Abstract
Regularity conditions are given under which the Laplace transform of the relaxation modulus of a viscoelastic material can be represented by a Stieltjes continued fraction. It is shown how this fraction generates a sequence of exponential decay modes for representing experimental stress relaxation data. The article addresses the theoretical underpinning of the process whereby the continuous relaxation spectrum is replaced by a set of discrete modes, as well as demonstrating the practical applicability of the process. On the theoretical side, we appeal to the Stieltjes moment problem and its elegant solution by Stieltjes, while on the practical side we choose Riesz bases for the continuous relaxation spectrum which generate spectral sets of discrete relaxation times for fitting experimental data. The associated discrete retardation spectrum and Prony series for the creep compliance is then obtained directly from the discrete relaxation spectrum.
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