Numerical Modelling of Tunable Spinodal Microstructures for Biomimetic Design
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Bone implants must accommodate pronounced variations in microstructural features such as anisotropy and porosity arising from patient age, anatomy, and functional loading. Capturing this variability requires computational design tools capable of generating complex porous architectures while retaining physical consistency and scalability. Spinodal decomposition described by the Cahn–Hilliard equation offers a compelling foundation, naturally producing smooth, interconnected microstructures subject to mass conservation. We present a computational framework that repurposes phase-field modeling as a practical design tool for generating tunable spinodal microstructures tailored to bone scaffold applications. Anisotropy is introduced through anisotropic interface energy densities, allowing preferred interface orientations and internal faceting to be prescribed explicitly. Control of properties such as surface curvature and porosity naturally integrates into this framework, bridging physics-based modeling and architected material design. Efficient three-dimensional simulations are achieved using a Fourier-spectral spatial discretization and a semi-implicit time integration scheme based on convex–concave splitting of the free energy. Anisotropic terms are treated explicitly, while stabilizing contributions are handled implicitly, resulting in a numerically robust solver that supports significantly larger time steps than explicit approaches. This efficiency enables high-throughput generation of large ensembles of physically realistic microstructures. We demonstrate the rapid computational synthesis of two- and three-dimensional anisotropic spinodal structures across a wide parameter range, resulting in microstructures with markedly different effective mechanical properties and establishing the proposed method as a practical design tool rather than a purely descriptive model. The resulting datasets provide a foundation for inverse design workflows that map target mechanical properties to scaffold architectures, and for future integration with homogenization and learning-based design strategies for patient-specific bone implants.
