Modal Response Improvement of Periodic Lattice Materials with a Shear Modulus-Based FE Homogenized Model

Lattice materials are widely used in industries due to their designable capabilities of specific stiffness and energy absorption. However, evaluating the mechanical response of macroscopic lattice structures can be computationally expensive. Homogenization-based multi-scale analysis offers an efficient approach to address this issue. To achieve a simpler, while precise, homogenization, the authors proposed an equidistant segmentation (ES) method for the measurement of the effective shear modulus. In this method, the periodic boundary conditions (PBCs) are approximated by constraining the lateral displacement of nodes between parallel layers of periodic cells. The validations were applied to three typical lattice topologies: body-centered cubic (BCC) lattices, gyroid-, and primitive-triply periodic minimal surface (TPMS) lattices, to predict and compare their anti-vibration capacities. The results demonstrated the rationality and the promising precision of the multi-scale-based equivalent modal analysis through the proposed method and that it eliminated the geometric limitation of lattices with diverse frameworks. Overall, a higher anti-vibration capacity of TPMS was observed. In the study, the authors examined the influence of the relative densities on the balance between the anti-vibration capacity and loading capacity (per unit mass) of the TPMS topologies. Specifically, the unit mass of the TPMS with lower relative densities was able to resist higher frequencies, and the structures were dominated by the anti-vibration capacity. In contrast, a higher relative density is better when emphasizing the loading capacity. These findings may provide notable references to the designers and inform the selection of lattice materials for various industrial applications.