Computational homogenization of additively manufactured lightweight structures with multiscale topology optimization

Topology optimization (TO) is an optimal design method to obtain an efficient structure with minimal usage of material by satisfying two conflicting objectives of weight reduction and structural safety. Owing to the recent advances in additive manufacturing technology, TO has been developed in connection with the use of microscale lattices, of which complicated geometries require considerable computational loads to verify their structural performance. This study aims to develop an efficient computational method to analyze a complex TO model. Computational homogenization was then developed for efficient computation of the TO model that contains a number of microscale lattices. The proposed homogenization scheme was then applied to perform three-dimensional (3D) finite element analysis (FEA) on various TO models with three scales (i.e., macroscale, microscale, and multiscale TOs). The homogenized FEAs were conducted to verify the static and dynamic deformation behaviors of three optimized meta-sandwich beams, and their results and computational efficiency were compared with those from full solid FEAs. Experimental verification revealed that the proposed homogenized FEA provided more reliable results and better computational efficiency for the microscale and multiscale TO models, whereas the conventional solid FEA was advantageous for the macroscale TO model. To apply the proposed simulation strategy to a more complex 3D geometry, three TO models were calculated for a 3D block under a compression load. The simulation strategy combining the full solid and homogenized FEAs was then applied to analyze the static and dynamic deformation behaviors of various TO models, which provided reliable predictions of the experimentally observed behaviors within an acceptable computational time.