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

• A clustering-aware, data-efficient inverse design approach was developed for 3D plate metamaterials. • The approach integrates a deep neural network with a genetic algorithm, guided by finite element simulations. • The framework outputs are lightweight structures with tunable stiffness and high energy absorption. • A case study is presented on optimized implants with biocompatible stiffness and improved impact energy dissipation. 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.