Independent scattering and wave attenuation in viscoelastic composites

A theoretical model for ultrasonic attenuation in viscoelastic composite materials is examined which is based on the evaluation of scattering as well as absorption losses. The theoretical formulation explicitly takes into account the viscoelastic nature of the matrix. The model gives an expression for the attenuation coefficient of the plane wave propagating in the composite in terms of the scattering and absorption cross-sections of a single inclusion and the attenuation properties of the matrix. To gain first insight into the problem, the single and independent scattering approximation is considered, although extension to a more elaborate scheme is briefly discussed. The model is applied to a special case of shear horizontal waves in a unidirectional fiber reinforced viscoelastic composite. In particular, the frequency dependence is demonstrated for the scattering cross-section of an elastic fiber embedded in a viscoelastic matrix. In contrast to the classical Rayleigh scattering where the normalized cross-section of a fiber scales to the third power of the normalized frequency, it is found that the frequency dependence of a lower order is possible when viscoelasticity of the matrix is accounted for. Shear wave attenuation spectrum of the viscoelastic composite is also illustrated, for which the contributions of scattering and absorption are discussed.

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