A multi-objective framework for Pareto frontier exploration of lattice structures

Multi-scale topology optimisation has received renewed research interest in the last decade due to the potential for increased mechanical performance and improved additive manufacturing capabilities. Most multi-scale routines rely on homogenization to bridge the scale difference, simulate part performance and eventually drive it towards an optimum. Key to macroscale performance is the search for optimal metamaterials. In this work, a multi-objective framework is proposed to reformulate this classical problem, which is to the authors' knowledge the first work to do so. The use of multiple objectives implies that the underlying structure of the optimal metamaterial performance space is a Pareto frontier: a manifold of solutions which cannot be improved upon without compromising on either stiffness or weight. The proposed framework is applied to a lattice unit cell and the map between the optimal design and performance space, through the so-called compromise space, is studied numerically. Deficiencies that cause a collapse of the Pareto frontier are resolved and the effect of design constraints is examined. In the end, it is shown that a 14-dimensional compromise space is capable of accurately capturing every Pareto-optimal performance while also ensuring a bijective map to the design space. Therefore, these properties make this lattice material model an attractive target for usage inside multi-scale routines.