PSI - Issue 79

A. Della Rocca et al. / Procedia Structural Integrity 79 (2026) 475–484

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25%—where BV is bone volume and TV is total volume—consistent with physiological trabecular bone densities reported in the literature (15–30%) Maquer et al. (2015).

Fig. 1. (a) 3D structures generated for different D and γ values. (b) 2D Structures generated for different D and γ values

2.3 Morphological and Topological Analysis Spinodal structures were analyzed using two-dimensional (2D) and three-dimensional (3D) topological methods to establish a link between the structure morphology and its mechanical properties. To quantify the influence of design parameters, a 2D island counting algorithm was newly implemented. Given that the spinodal structure is a two-phase system (solid and void, see Fig. 2), a cross-section reveals distinct solid regions, or "islands," surrounded by the void phase. Counting these islands provides a simple, quantitative measure to correlate with the structure's mechanical properties, such as effective stiffness. To visualize and execute the algorithm, a 200×200 pixel 2D square section of the structure was used. The counting process begins at the top-left corner of the image (Fig. 2). The algorithm proceeds to intercept the first black (solid) island, then traces its entire border until the starting point is reached. Once traced, the island is counted (incrementing the counter) and subsequently deleted from the image to prevent it from being recounted. The scan then continues down the current column until no more islands are found. Upon reaching the bottom, the process moves one pixel to the right and repeats the downward scan. This cycle continues until the entire image area is processed and all solid islands are counted (Fig. 2). The resulting total island count is utilized as a parameter to identify a potential correlation between the structure's predicted and effective stiffness.

Fig. 2. Island counting function working mechanism in three steps to count a total of 21 islands.