We propose to couple finite element simulations and wavelet-based post-processing analysis to explore deeply the interaction degree of microscopic events on the gross behavior of complex bodies (which class includes metamaterials), above all around material or load discontinuities. After summarizing the theoretical structures our procedure refers to, as a sample case we select a special class of complex materials, namely, quasicrystals, and show how the proposed scheme works. As a result, we point out the effects of atomic rearrangements characterizing the quasicrystal structure on the stress field around a crack tip in static and dynamical setting. Our procedure can be also used for the analysis of dynamic experimental data. In this case, it allows us to detect discontinuities at least along directions selected within the body. In turn, our procedure can be used for monitoring purposes.

中文翻译：

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复杂物体中的微观到宏观相互作用：基于小波的后处理检测

我们建议结合有限元模拟和基于小波的后处理分析，以深入探索微观事件对复杂物体（该类包括超材料）的总体行为的相互作用程度，尤其是围绕材料或负载不连续性。在总结了我们的程序所涉及的理论结构之后，作为示例案例，我们选择了一类特殊的复杂材料，即准晶体，并展示了所提出的方案是如何工作的。因此，我们指出了表征准晶结构的原子重排对静态和动态环境中裂纹尖端周围应力场的影响。我们的程序也可用于动态实验数据的分析。在这种情况下，它允许我们至少沿着身体内选择的方向检测不连续性。反过来，