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