In this paper, we explore the use of micromorphic-type interface conditions for the modeling of a finite-sized metamaterial. We show how finite-domain boundary value problems can be approached in the framework of enriched continuum mechanics (relaxed micromorphic model) by imposing continuity of macroscopic displacement and of generalized tractions, as well as additional conditions on the micro-distortion tensor and on the double-traction. The case of a metamaterial slab of finite width is presented, its scattering properties are studied via a semi-analytical solution of the relaxed micromorphic model and compared to a direct finite-element simulation encoding all details of the selected microstructure. The reflection and transmission coefficients obtained via the two methods are presented as a function of the frequency and of the direction of propagation of the incident wave. We find excellent agreement for a large range of frequencies going from the long-wave limit to frequencies beyond the first band-gap and for angles of incidence ranging from normal to near-parallel incidence. The present paper sets the basis for a new viewpoint on finite-size metamaterial modeling enabling the exploration of meta-structures at large scales.

中文翻译：

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通过松弛微形态模型对有限尺寸的元结构进行频率和角度相关的散射

在本文中，我们探索了使用微晶型界面条件对有限尺寸的超材料进行建模的方法。我们展示了如何通过施加宏观位移和广义牵引力的连续性，以及在微变形张量和双精度上施加附加条件，在丰富的连续体力学（松弛的微形态模型）的框架内如何解决有限域边界值问题。 -牵引。介绍了一个有限宽的超材料平板的情况，通过松弛微形态模型的半解析解研究了它的散射特性，并将其与编码所选微结构所有细节的直接有限元模拟进行了比较。通过两种方法获得的反射系数和透射系数表示为入射波的频率和传播方向的函数。对于从长波极限到超过第一个带隙的频率的大范围频率以及入射角（从法向入射到近乎平行入射），我们都找到了极好的协议。本文为有限尺寸超材料建模的新观点奠定了基础，从而使大规模研究超结构成为可能。