Multi-material topology optimization and additive manufacturing for metamaterials incorporating double negative indexes of Poisson’s ratio and thermal expansion

Advances in the multi-material additive manufacturing promote a new opportunity for developing metamaterials integrating complex functionalities, especially the metamaterial incorporating double negative indexes of Poisson’s ratio and thermal expansion. However, the systematic design and additive manufacturing of such metamaterial are stilling not developed. Here, an improved multi-material topology optimization method, Alternating Active Phase & Objective (AAPO) algorithm, was developed. A new optimization formulation, in which the core contribution was the dynamical switch of the objective functions according to the active phases, was proposed to successfully overcome the convergence oscillation. The optimization formulation and sensitivity analysis based on the numerical homogenization were established. A series of multi-material re-entrant and chiral metamaterials, which exclusively realized the double negative indexes of Poisson’s ratio and thermal expansion, were devised. Especially, the tri-material and chiral metamaterials were originally obtained through the topology optimization. More importantly, metamaterials were well additively manufactured through the multi-material fused deposition modeling. The experimentally tested Poisson’s ratio and thermal expansion suggest a good agreement between the experiments and topology-optimized results. The multi-material design and additive manufacturing developed here provide a general guidance to develop the multi-functional metamaterials.