Microtwist homogenization of three-dimensional Pyrochlore lattices on zero modes and mechanical polarization
Microtwist homogenization of three-dimensional Pyrochlore lattices on zero modes and mechanical polarization
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DOI：
10.1016/j.jmps.2021.104564
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发表时间：
2021-07
影响因子：
5.3
通讯作者：
Rongyu Xia;H. Nassar;Hui Chen;Zheng Li;Guoliang Huang
中科院分区：
文献类型：
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作者：
Rongyu Xia;H. Nassar;Hui Chen;Zheng Li;Guoliang Huang
对机械烧绿石晶格进行实验测试，以证明材料的固有极性行为，其在一侧上是软的，在相对侧上是硬的（Bilal等人，2017年）。烧绿石晶格中的拓扑极化现象要求发展一种新的有效介质理论，因为传统的柯西有效介质理论不能预测这种极化现象。在这项研究中，我们发展了一个烧绿石晶格的三维微扭曲有效理论，以捕获的P-非对称零模式的偏振出现或在宏观尺度上衰落。通过将三个周期性零模映射到三个宏观自由度，三维微扭转理论最终成为一个运动学丰富的理论。采用双尺度渐近方法，推导了三维微扭转弹性力学的本构方程和平衡方程。所提出的理论的性能进行了验证的精确解的离散模型再现零模式和色散关系，并定量预测非对称压痕响应。该研究将有助于在传统的对称群框架之外，揭示三维极化超材料的新弹性理论，这是以前从未报道过的。
The mechanical Pyrochlore lattice was experimentally tested to demonstrate an intrinsically polar behavior of the material, which is soft on one side and hard on the opposite side (Bilal et al., 2017). The topological polarization in Pyrochlore lattices begs for developing a new effective medium theory because conventional Cauchy effective theories cannot predict the polarization phenomenon. In this study, we develop a 3D microtwist effective theory of Pyrochlore lattices to capture the P-asymmetric zero modes by which polarization emerges or fades on a macroscopic scale. By mapping three periodic zero modes to three macroscopic degrees of freedom, the 3D microtwist theory ends up being a kinematically enriched theory. The 3D microtwist elasticity is formulated by using two-scale asymptotic approach and its constitutive and balance equations are derived for a fairly generic isostatic lattice. Performance of the proposed theory is validated by the exact solution of the discrete model for reproducing zero modes and dispersion relations and quantitatively predicting asymmetric indentation responses. The study could shed lights on novel elastic theory of 3D polarized metamaterials outside the conventional framework of symmetry groups, which is never reported before.