PSI - Issue 79

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

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© 2025 The Authors. Published by ELSEVIER B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0) Peer-review under responsibility of IGF28 - MedFract3 organizers

Keywords: Spinodal structure; trabecular bone; morphological and topological analysis; finite element analysis; effective stiffness

1. Introduction Trabecular bone is one of the most intricate biological materials, both structurally and functionally. Its lattice-like microarchitecture provides lightweight yet resilient mechanical support, distributing loads efficiently through a complex porous geometry Martin et al. (1991). This combination of stiffness, strength, and low density makes trabecular bone a subject of fundamental interest across biomechanics, orthopedics, and bio-inspired material design. Understanding its effective stiffness is essential for predicting fracture risk, disease progression (e.g., osteoporosis), and developing implants or prosthetics that replicate native bone behavior. Traditional approaches for studying trabecular bone microarchitecture rely on high-resolution imaging techniques such as micro-computed tomography (µCT). When coupled with finite element analysis (FEA), µCT data enable accurate predictions of both local and global mechanical properties Guo (2008). However, these methods face two key limitations: (1) high computational costs due to the need for extremely fine resolution, and (2) potential imaging artifacts and irregularities that compromise reproducibility and generalization across samples. To overcome these challenges, spinodal architecture offers a powerful and mathematically defined alternative. Derived from the Cahn–Hilliard equation, which describes phase separation in thermodynamically unstable systems, spinodal decomposition produces continuous, isotropic, and bicontinuous porous structures that closely resemble the morphology of trabecular bone Wang et al. (2023). These spinodal-like structures are not direct replicas of biological tissues but controlled analogues with tunable geometrical and topological parameters such as porosity, connectivity, and feature size. One of the key advantages of spinodal architectures lies in their parameterization: the ability to systematically adjust generation parameters enables controlled exploration of structure–property relationships. This makes them ideal for studying how topological and morphological features influence mechanical performance. Their bicontinuous nature, where both solid and pore phases are continuous and fully interpenetrating, ensures efficient load transfer and uniform fluid or nutrient transport, key characteristics of functional biological systems. Furthermore, their isotropic topology provides uniform mechanical properties in all directions, avoiding directional dependencies typical of lattice or layered structures. From a computational and manufacturing standpoint, spinodal structures offer additional benefits. Their smooth, self supporting topology minimizes stress concentrations and sharp re-entrant angles, reducing numerical artifacts during simulation and print defects during additive manufacturing. Such geometries are particularly suited for metal or polymer-based 3D printing techniques, including selective laser melting (SLM), selective laser sintering (SLS), and stereolithography (SLA), making them highly promising for patient-specific implants and biomimetic materials. Finally, finite element analysis of these spinodal structures can be computationally optimized through topological analysis Bandyopadhyay et al. (2022). By capturing essential descriptors—such as connectivity, node classification, and surface-to-volume ratios—it becomes possible to correlate structural metrics with effective stiffness, thereby reducing simulation time without sacrificing accuracy. 1.1 Structure and objectives of the paper In this context, the present study extends previous work by developing a numerical workflow to predict the effective stiffness of spinodal-like trabecular bone models. The objectives are to (i) systematically generate 2D and 3D spinodal structures under controlled parameters, (ii) analyze their morphological and topological descriptors, (iii) simulate their mechanical response under uniaxial compression using FEA, and (iv) correlate structural metrics with effective stiffness to enable predictive modeling. This work contributes to biomechanics by providing a scalable and reproducible framework to mimic trabecular bone, while also informing materials science on the design of bio-inspired porous materials for lightweight engineering and biomedical applications.