Abstract
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.
Highlights
We call complex those bodies in which microstructural events influence the gross behavior in a way hardly detectable by using only the traditional format of continuum mechanics
Besides formal aspects just recalled, it emerges because the description of microstructures within a material element is relative to the gross behavior of the material element itself
We consider phasons as atomic flips, that is, localized atom rearrangements that assure quasi-periodicity in space through the construction of atomic clusters with symmetry different from the prevailing one—the so-called worms. This view suggests us that the phason vector attached at a point can be, interpreted as an entity collecting the degrees of freedom exploited by atomic flips within the patch of matter the properties of which are associated with that point
Summary
We call complex those bodies in which microstructural events influence the gross behavior in a way hardly detectable by using only the traditional format of continuum mechanics (the one referred to Cauchy and later Truesdell's school axiomatization[1,2,3]). In the sense sketched above, requires a more refined view on material elements: they behave as (and are ) systems, at a microscopic scale Their peculiar morphology, requires to be described through appropriate observable entities—call them morphological descriptors or phase fields (the latter a syntagma pertaining to Landau's theory of second-specie phase transitions). We show the procedure by referring in static and dynamic setting to a sample family of complex materials: quasicrystals They are Aluminum-based alloys, with natural and synthetic origin, characterized by quasi-periodic arrangement of atoms, at variance of the basic requirements of classical crystallography.[25,26] Atomic rearrangements assure quasi-periodic structure by annihilating and reforming topological alterations of a periodic structure, the so-called worms.
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