Inverse homogenization design of lattice structures without scale separation

Scale separation is often assumed in most homogenization-based topology optimization (TO) frameworks for design of material microstructures. This work goes beyond the mainstream TO contributions by abandoning scale hypothesis. First, it puts to evidence limits approach when size Representative Volume Element (RVE) not negligible with respect structure. Then, a re-localized scheme bridging RVE and structure proposed reproduce microscopic fields, while problem at macroscopic solved only based on coarse mesh. Finally, numerical experiments show interesting results 2D lattice structures within framework giving hint towards feasible realization finite-scale current resolution additive manufacturing technologies. Reported that present method can lead same stiffness optimized as reference solution number unit cell relatively large, reducing computational costs significantly.