Graph neural networks for strut-based architected solids

Machine learning methods for strut-based architected solids are attractive for reducing computational costs in optimisation calculations. However, the space of all realizable strut-based periodic architected solids is vast: not only can the number of nodes, their positions and the radii of the struts be changed but the topological variables such as the connectivity of the nodes brings significant complexity. In this work, we first examine the structure-property relationships of a large dataset of strut-based architected solids (lattices). We enrich the dataset by perturbing nodal positions and observe four classes of mechanical behaviour. A graph neural network (GNN) method is then proposed that directly describes the topology of the strut-based architected solid as a graph. The differentiating feature of our work is that key physical principles are embedded into the GNN architecture. In particular, the GNN model predicts fourth-order tensor with the required major and minor symmetries. The predictions are equivariant to rigid body and self-similar transformations, invariant to the choice of unit cell and constrained to provide a positive semi-definite stiffness tensor. We further demonstrate that augmenting the training dataset with nodal perturbations enables the model to better generalize to unseen lattice topologies.