Data-driven characterization of viscoelastic materials using time-harmonic hydroacoustic measurements

Any numerical procedure in mechanics requires choosing an appropriate model for the constitutive law of the material under consideration. The most common assumptions regarding linear wave propagation in a viscoelastic material are the standard linear solid model, (generalized) Maxwell, Kelvin-Voigt models or the most recent fractional derivative models. Usually, once the frequency-dependent constitutive law is fixed, the intrinsic parameters of the mathematical model are estimated to fit the available experimental data with the mechanical response of that model. This modelling methodology potentially suffers from the epistemic uncertainty of an inadequate a priori model selection. However, in this work, the mathematical modelling of linear viscoelastic materials and the choice of their frequency-dependent constitutive laws is performed based only on the available experimental measurements without imposing any functional frequency dependence. This data-driven approach requires the numerical solution of an inverse problem for each frequency. The acoustic response of a viscoelastic material due to the time-harmonic excitations has been calculated numerically. In these numerical simulations, the non-planar directivity pattern of the transducer has been taken into account. Experimental measurements of insertion loss and fractional power dissipation in underwater acoustics have been used to illustrate the data driven methodology that avoids selecting a parametric viscoelastic model.

Automated summary

Any numerical procedure in mechanics requires selecting an appropriate constitutive model for the material. The common assumptions for linear wave propagation in viscoelastic materials include the standard linear solid, Maxwell, Kelvin-Voigt, and fractional derivative models. Typically, the intrinsic parameters of the mathematical model are estimated based on available experimental data to fit the mechanical response of the chosen constitutive law. However, this approach may suffer from the uncertainty of inadequate model selection. In this work, the mathematical modeling and selection of frequency-dependent constitutive laws for linear viscoelastic materials are solely performed based on experimental measurements without imposing any functional frequency dependence. This data-driven methodology involves solving an inverse problem for each frequency.