PSI - Issue 79

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

484

4. Conclusions and Future Work This study highlights the ability of spinodal-like structures to mimic trabecular bone architectures and their mechanical performance. Despite stochastic variability, the generated models reproduce fundamental traits: bi continuous networks, high porosity, and nonlinear morphology-stiffness relationships. In terms of implications for bone mechanics, the lack of linear dependence between generation parameters and stiffness underscores the importance of topology over density alone. This aligns with clinical findings in osteoporosis, where loss of connectivity—not simply density reduction—drives mechanical weakening. Morphological descriptors such as branch node density and BV/TV ratios provide stronger predictive power than isolated structural measures. Then discussing possible applications to engineering, the Spinodal-like models offer practical benefits for bio-inspired material design. Additive manufacturing could replicate these morphologies, enabling lightweight lattices with tunable stiffness. Moreover, the methodology could inform implant design by tailoring connectivity and porosity to match patient-specific bone quality. Critically analyzing the methodological approach, it is evident as the small voxel domain (64³ pixels) limited the statistical robustness of stiffness predictions. Larger domains may average out stochastic variability and yield more reliable trends. Additionally, the assumption of isotropic, homogeneous material neglects trabecular bone’s anisotropic mineral distribution and viscoelasticity. The key limitations identified include: (1) small simulation domain sizes; (2) nonlinear material behaviors negligibility; and (3) absence of a validation study with µCT-based FEM. Overall, this research contributes to the field of biomechanics by providing a scalable, reproducible framework capable of mimicking the complex architecture of trabecular bone. Beyond biological relevance, the outcomes hold significance for material science, offering insights for the design of porous, lightweight, and mechanically efficient structures suitable for applications such as bone implants and advanced engineering materials. The work has demonstrated that spinodal decomposition can generate trabecular bone analogues with tunable morphology. Then that - through finite element analysis - effective stiffness has been shown to depend primarily on connectivity descriptors rather than generation parameters. Future research should therefore expand simulations to larger volumes, integrate anisotropic constitutive models, and validate against µCT datasets. Machine learning could also enhance stiffness prediction from morphological descriptors. Acknowledgements The authors acknowledge the partial support from MSCA DN GAP project (No. 101120290). References Bandyopadhyay, A. C. (2022). Metal Additive Manufacturing for Load-Bearing Implants. Journal of the Indian Institute of Science , Volume 102. Cahn, J. W. (1958). Free Energy of a Nonuniform System. I. Interfacial Free Energy. Journal of Chemical Physics , 258-267. Cuppone, M. S. (2004). The longitudinal Young's modulus of cortical bone in the midshaft of human femur and its correlation with CT scanning data. Calcif Tissue Int 74 , 302-309. Dan, W. P. (2018). Young’s modulus of trabecular bone at the tissue level: A review. Acta Biomaterialia , 1-12. Guo, X. E. (2008). Nanomechanical properties of bone. Journal of musculoskeletal & neuronal interactions , 8(4):325-6. Maquer, G. S. (2015). Bone volume fraction and fabric anisotropy are better determinants of trabecular bone stiffness than other morphological variables. Journal of Bone and Mineral Research . Martin, R. (1991). Determinants of the mechanical properties of bones. Journal of Biomechanics, Volume 24, Supplement 1 , 79-88. Morgan, E. B. (2003). Trabecular bone modulus-density relationships depend on anatomic site. J Biomech , 897-904. Wang, Z. D. (2023). Machine learning unifies flexibility and efficiency of spinodal structure generation for stochastic biomaterial design. Scientific Reports .