PSI - Issue 79

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

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skeleton, and branch points, and (4), the fourth percentile, P4, of the solid region's area observed in a circular cross section, which served as a crucial predictor for the correlation between the real (FEA-derived) effective stiffness and the predicted values.

Table 1. Name and description of each parameter used in the polynomial regression. Input parameter Description SV ratio The ratio between the surface area of a structure and its volume TbTh An estimate of the mean thickness of the trabecular rods Var TbTh

The statistical variance of the local trabecular thickness across the structure

N nodes

Count of skeletal graph nodes

N branches Mean deg Frac deg 2

Count of branch nodes

The average number of connections per node in the skeleton

The fraction of all nodes in the skeleton graph that have exactly two connections The ratio between the surface area of a structure and its volume An estimate of the mean thickness of the trabecular rods The statistical variance of the local trabecular thickness across the structure

ConnD

Lambda2

DA

BVTV min Y BVTV p5 Y

Count of skeletal graph nodes

Count of branch nodes

MinA

The average number of connections per node in the skeleton

P4

The fraction of all nodes in the skeleton graph that have exactly two connections

3. Results 3.1. 2D Morphological Analysis

Bidimensional structures provided preliminary insights into the effects of the design parameters. The analysis involved dissecting the 3D spinodal structures with multiple planes—specifically, 65 sections taken along the y-axis (from bottom to top) with a step of 0.1 mm, corresponding to one pixel. In each cross-section, a central circular region with a radius of 3.0 mm (30 pixels) was analyzed. This specific radius was selected a posteriori because it yielded the highest correlation (R ≈ 0.6) between the circle's radius and the calculated effective stiffness, establishing a targeted analysis region. Within these circles, the fourth percentile (P4) of the intersected solid structure area was calculated for each structure, as this metric best represented the correlation with effective stiffness. This preliminary study highlights P4 as a critical structural descriptor, though further investigations into a more comprehensive structure property relationship will be conducted subsequently. 3.2. 3D Morphological Analysis Transitioning to 3D analysis amplified the parameter sensitivity and provided a clearer understanding of the trabecular network. Lower values of both D and γ produced dense, highly connected trabecular networks, while increasing these parameters generated sparser lattices with thicker struts. The skeletonization process, which reduced the solid domains to a 1-voxel-thick medial axis, allowed for the topological classification of nodes (end, intermediate, and branch points). The distribution of these nodes exhibited clear hyperbolic trends correlated with the design parameters (see Fig. 5). The connectivity counts for each node type were normalized by the maximum count within their respective categories to enable direct comparison across structures. Specifically, the counts of nodes with single connectivity (end points) and double connectivity (intermediate points) showed a largely random pattern that