Inverse multi-objective design of three-dimensional plate-based heterogeneous mechanical metamaterials

Energy-absorbing architected metamaterials, featuring dissimilar sub-elements arranged in deliberate patterns, can achieve a notably wider array of mechanical properties compared to their uniform counterparts. The traditional design of these heterogeneous structures typically depends on expert knowledge and requires considerable trial-and-error effort. Here, we introduce a data-efficient approach for the inverse multi-objective design of high-energy absorbing, three-dimensional, heterogeneous mechanical metamaterials comprised of the combination of two distinct plate-based unit cell topologies. This approach proposes a framework that pairs a Deep Neural Network (DNN) with a Genetic Algorithm (GA), supported by finite element (FE) simulations, to inverse design heterogeneous metamaterials with tailored Young's modulus (E), while maximizing energy absorption capacity and minimizing relative density (ρ). We applied this method to orthopaedic implants, as a case study, to design structures with a desirable biocompatible elastic modulus, enhanced energy absorption efficiency and minimized ρ. To the best of our knowledge, this is the first inverse design framework that integrates clustering-aware deep neural networks with evolutionary optimization, enabling accurate and efficient design of heterogeneous plate-based lattices with tailored mechanical performance.