Multi-material decomposition optimization for topology-optimized structures considering additive manufacturing build volume and material cost

Topology-optimized structures can exploit the geometric freedom of additive manufacturing (AM), but their direct fabrication is often restricted by the finite build volume of AM machines. Part decomposition (PD) enables oversized structures to be divided into manufacturable components, while multi-material assignment substantially expands design freedom for controlling the structural performance–material cost trade-off. However, existing approaches have treated these capabilities separately, with manufacturability-oriented decomposition optimization focusing on single-material designs satisfying build volume feasibility and productivity-oriented PD approaches targeting material-related cost drivers without integrating joint-aware structural decomposition, element-wise material assignment, and analytical sensitivities. Consequently, the structural performance–material cost trade-off in multi-component, multi-material design of topology-optimized structures remains insufficiently addressed. This study presents the first multi-material decomposition optimization (MMDO) framework that simultaneously enforces build volume feasibility and performs element-wise multi-material assignment to balance structural performance and material cost. The proposed multi-objective formulation achieves this by coupling cuboid-based mapping with decomposition-oriented multi-material interpolation and cost evaluation for structural and joint regions under an AM build volume constraint. Analytical sensitivities with respect to cuboid geometry and material selection variables are derived and verified, enabling scalable and efficient gradient-based optimization. 3D numerical examples based on topology-optimized reference designs demonstrate the proposed MMDO framework and quantify structural performance–material cost trade-offs under varying weighting factors and candidate material sets.