The study of ultrasonic wave dispersion for mechanical characterization of cementitious materials by using different theoretical models

In this study, we explore the dispersion relation, i.e. the dependence of the plane wave velocity with respect to the frequency, for longitudinal ultrasonic waves from both experimental and modeling points of view. For the modeling point of view, we consider a 1D medium with different constitutive properties: from one hand we consider the non-dissipative strain-gradient elastic model and from the other hand the dissipative viscoelastic model. 1. Dispersion stemming from material microstructure: At low frequencies, the phase velocity correlates directly with material stiffness. Conversely, at higher frequencies (i.e. at low wavelengths), the phase velocity is influenced by the material's microstructure. The transition between these two velocity regimes occurs within a frequency range proportional to the characteristic length of the material. 2. Dispersion arising from material internal viscosity: Higher internal viscosity enhances material stiffening under dynamic loading, whereas lower viscosity necessitates higher frequencies to observe significant velocity variations. We derive the governing equations for both cases with the extended Rayleigh-Hamilton principle. The analysis shows good agreement with the experiments and further experimental investigations are designed for a clear and quantitative identification of the dissipative contribution.