拓扑超材料中自应力状态下的选择性屈曲
Selective buckling via states of self-stress in topological metamaterials
摘要：
导致零净力的结构元件的自应力、张力和压缩状态在确定从桥梁到具有可调机械性能的超材料的结构的承载能力方面起着重要作用。我们利用最近引入的一类类似于拓扑量子态的自应力态，在周期性细胞异向材料的内部塑造局部屈曲区域。虽然拓扑状态的自应力出现在一个理想化的机械框架的线性响应的谐波弹簧连接的自由铰链关节，他们留下了一个独特的签名，在非线性屈曲行为的蜂窝材料的弹性梁与刚性关节。这些局部屈曲区域的显著特征是，就其组成元素的材料参数或连接性而言，它们与周围环境无法区分。此外，它们对广泛的结构扰动具有鲁棒性。我们证明了这种拓扑设计的有效性，通过分析和数值计算，以及屈曲实验上的二维和三维的超材料建成的堆叠戈薇晶格。
英文摘要：
States of self-stress, tensions and compressions of structural elements that result in zero net forces, play an important role in determining the load-bearing ability of structures ranging from bridges to metamaterials with tunable mechanical properties. We exploit a class of recently introduced states of self-stress analogous to topological quantum states to sculpt localized buckling regions in the interior of periodic cellular metamaterials. Although the topological states of self stress arise in the linear response of an idealized mechanical frame of harmonic springs connected by freely-hinged joints, they leave a distinct signature in the nonlinear buckling behaviour of a cellular material built out of elastic beams with rigid joints. The salient feature of these localized buckling regions is that they are indistinguishable from their surroundings as far as material parameters or connectivity of their constituent elements are concerned. Furthermore, they are robust against a wide range of structural perturbations. We demonstrate the effectiveness of this topological design through analytical and numerical calculations as well as buckling experiments performed on two- and three-dimensional metamaterials built out of stacked kagome lattices.
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