractions obtained by summing 64 cross-sectional areas across the structural height h using the numerical trapezoid rule. The table shows that the summations of discretized cross-section volumes in each structure are slightly lower than the expected volume fraction. This deviation can be minimized by increasing the number of cutting planes.

Table 2. Volume fraction obtained by summing discretized cross-section volumes Primitive Gyroid Neovius IWP 0.21904 0.21700 0.21278 0.21658

The cross-sectional analysis of Primitive, Gyroid, Neovius, and IWP unit cells are presented in Fig. 6, Fig. 7, Fig. 8, and Fig. 9, respectively. These Figures include the area of 64 sequential cross-sections from top to bottom and the corresponding shapes of the graph’s low and high values in the upper half of the structure. In the other half, these shapes are repeated in a reversed sequence. High values on the graph correspond to regions with a larger cross sectional area and a higher ceramic content. In contrast, low points represent regions with small cross-sectional areas and less ceramic fraction. In all structures, the graph of the cross-sectional area exhibits a symmetric pathway, which reflects the structure’s geometry. Compared to other structures, the graph of Primitive unit cell in Fig. 6 has the least number of extremal values, resulting in slowly changing cross-sectional areas. While the graph of Gyroid (Fig. 7) has the same number of peaks and valleys as Neovius (Fig. 8) and IWP (Fig. 9), its transitions between these extremal values are notably smoother. Conversely, the graphs of Neovius and IWP exhibit some abrupt transitions between the highest and lowest points in their cross-sectional profiles. In each structure, the relative maximum values are just slightly varied, and so are the relative minimums. It means that despite differences in the shapes of the largest or smallest cross-sections, their surface areas do not differ much from each other. Fig. 10a combines a comprehensive overview of the cross-sectional area in four structures. The histograms in Fig. 10b demonstrate the frequency distribution of their area across five intervals.