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Auxetic materials belong to a class of well-organized manmade materials that possess negative Poisson’s ratio when applied load. Typically, they consist of periodic unit cells that show low Young’s and bulk moduli due to their unique structure. Thus, most of the classical auxetic materials exhibit soft behavior. Recently, some of the works investigated auxetic materials with stiff mechanical behavior. In this paper, we review auxetic structures and design methods to design soft or stiff auxetic materials, as well as their potential applications. Generally, auxetic materials fabricated using soft base material or curved microstructural ribs possess soft behavior, while auxetic materials fabricated using hard base material or adding additional ribs in the original microstructure possess stiff behavior. Possible study areas in the future for the soft and stiff auxetic materials are also presented.

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