Efficient Mechanical Design of Lattice Metamaterials: a Multiscale Homogenization-based Approach

Recent advancements in Additive Manufacturing have revolutionized mechanical component design. Lattice metamaterials, thanks to the possibility for effective control over their properties through the tuning of geometry layout, have gained great attention. However, the high computation time, required in all phases of numeric analyses is still a major challenge. The homogenization-based multi-scale analysis is a computationally efficient numerical approach, able to extrapolate the macroscopic behavior from microscopic analyses of unit cells. Microscale properties are employed to model and simulate the metamaterial as a bulk domain, resulting in a substantial reduction in overall computation time. This work introduces a comprehensive and universally applicable methodology, that provides essential mechanical data to evaluate component designs. Starting from the microscale with the homogenization, homogenized properties are employed in the simulation of the macroscopic component. Homogenized strain is then used to identify critical cells, that are then de-homogenized to retrieve microscale stresses, necessary to assess design constraints. The proposed framework is rigorously validated on a test case through the comparison between the numerical data obtained from homogenized component and its real counterpart.