Due to the ability to create structures with complex geometry at micro- and nanoscales, modern additive technologies make it possible to produce artificial materials (metamaterials) with properties different from those of conventional materials found in nature. One of the classes with special properties is auxetic materials-materials with a negative Poisson's ratio. In the review, we collect research results on the properties of auxetics, based on analytical, experimental and numerical methods. Special attention of this review is paid to the consideration of the results obtained in studies of hierarchical auxetic materials. The wide interest in the hierarchical subclass of auxetics is explained by the additional advantages of structures, such as more flexible adjustment of the desired mechanical characteristics (the porosity, stiffness, specific energy absorption, degree of material release, etc.). Possibilities of biomedical applications of hierarchical auxetic materials, such as coronary stents, filtration and drug delivery systems, implants and many others, where the ability for high-precision tuning is required, are underlined.
Keywords: additive manufacturing; auxetic materials; energy absorption; meta-implants; metamaterials.