An efficient multiscale optimization method for conformal lattice materials

This article presents a multiscale optimization method to solve size distribution problem of conformal lattice materials (CLMs). Full-scale analyses are not needed during optimization process, so this method is much more efficient compared with other optimization methods for CLMs, especially when the number of microbars is considerably large. On microscope, inherent heterogeneity of CLM makes it hard to introduce homogenization method to scale down the problem. For substitute, a new method derived from extended multiscale finite element method (EMsFEM) is used to calculate the effective stiffness of the microlattice structures, and two improvements are given to increase the accuracy and extend its application to CLM. On macroscope, based on gradient-based topology optimization method, a multiscale optimization algorithm is raised for a minimum compliance design under volume constraint. The diameters of microbars are set to be design variables. Sensitive analyses based on EMsFEM are carried out, so the effective calculating process can be seamlessly integrated in the optimization algorithm. Furthermore, considering the discontinuity of bars laid on elements’ edges, a post-processing method is proposed to determine the diameters of these bars. This optimization method is validated by two mechanical experiments on specimens fabricated by 3D printing, and its efficiency is tested by comparing with the optimization method with full-scale FE analyses. The results of both mechanical experiments and finite element simulations show that the optimized structures do have better mechanical properties, exposing the material redistribution tendency during optimizing process.