GNN-based Inverse Design of Three-Dimensional Aperiodic Metamaterials Enabling Programmable Shapes

Artificially structured materials including metamaterials can exhibit unique or target properties via the rationally designed microstructures. Compared with the periodic design of metamaterials, an aperiodic configuration enables a more flexible design space and more sophisticated responses, which shows promise for many engineering applications. However, the corresponding complex modelling method and expensive calculation cost make the inverse design of big metamaterial-based system a big challenge. Here, an aperiodic design method of three-dimensional (3D) lattice metamaterials that enables tunable morphing distributions is proposed. First, we develop a theoretical model for arbitrary curled truss microstructures which are then assembled into the lattice metamaterials in three dimensions. Next, the constitutive relation and Poisson's ratio of the 3D metamaterial are predicted by the proposed model along with the validations of finite-element analysis (FEA) and mechanical experiment. Furthermore, by a parametric design modelling considering deep learning (DL), a GNN-trained database of the structure-property relationship is constructed. Finally, given a certain size of metamaterials with target shape under external load, the optimal geometry parameters are identified via an improved particle swarm algorithm. Our work shows an effective and efficient inverse design framework to program the shape of 3D metamaterials.