Homogenisation for elastic photonic crystals and dynamic anisotropy
Homogenisation for elastic photonic crystals and dynamic anisotropy
复制标题
DOI：
10.1016/j.jmps.2014.06.006
复制
发表时间：
2014-11-01
影响因子：
5.3
通讯作者：
Guenneau, S.
中科院分区：
文献类型：
--
作者：
Antonakakis, T.;Craster, R. V.;Guenneau, S.
我们开发了一个在高频下有效的连续介质模型，用于通过包含周期性或近周期性、无牵引或夹紧夹杂物排列的弹性介质的波传播。我们创建的均质化方法允许波长和周期间隔可能具有相似的尺度，因此不限于纯粹的长波和低频。我们处理面内弹性，耦合剪切波和压缩波，因此处理全矢量问题，证明使用宏观尺度和微观尺度的两尺度渐近方法会产生完全基于 宏观尺度；问题的向量性质被纳入微观尺度。通过将所得到的渐进结果与完美周期介质布洛赫问题的完整数值模拟进行比较，全面验证了这一相当令人惊讶的结果。该布洛赫问题的色散图可以通过数值和渐近方式找到。周期性介质表现出动态各向异性，例如特定频率下的强方向场，有限元计算和渐近理论都预测了这一点。弹性周期性介质可以与电磁学中超材料和光子晶体的涌现场相关，并得出相关类比。作为说明，我们考虑高度各向异性的情况，并展示如何从均质化理论自然地预测它们的存在。 (C) 2014 Elsevier Ltd. 保留所有权利。
We develop a continuum model, valid at high frequencies, for wave propagation through elastic media that contain periodic, or nearly periodic, arrangements of traction free, or clamped, inclusions. The homogenisation methodology we create allows for wavelengths and periodic spacing to potentially be of similar scale and therefore is not limited to purely long-waves and low frequency.We treat in-plane elasticity, with coupled shear and compressional waves and therefore a full vector problem, demonstrating that a two-scale asymptotic approach using a macroscale and microscale results in effective scalar continuum equations posed entirely upon the macroscale; the vector nature of the problem being incorporated on the microscale. This rather surprising result is comprehensively verified by comparing the resultant asymptotics to full numerical simulations for the Bloch problem of perfectly periodic media. The dispersion diagrams for this Bloch problem are found both numerically and asymptotically. Periodic media exhibit dynamic anisotropy, e.g. strongly directional fields at specific frequencies, and both finite element computations and the asymptotic theory predict this. Periodic media in elasticity can be related to the emergent fields of metamaterials and photonic crystals in electromagnetics and relevant analogies are drawn. As an illustration we consider the highly anisotropic cases and show how their existence can be predicted naturally from the homogenisation theory. (C) 2014 Elsevier Ltd. All rights reserved.