EXPERIMENTAL IDENTIFICATION OF THE DYNAMICAL MODEL OF VISCOELASTIC HOMOGENEOUS ISOTROPIC MATERIALS.

The standard dynamical model of a viscoelastic homogeneous isotropic material [1] only depends on two parameters, e.g. the E tension-compression and the G shear moduli, the value of these parameters being expected to vary with respect to f frequency. E(ω=2‧pi‧f) and G(ω) estimates can typically be obtained from measurements made on slender beam specimens under uniaxial harmonic stress experimental conditions, e.g. tension compression for E and torsion-shear for G [1]. An extensive number of works is also known for E(ω), G(ω) modeling in the frequency domain [2] under the material linear viscoelastic behavior assumption. In previous works the authors of this paper proposed some techniques to identify the E(ω) model from forced harmonic flexural vibration measurements on a beam specimen made of the material under study [3], and such approach could be adopted to the G(ω) identification as well. Nevertheless, it can be found that for a linear viscoelastic material E(ω) and G(ω) real and imaginary parts are bounded [4]. Some more general constraining relations between E(ω) with respect to G(ω) are shown in this work, so that an experimentally identified material model is expected to satisfy such relations to be consistent. A E(ω), G(ω) model identification procedure from measurements with different experimental set-ups on beam specimens made of the same material may be uneffective, errors arising from measurement and model (boundary conditions and other model-based assumptions) lack of accuracy, so that locally identified E(ω) and G(ω) values are not expected to satisfy the previously cited consistency conditions. In this work E-1(ωk) and G-1(ωk), k=1...Nω, estimates are simultaneously obtained by means of an algebraic iterative robust algorithm, adopting a set of H(ωk)= v(ωk)/F(ωk) estimates, where (~) is the Fourier transform operator, v(ωk) is the measured displacement and F(ωk) is the measured force at one end of the beam specimen end. The H(ωk) set contains measurements made on Nm beam specimens, same material but different geometry. A flexural experimental set-up is adopted, and the choice of the geometrical dimensions of each measured specimen beam is made in order to differentiate the beam shear contributions, mainly dependent on G(ω), with respect to the beam axial contributions, mainly dependent on E(ω). Model behavior of many highly-damped polymeric materials at low frequency values is expected to be fully different from the same behavior in the medium to high frequency range, E(ωk) and G(ωk) estimates from H(ωk). in the low frequency range should be experimentally identified and cannot be extrapolated from measurements in the medium frequency range. Forced harmonic flexural vibration v(ωk), F(ωk) measurements are used to obtain H(ωk), but low frequency H(ωk) estimates, e.g. ω/2‧ᴨ‧<0.01 Hz , cannot be performed since the required experimental time is too high. Some algorithms were proposed in the past [5] to estimate E(ω) or G(ω) at low frequency values by processing creep-relaxation measurements under ideal assumptions, i.e. an ideal time step applied stress. An algorithm for the H(ωk) numerical estimate from ν(t) and force F(t) measurements under general relaxation conditions is proposed. A material E(ω) and G(ω) identification procedure from the H(ωk) experimentally estimated values is then discussed and some results are also shown.