We describe the out-of-plane bending of chiral fractal lattices metamaterials by using a combination of theoretical models, full-scale finite elements and experimental tests representing the flexural behaviour of metamaterial beams under three-point bending. Good agreement is observed between the three sets of results. Parametric analyses show a linear log-log relation between bending modulus and aspect ratios of the unit cells, which are indicative of the fractal nature of the metamaterial. The ratio between the bending and in-plane tensile moduli of these chiral fractal metamaterials ranges between ~ 5 and ~ 34 and is linearly proportional to the square of the ratio between length and width of the ribs of the chiral unit cells at different fractal orders. These properties suggest that the class of chiral fractal lattice metamaterials offer metacompliance properties between the flexural and in-plane stretching behaviours, which can be tailored by the adoption of the fractal scales.

中文翻译：

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手性分形晶格超材料的弯曲

我们通过结合理论模型、全尺寸有限元和代表超材料梁在三点弯曲下的弯曲行为的实验测试来描述手性分形晶格超材料的面外弯曲。观察到三组结果之间的良好一致性。参数分析显示弯曲模量和晶胞的纵横比之间的线性对数关系，这表明了超材料的分形性质。这些手性分形超材料的弯曲模量和面内拉伸模量之间的比率在~5和~34之间，并且与不同分形阶的手性晶胞的肋的长度和宽度之比的平方成线性比例。