PSI - Issue 79

Marco Piacentini et al. / Procedia Structural Integrity 79 (2026) 394–403

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data. For the simplified problem considered here, one could engineer additional descriptors or reduced-order geometric indices to improve MLP performance. However, in view of the long-term goal of developing a general predictive framework for nonlinear mechanical behavior of disordered, anisotropic Voronoi-based structures, graph neural networks represent a more promising direction. Indeed, recent studies have demonstrated their capability in predicting damage propagation in disordered isotropic Voronoi lattices Karapiperis and Kochmann (2023), as well as buckling in lattice materials Maurizi et al. (2022b), and e ff ective sti ff ness in other disordered structures Bonfanti et al. (2025). Finally, it is worth noting that the training dataset includes several high-performance structures that are absent from the test dataset. This imbalance arises from the intrinsic rarity of extreme cases. Such rarity also consequently limits model accuracy in regions of the design space corresponding to the highest sti ff ness and strength. Future datasets should aim for a more uniform sampling of the property space—particularly in these sparsely populated regions—to enable proper learning of rare but mechanically significant behaviors. This study presented the first step towards developing a general predictive framework for nonlinear mechanical behavior of disordered, anisotropic Voronoi-based structures inspired by trabecular bone architecture. Using parameterized anisotropic Voronoi-based unit cells and automated finite element simulations results, three Multi-Layer Perceptron models were trained to correlate structural descriptors with e ff ective sti ff ness and strength. The results showed that global parameters are reasonable but limited predictors of mechanical behavior, whereas input based on explicit structural details are not suitable for such simple architectures. The findings, in accordance with expectations from literature, confirm the need for architectures that can process graph-based encodings—such as graph neural networks—for future exploration and generalization. Key identified limitations are (i) the simplified modeling through 2D beam approximation and isotropic bilinear hardening elastic–plastic material with no-contact, (ii) restriction of predictions to two global mechanical properties under specific loading condition, (iii) the use of MLPs instead of more advanced deep learning architectures, (iv) limited sampling of extreme properties, and (v) excluding parametric variations of disorder and morphologies. Based on these findings and limitations, priorities for future development are: (1) adopt graph-based architectures to improve robustness, leverage connectivity and predict field quantities; (2) improve dataset sampling to populate rare high-performance regions; and (3) extend simulations to 2D solids and 3D volumetric models, incorporating richer constitutive behavior and additional output descriptors, and (4) gradually include more parametric variations. These steps will directly address the limitations identified in Section 3 and move the framework toward a general, predictive tool for bone-inspired and architected materials. 4. Conclusions and Future Work

Acknowledgments

The authors acknowledge the support from MSCA DN GAP project (No. 101120290).

References

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