A multi-step auxetic metamaterial with instability regulation

A stable deformation mode is highly desired for mechanical metamaterials, especially when coupled with a negative Poisson’s ratio. However, such metamaterials often face challenges in terms of scalability toward large deformation or strain. In response, we propose a multi-step hierarchical auxetic metamaterial design paradigm, incorporating a series of incrementally scaled-down structures with same scale factor $\alpha$ into a re-entrant framework. This design enables instability regulation and multi-step deformation capabilities while preserving auxetic behavior, even under significant strain. Such multi-step metamaterials exhibit excellent properties, including tailored multi-phase compression modulus and strength, along with an enhanced energy absorption capacity that is as large as 2.1 times that of the original auxetic metamaterial. Experiments and simulations demonstrate that the deformation mechanism and compression response of the proposed multi-step auxetics are strongly influenced by the reduction factor and the order of the inner structure. A particularly intriguing observation is that the incorporation of embedded microstructures can restore stable deformation, even in the presence of significant initial instability, particularly with a reduction factor of $1/5$. At high relative density, its specific energy absorption stands out favorably compared to other configurations, highlighting the success of the recoverable buckling mechanism. This work paves the way for designing multi-step mechanical metamaterials for use in impact resistance and body protection.