Abstract
Mathematical model for viscous internal friction is suggested. The model relates the viscous phenomena on the grain boundaries in a polycrystalline composite to the spectral measure in the analytic representation of the effective viscoelastic properties. This spectral measure contains all information about the geometry of a finely structured material. The spectral measure can be recovered from the measurements of viscoelastic effective properties over a range of frequencies. The Stieltjes analytic representation of the effective modulus is derived for the two-dimensional viscoelastic problem. It is shown that the spectral function in this representation determines the internal memory variables and the viscous internal friction.
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