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 引用本文: 黄小华 冯夏庭 陈炳瑞. 广义黏弹组合模型的等效性及其基本性质[J]. 力学学报, 2010, 42(1): 65-73.
Xiaohua Huang, Xiating Feng, Bingrui Chen. Equivalences of the generalized viscoelastic models and their inherent properties[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(1): 65-73.
 Citation: Xiaohua Huang, Xiating Feng, Bingrui Chen. Equivalences of the generalized viscoelastic models and their inherent properties[J]. Chinese Journal of Theoretical and Applied Mechanics, 2010, 42(1): 65-73.

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

• 摘要: 对广义黏弹组合模型的等效性及其基本性质进行了研究，结果表明：广义Maxwell模型由于并联结构，其蠕变柔量很难得到. 但提出了求解广义Maxwell模型蠕变柔量的方法，给出了其具体表达式，且在此基础上证明了广义Maxwell模型与Kelvin链的等效性，建立了这两个模型物理参数间的转换关系式. 证明了广义黏弹组合模型的一个基本性质：当将模型的松弛时间谱和延迟时间谱由大到小顺序排列时，松弛时间与延迟时间互不相等，且相互交织，两相邻松弛时间中间有且仅有一个延迟时间，同时，两相邻延迟时间中间有且仅有一个松弛时间；当两者同阶相比时，延迟时间总是大于松弛时间. 这一基本性质明确了使用广义黏弹组合模型来描述现实中某种特定材料的黏弹性行为时，该材料必须具备的基本条件，因此，它可作为这类流变模型在工程应用中的一个实用判据. Wiechert模型和广义中村模型、广义Jeffreys模型和广义N-K模型、Maxwell链和广义Kelvin模型之间的等效性可作为特例.最后，实例验证了所提出的求解广义黏弹组合模型蠕变柔量方法及其基本性质.

Abstract: 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.

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