Modular architectured materials and structures: Design synergy of free-material and topology optimization*

Modular design offers efficient solutions for manufacturing, reusability, and sustainability while maintaining optimized performance. The modular approach presents a two-level optimization challenge comprising of (i) efficient module distribution within a product-scale domain and (ii) optimizing individual module topologies for seamless assembly. Improving on our previous work that rested on metaheuristics and second-order cone programming for truss-like structures, we propose an efficient bi-level sequential strategy applicable to continuum structures and mechanisms, including module manufacturing and handling concerns. The assembly plan is determined first via the free material optimization and symmetry-preserving, hierarchical clustering of the resulting stiffness tensors. Individual module topologies are then obtained via single-scale topology optimization with embedded modularity. With robotic-assisted manufacturing envisioned for these designs, we incorporate a connectivity constraint for each module. We showcase our method with module designs reusable in two compliant mechanisms: gripper and inverter, and we confirm their performance with experiments on 3D printed samples.