Equivalences of the generalized viscoelastic models and their inherent properties

The equivalences of generalized viscoelastic models andtheir inherent properties are investigated. The creep compliance of thegeneralized Maxwell model is difficult to obtain due to its parallelconnection. However, a method by using Laplace transform is proposed in thepresent paper to solve this problem and a theoretical expression isobtained. The equivalence of the generalized Maxwell model and the Kelvinchain is proved and the conversion relations of the parameters between thesetwo models are also derived. Moreover, an inherent property of thegeneralized viscoelastic model proved here is that relaxation times anddelay times are mutually interlaced, and the former is always greater thanthe latter when the spectrums of relaxation time and delay time are placedin order. This property is also the imperative condition when thegeneralized viscoelastic model is applied to describe the rheologicalbehavior of materials in engineering. As special instances of theequivalence of the generalized Maxwell model and the Kelvin chain, there arethe equivalence between the Wiechert model and the generalized Zhong-cunmodel, the Generalized Jeffreys model and the Generalized N-K model, theMaxwell chain and the Generalized Kelvin model. Finally, the proposed methodis demonstrated by an example.