Metamaterials with extraordinary material properties, not easily found in nature, are of great interest. In this paper, the authors employ topology optimization with a reconciled level-set method in order to design 3D negative Poisson’s ratio designs. The strain energy method has been used to predict the effective properties of the periodically assembled metamaterial, which is based on the resulted unit cell. The sensitivity analysis is derived utilizing the adjoint variable method with the general linear elastic equation combined with a weak imposition of the Dirichlet boundary condition. 3D single-material and multi-material designs have been generated showing the effectiveness of the proposed method. The advantage of the method can be located on the fact that the design can be manufactured by 3D printing, without any post-processing work on the result of the topology optimization, due to the clear boundaries between the different materials.

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