Efficient Mechanical Design of Lattice Metamaterials: a Multiscale Homogenization-based Approach
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Recent advances in Additive Manufacturing (AM) 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 adjustment of geometric parameters. One of the biggest limitations in the mechanical design and optimization of lattice-based structures is represented by the computational time required in all the phases of the numeric analysis (modelling, meshing and simulation) due to the high complexity and number of small features of these structures. Hence, a computationally viable numerical approach is required. The most known and used technique is the multiscale approach with homogenization, that is able to extrapolate the behavior of the smallest control volume, called Representative Volume Element (RVE), representing the whole structure. Subsequently, microscale properties are employed to model and simulate the metamaterial as a bulk domain, resulting in a substantial reduction in overall computation time. While the validity of homogenization to capture the displacement field has been proven in numerous studies, a comprehensive and universally applicable procedure that furnishes essential mechanical data, such as stresses in the most critical areas, essential to metamaterial design, is absent in literature. The paper introduces a methodology starting at the microscale, involving RVE identification, homogenization, and simulation of the entire component. The homogenized stress is then used to identify critical areas, and specific cells are simulated to retrieve microscale stresses for assessing design constraints. The proposed framework is rigorously validated through numerical comparisons between the homogenized component and its real counterpart.