A preliminary study of the mechanical properties of auxetic cellular material consisting of re-entrant hexagonal honeycombs is presented. For different scales of the honeycombs, the finite element method (FEM) and experimental models are used to perform a parametric analysis on the effects of the Poisson’s ratio (cell angle) and the relative density (cell thickness) of honeycombs on bearing capacity and dynamic performance of the auxetic material. The analysis demonstrates that the ultimate bearing capacity of the presented auxetic cellular material is scale-independent when the Poisson’s ratio and the relative density are kept constant. The relationship between the geometric parameters and vibration level difference of the honeycombs is also revealed, which can be divided into two converse parts around the Poisson’s ratio v=−1.5. When v is smaller than −1.5, increasing the cell thickness leads to an increase in the vibration level difference of the honeycombs. Moreover, the dynamic performance of thin-walled honeycombs is greatly influenced by the scale of the honeycombs, especially for the ones with small Poisson’s ratio. These conclusions are verified by a frequency response test and a good agreement between the numerical results and experimental data is achieved.
Unidirectional, bidirectional and tridirectional Buckling-based Negative Stiffness (BNS) lattice metamaterials are designed by adding prefabricated curved beams into multidimensional rigid frames. Finite Element Analysis models are built, and their mechanical performance is investigated and discussed. First, geometric parameters of the curved beam were systematically studied with numerical analyses and the results were validated by theoretical solutions. Next, within unidirectional designs of different layer numbers, the basic properties of multilayer BNS metamaterials were revealed via quasi-static compressions. Then, the bidirectional and tridirectional designs were loaded on orthogonal axes to research both the quasi-static and dynamic behaviors. For dynamic analysis conditions, simulation scenarios of different impact velocities were implemented and compared. The results demonstrate that the proposed numerical analysis step has accurately predicted the force-displacement relations of both the curved beam and multilayer designs and the relations can be tuned via different geometric parameters. Moreover, the macroscopic performance of the metamaterials is sensitive to the rigidity of supporting frames. The shock force during impact is reduced down below the buckling thresholds of metamaterial designs and sharp impact damage is avoided. The presented metamaterials are able to undergo multiaxial stress conditions while retaining the negative stiffness effect and energy-absorbing nature and possess abundant freedom of parametric design, which is potentially useful in shock and vibration engineering.
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