Spinodal metamaterials optimization based on genetic algorithm: controlling mechanical anisotropy via dimensionless Cahn-Hilliard equation

Additive manufacturing (AM) has shifted radically the design of metamaterials by enabling the fabrication of complex architectures with tailored anisotropic properties. While periodic lattice structures have been extensively explored to mimic naturally anisotropic materials such as bone and wood, their design flexibility remains inherently limited by tessellation constraints. Spinodal metamaterials, inspired by the eponymous phase-separation transformation, offer an attractive alternative due to their intrinsic tunability and non-periodic nature. In this work, both isotropic and anisotropic spinodal decomposition processes are simulated by solving the dimensionless Cahn–Hilliard partial differential equation (PDE), where directional diffusivity is modeled through directional dependent mobility coefficients along Cartesian directions. The results demonstrate that anisotropic diffusion enables the generation of metamaterials with strong anisotropic topologies and spatially varying mechanical properties. A clear correspondence is established between the anisotropy (or isotropy) of the underlying physical model and the resulting mechanical behavior of the material. To design spinodal metamaterials with strong mechanical anisotropy, the dimensionless form of the Cahn–Hilliard equation, governed by two key parameters, is first solved. The resulting solution fields are converted into STL models and meshed for finite element analysis (FEA) to evaluate homogenized elastic properties. This study focuses on understanding how governing parameters affect stiffness, with focus on Young's moduli in all spatial directions. A genetic algorithm is employed to explore the design space and maximize stiffness in a chosen Cartesian direction. Experimental validation confirms the accuracy of this homogenization approach and emphasizes the potential of spinodal decomposition-inspired architectures in achieving mechanically anisotropic metamaterials.