Micro-to-macro interactions in complex bodies: Wavelet-based post-processing detection

We propose to couple finite element simulations and wavelet-based postprocessing analysis to explore deeply the interaction degree of microscopic events on the gross behavior of complex bodies (which class includesmetamaterials), above all around material or load discontinuities. After summarizing the theoretical structures our procedure refers to, as a sample casewe 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.