PSI - Issue 79

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

483

3.3 Finite Element Analysis Results Following the FEA simulations, a custom MATLAB pipeline was used for automated data extraction and processing. This script accessed the output .dat files for each simulation, reporting the reaction force and displacement of the structure under the prescribed load, which varied based on the specific D and γ parameters used to generate the structure. These raw data points were then transformed into stress and strain to calculate the effective stiffness (E eff ) for each structure. The calculated E eff values demonstrated a significant range, varying between 0.1 GPa and 1.8 GPa across the different parameter sets. The overall average effective stiffness across all simulated structures was found to be approximately 600 MPa, which aligns with typical values for human trabecular bone Morgan et al. (2003). Visual analysis revealed pronounced stress concentrations consistently localized in thinner trabeculae, underscoring their critical role as failure-prone regions within the network. Despite the physiological consistency of the magnitude, the plots of E eff against the design parameters D and γ revealed no clear linear dependency on either parameter (Fig. 6). The scattering of stiffness values suggest that structural mechanics are governed by a complex, potentially non linear interaction of multiple morphological features rather than simple proportionality to the input parameters, underlying the limitation of the present preliminary results.

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= 1 = 3 = 5 = 7 = 9

= 11 = 13 = 15 = 17 = 19

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Figure 6. Effective stiffness for each D value and for different γ . (a) γ = 1, 3, 5, 7, 9. (b) γ = 11, 13, 15, 17, 19.

Finally, to capture the underlying complexity and predict effective stiffness, a Polynomial Regression model was subsequently developed on a total of 14 structural input parameters. This approach, achieving a coefficient of determination (R 2 ) of 0.73, demonstrated significant explanatory power for predicting the trend in effective stiffness (Fig. 7b).

Correlation of each feature

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R 2 = 0.731

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Real effective stiffness [MPa]

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BVTV p5 Y

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BVTV minY

Figure 7: (a) Correlation for each of the variables studied. (b) Polynomial regression results.