Speaker
Description
We investigate the propagation of elastic waves with time-varying amplitudes in solids with "active" microstructure described by vector-valued phase fields. Depending on the constitutive choices adopted for the microstructural actions, the linearized evolution equations involve a non-normal matrix.
The spectra of non-unitarily diagonalizable matrices can be extremely sensitive to small perturbations in the matrix entries, making stability predictions based solely on spectral analysis unreliable, especially when uncertain constitutive parameters vary.
To obtain a more robust characterization of the dynamical response, we analyze the pseudospectrum of the associated operators, distinguishing between complex perturbations related to finite-precision computations and structured perturbations reflecting uncertainties in the values of the material parameters.
As a case study, we consider the linearized dynamics of quasicrystals, metallic alloys characterized by quasicrystalline symmetry groups. For these materials, the phase field, or phason field, represents atomic rearrangements that ensure the quasiperiodicity of the lattice. In particular, we investigate the influence of a microstructural self-action on the stability of elastic wave propagation through a parametric analysis. The results show that, for some specific choices of the phason self-action, the eigenvalues of the matrix are highly sensitive to small variations in the constitutive parameters, and that the structured pseudospectrum predicts instability of the material, whereas spectral analysis indicates, instead, stability.