Wavelet analysis of atomic rearrangements in quasicrystals

Quasicrystals are intrinsically quasi-periodic crystalline structures in which local rearrangements of atoms, coupled with the gross deformation, occur [1]. These atomic rearrangements (the so-called phason activity) have a significant influence on the gross mechanical behaviour. For this reason the analysis of quasicrystals falls within the setting of the general format of the mechanics of complex bodies. Specifically for this class of materials, substructural events within each material element are described by a vector ν collecting the degrees of freedom associated with the atomic rearrangements inside the material element itself. Microstresses and self-actions arise as entities powerconjugated with the rate of ν. On the basis of the mechanics of quasi-periodic alloys presented in [2], by a finite element scheme we analyze a standard four-point-bending test on a two-dimensional specimen with a crack, made of Al70.3Pd21.5Mn8.2 alloy and subjected to a couple of impulsive forces. Haar and biorthogonal wavelets are used to analyze data of standard displacements and phason activity obtained by finite element simulations in dynamic setting and infinitesimal deformation regime. The data are evaluated at horizontal and vertical sections of the sample. Wavelet analysis reveals that the influence of the tip of the crack results localized for the phason degrees of freedom. Localization effects due to concentrated forces are also pointed out (Fig. 1). In the dynamics under impulsive loads, localization of phason activity occurs for large friction coefficients. Concentration effects due to concentrated forces are also pointed out. In the dynamics under impulsive loads, localization of phason activity occurs for large friction coefficients. In the standard displacements (phonon activity) instead, the propagation of the perturbation induced by the crack is more pronounced than the one due to substructural activity. Comparison with analyses on a standard elastic body in the same conditions points out the amplitude and the nature of the interaction between phonon and phason activity (Fig. 2). The paper summarizes results collected in [3].