机制基超材料的共形弹性
Conformal Elasticity of Mechanism-Based Metamaterials
摘要：
传统固体的变形是通过弹性来描述的，弹性是一种经典的场论，其形式受到平移和旋转对称性的约束。然而，柔性超材料往往包含一个额外的近似对称性，由于设计师的软应变路径的存在。在这里，我们表明，低能量变形的设计师扩张超材料将由一个新的场论，共形弹性，其中的非均匀，非线性变形下观察到的一般负载对应于良好的共形映射。我们使用实验和有限元模拟验证了这种方法，并进一步表明，这样的系统服从全息体边界原理，这使得一个前所未有的分析方法来预测和控制不均匀，非线性变形。这项工作既提出了一种新的方法，精确的变形控制，并证明了一般原则，机构可以产生特殊类别的软变形。
英文摘要：
Deformations of conventional solids are described via elasticity, a classical field theory whose form is constrained by translational and rotational symmetries. However, flexible metamaterials often contain an additional approximate symmetry due to the presence of a designer soft strain pathway. Here we show that low energy deformations of designer dilational metamaterials will be governed by a novel field theory, conformal elasticity, in which the nonuniform, nonlinear deformations observed under generic loads correspond with the well-studied conformal maps. We validate this approach using experiments and finite element simulations and further show that such systems obey a holographic bulk-boundary principle, which enables an unprecedented analytic method to predict and control nonuniform, nonlinear deformations. This work both presents a novel method of precise deformation control and demonstrates a general principle in which mechanisms can generate special classes of soft deformations.
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