Equivalent solid modeling of periodic lattice structures having different mechanical properties by homogenozation method

Lattice cells are unique structures with interconnected strut elements that exhibit different mechanical behaviors, possessing high strength and energy absorption properties while being light and low in weight. Due to their complex geometries, finite element analysis of lattice designs is expensive in terms of time and processing power. Therefore, by homogenization methods, the effective properties of the lattice cells can be determined and the cost required for the analysis can be reduced. Even if each lattice cell has cubic symmetry, it does not have the same mechanical behavior in all directions, which means that it is not isotropic. In this study, a comparison was made between the results of finite element analysis when the equivalent solid models are created using isotropic effective properties for two types of lattice cells, one with non-isotropic and the other with isotropic effective properties. These lattice unit cells are Body Centered Cubic (BCC) with non-isotropic properties and Face- and Simple-Centered Cubic (FSCC) cells with isotropic properties. The equivalent mechanical properties considered to define the mechanical properties of lattice unit cells are the equivalent elasticity modulus, equivalent shear modulus and equivalent Poisson's ratio. The effective properties of BCC and FSCC lattice cells were determined using the homogenization method based on models with different strut diameters and cell lengths, and the relationship between the effective properties and the ratio of the strut diameter to cell length was modeled. In these relationship modeling processes, regression and artificial neural networks were used and the prediction performances of these two methods were examined. The results of these methods were verified by comparing them with the results of finite element analyses. In addition, an equivalent solid model of a compression test specimen was created using the effective property values predicted by the numerical prediction methods, and the consistency of the finite element analysis results of this model with the analysis results of the detailed lattice structure model was demonstrated. As a result of this study, it was shown that the equivalent solid model created with isotropic effective properties for the non-isotropic BCC cell did not yield accurate results, while the solid model created with isotropic effective properties for the isotropic FSCC cell gave accurate results and that equivalent mechanical properties could be predicted with high accuracy for lattice cells with different diameters and lengths using the regression method.