Impact resistance of uniform and functionally graded auxetic double arrowhead honeycombs

•The impact responses of auxetic double arrowhead honeycombs are simulated.•Analytical expressions for elastic constants and yield stress are derived.•Beyond a critical impact velocity, the plateau stress is insensitive to the auxetic effect.•Functionally graded design is advantageous for energy absorption under high velocity impacts.

Double arrowhead honeycombs (DAHs) are auxetic cellular materials with negative Poisson's ratio (NPR). The quasi-static and impact behaviors of both uniform and functionally graded DAHs are explored. Analytical expressions for the in-plane Young's modulus, Poisson's ratio and quasi-static yield stress of uniform DAHs are derived and are found to be consistent with finite element (FE) predictions, showing that the quasi-static yield stress of DAHs is dependent upon the geometrical parameters and NPR. Systematical simulations of uniform DAHs subject to different impact velocities reveal that there exists a critical impact velocity beyond which the dynamic plateau stress is insensitive to the effect of NPR. A semi-empirical expression of the plateau stress is obtained. For functionally graded DAHs, they are shown to only have improved energy absorption capacity under high velocity impacts. Moreover, the results of uniform DAHs are shown to be able to be adopted to interpret the simulated plateau stress of functionally graded DAHs under impact loading. The deformation mechanisms associated with the impact resistance of DAHs are also discussed.