Gross scale effects of atomic rearrangements in quasicrystals: numerical simulations and wavelet analysis

Quasicrystals are intrinsically quasi-periodic crystalline structures in which local rearrangements of atoms, coupled with the gross deformation, occur. These atomic rearrangements (the so-called phason activity) have a significant influence on the gross mechanical behavior. 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 w collecting the degrees of freedom associated with the atomic rearrangements inside the material element itself. Microstresses and self-forces arise as entities power-conjugated with the rate of w. On the basis of the mechanics of quasi-periodic alloys presented in [1], by a finite element scheme we analyze a standard four-point-bending test on a notched sample made of an Al70.3Pd21.5Mn8.2 alloy and subjected to two types of loads: (i) a couple of static forces and (ii) 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 [2]. The data are analyzed 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. Comparison with analyses on a standard elastic body in the same conditions points out the amplitude and the nature of the interaction between standard displacements and phason activity.