Recently, engineered metamaterials have aroused considerable interests in many fields, due to their distinctive characteristics different from conventional materials. This paper proposes a level-set based topological optimization method for design of the mechanical metamaterials with negative Poisson's ratio. The strain energy method is employed to predict the effective properties of the periodic microstructure. The adjoint variable method is applied to calculate the shape sensitivity, which is further used to construct the design velocity field. Finally, the level set method is applied to achieve shape evolution and topological changes of the microstructure until the desired materials properties like negative Poisson's ratios are achieved.
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