Mechanical Design of Lattice Metamaterials: a Multiscale Homogenization-Based Operational Procedure

Recent advancements in Additive Manufacturing technology have enabled the creation of components with innovative shapes, surpassing the limitations of conventional manufacturing methods. Lattice materials, also known as metamaterials, are a noteworthy example due to the possibility for effective control over mechanical and physical properties through the tuning of geometric parameters. One of the biggest limitations in the mechanical design and optimization of lattice-based structures is represented by the high computational time required in all the phases of numerical analyses due to their geometric complexity and the large number of repeated cells. The homogenization-based multiscale analysis is a computationally efficient numerical approach, able to extrapolate the macroscopic behavior of the lattice material from microscopic analyses. While the validity of homogenization to capture the displacement field has been proven in numerous studies, a comprehensive and operational procedure for the mechanical design of lattice metamaterials is absent in literature. Thus, the present paper introduces a methodology that couples micro and macroscale analyses to provide the essential mechanical data for design evaluation. Moreover, the proposed framework is rigorously validated on test cases through the comparison between the numerical data obtained from the homogenized component and its high-fidelity counterpart.