真实带隙超材料非定域性的第一个证据：确定松弛微观模型中的参数
First evidence of non-locality in real band-gap metamaterials: determining parameters in the relaxed micromorphic model
摘要：
在本文中，我们提出了一些弹性参数的松弛微观模型的基础上的实际实验的纵向平面波传输的界面分离的经典柯西材料（钢板）和声子晶体（钢板与充满流体的孔）的第一次估计。建立了一个程序，以确定我们的模型的参数，通过叠加的反射系数的实验为基础的配置文件（绘制为行波的频率的函数）与类似的配置文件，通过模拟的基础上放松微观模型。最后，我们确定了6个本构参数中的5个，这些本构参数在各向同性情况下由松弛的微观模型表征，再加上微惯性参数的确定。第六个弹性参数，即Cosserat耦合模量$μ_{c}$，仍然是未定的，因为实验数据有关的传输性能的考虑界面的横向入射波还没有。本论文的一个基本结果是估计的非局部性本质上相关的超材料的底层微观结构。事实上，我们估计测量所考虑的声子晶体的非定域性的特征长度$L_{c}$是所考虑的流体填充孔的直径的$1/3$的数量级。
英文摘要：
In this paper we propose the first estimate of some elastic parameters of the relaxed micromorphic model on the basis of real experiments of transmission of longitudinal plane waves across an interface separating a classical Cauchy material (steel plate) and a phononic crystal (steel plate with fluid-filled holes). A procedure is set up in order to identify the parameters of our model by superimposing the experimentally-based profile of the reflection coefficient (plotted as function of the frequency of the traveling waves) with the analogous profile obtained via simulations based upon the relaxed micromorphic model. We end up with the determination of 5 out of 6 constitutive parameters which are featured by the relaxed micromorphic model in the isotropic case, plus the determination of the micro-inertia parameter. The sixth elastic parameter, namely the Cosserat couple modulus $μ_{c}$, still remains undetermined, since experimental data concerning the transmission properties of the considered interface for transverse incident waves are not yet available. A fundamental result of the present paper is the estimate of the non-locality intrinsically associated to the underlying microstructure of the metamaterial. As a matter of fact, we appraise that the characteristic length $L_{c}$ measuring the non-locality of the considered phononic crystal is of the order of $1/3$ of the diameter of the considered fluid-filled holes.
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