• Research paper •

### Equivalences of the generalized viscoelastic models and their inherent properties

Xiaohua Huang Xiating Feng Bingrui Chen

• Received:2008-03-10 Revised:1900-01-01 Online:2010-01-18 Published:2010-01-18

Abstract: The equivalences of generalized viscoelastic models and their inherent properties are investigated. The creep compliance of the generalized Maxwell model is difficult to obtain due to its parallel connection. However, a method by using Laplace transform is proposed in the present paper to solve this problem and a theoretical expression is obtained. The equivalence of the generalized Maxwell model and the Kelvin chain is proved and the conversion relations of the parameters between these two models are also derived. Moreover, an inherent property of the generalized viscoelastic model proved here is that relaxation times and delay times are mutually interlaced, and the former is always greater than the latter when the spectrums of relaxation time and delay time are placed in order. This property is also the imperative condition when the generalized viscoelastic model is applied to describe the rheological behavior of materials in engineering. As special instances of the equivalence of the generalized Maxwell model and the Kelvin chain, there are the equivalence between the Wiechert model and the generalized Zhong-cun model, the Generalized Jeffreys model and the Generalized N-K model, the Maxwell chain and the Generalized Kelvin model. Finally, the proposed method is demonstrated by an example.