A new multi-material topology optimization algorithm and selection of candidate materials

With the availability of multi-material additive manufacturing , topology optimization of a multi-material structure and the selection of candidate materials become increasingly important. This paper aims to develop a new multi-material topology optimization algorithm and propose the guidelines for the selection of candidate materials from the database. The multi-material design variables and their inequality relationship are built on volume fractions of multiple materials within each element. The multi-material design variables are relaxed and multiple floating projection constraints simulate their discrete constraints by pushing design variables towards 0 or 1. Meanwhile, their inequality relationship is enforced by their variation limits. The proposed multi-material topology optimization algorithm can be applied to the compliance minimization problem constrained by a single mass or multiple volumes, as demonstrated in numerical examples. This paper mainly focuses on a single mass constraint, and 2D and 3D numerical examples systematically demonstrate that an optimized design under a mass constraint achieves a lower compliance when more materials appear in the final design simultaneously. Furthermore, we establish an approach to predict the inclusion or exclusion of a material from the final design, and propose the conditions for the co-existence of candidate materials, which guide users to select candidate materials from the database. • A new multi-material topology optimization algorithm is proposed. • The algorithm can be directly applied to a single mass constraint or multiple volume constraints. • The results systematically demonstrate the advantage of the multi-material design. • The approach to predict the occurrence of candidate materials in the final design is developed. • The approach can guide the users to select materials for multi-material additive manufacturing.