Designing Multimaterial Spinodoid Structures with Tunable Anisotropic Elastic Behavior via Graph Neural Networks

The effectiveness of architected metamaterials in responding to stimuli is determined by the properties of the constituent elements and by their internal geometry. Spinodoid structures allow continuous, aperiodic and highly tunable morphologies, but the evaluation of large design populations in terms of a finite element analysis is computationally expensive. This thesis presents a graph-based machine learning framework for the prediction and interpretation of effective elastic properties of 2D multimaterial spinodoid structures and its extension to inverse design. A verified dataset of 8000 unique structures was generated using a Gaussian random-field formulation. Each structure contained compliant and stiff elastic phases with varying constituent moduli and phase fractions. The stiff-phase morphology was converted into a graph through skeletonisation, island detection, surrogate-node insertion, artificial bridging, and graph reduction. Finite element simulations in the x- and y-directions provided the normalised stiffnesses Ex/E1 and Ey/E1, together with the Poisson’s ratios νxy and νyx. The dataset was divided into 5600 training, 1200 validation, and 1200 independent test samples. On the test set, the message-passing neural network achieved R2 values of 0.9826, 0.9806, 0.8323, and 0.7367 for Ex/E1, Ey/E1, νxy, and νyx, respectively. In physical units, the predictions achieved R2 = 0.9793 for Ex and R2 =0.9776 for Ey, with mean absolute errors of 0.547 MPa and 0.583 MPa. Statistical analysis based on ranks showed that the normalised stiffness response is dominated by material contrast and soft-phase fraction. We found that graph-level variables (number of nodes, mean degree, and surrogate-node fraction) had weaker independent relationships when controlling for material composition. The global descriptors examined accounted for lower variation in Poisson’s ratios suggesting a stronger dependence on detailed directional and local geometric information. We also explored a conditional graph variational autoencoder. The direct decoding approach suffered from node-permutation ambiguity, coordinate collapse, and topology reconstruction errors for variable-sized irregular graphs. Nonetheless, the encoder generated a property-conditioned latent representation of the 8000 valid designs and allowed for a recovery of existing FEM-validated database structures. So the inverse-design contribution is framed as latent-space organization and valid-design retrieval, rather than the reliable generation of previously unseen topologies. All in all, the thesis demonstrates that graph neural networks can be applied for accurate and interpretable surrogate predictions of multimaterial spinodoid structures while paving the way towards future generative inverse-design techniques.