Effective constitutive relations for waves in composites and metamaterials
Effective constitutive relations for waves in composites and metamaterials
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DOI：
10.1098/rspa.2010.0620
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发表时间：
2011-07-08
影响因子：
3.5
通讯作者：
Willis, J. R.
中科院分区：
文献类型：
--
作者：
Willis, J. R.
提供了随机非均匀材料的“有效场”的定义，保证了运动方程的自动满足。包括具有周期性微结构的介质的重要情况。在这种特殊情况下，定义是完全明确的，可以不参考随机介质应用。该演示文稿主要以电磁波的形式表示。推理也适用于其他类型的波和弹性动力学的实现简要概述了结束。一些有效场被直接定义为系综平均，以确保运动方程的精确满足，但与它们相关的有效“运动学”场被更一般地定义为加权平均。这项工作的主要结果是一个显式的张量的有效属性。解释并解决了有效性质唯一性的重要问题。不假设原问题的自伴性。一个有吸引力的特点，制定的是，自伴随在当地一级意味着自伴随的水平上的“有效介质”。
Definitions of 'effective fields' for a randomly inhomogeneous material are offered, which guarantee automatic satisfaction of the equations of motion. The important case of a medium with periodic microstructure is included. In this special case, the definitions are completely explicit and can be applied without reference to random media. The presentation is mostly expressed in terms of electromagnetic waves. The reasoning is applicable also to other types of waves and its realization for elastodynamics is briefly outlined towards the end. Some of the effective fields are defined directly as ensemble averages, ensuring the exact satisfaction of the equations of motion, but the effective 'kinematic' fields to which they are related are defined more generally, as weighted averages. The main result of this work is an explicit formula for the tensor of effective properties. The important issue of uniqueness (or not) of the effective properties is explained and resolved. Self-adjointness of the original problem is not assumed. An attractive feature of the formulation is that self-adjointness at the local level implies self-adjointness at the level of the 'effective medium'.