Abstract Our chief target of this paper is to study the temperature-dependent Nishihara-type model(TDNM) with creep damage based on the Caputo fractional derivative. The Vogel–Fulcher–Tammann (VFT) law is considered due to its property between the viscoelastic and the temperature. Consequently, the improved Nishihara-type model coupled with the thermal effect is reassembled by the Caputo-Mainardi dashpot and the VFT-Caputo-Mainardi dashpot instead of the classical dashpot. According to the theory of the Weibull distribution statistics and the continuum damage mechanics, the thermal damage effective stress is presented to describe the accelerated creep stage. The adoption of the Laplace transform gives a convenient way to solve the proposed model and deduce the strain equation of it. Draw support from the numerical simulation software, the parameters of the improved fractional TDNM were determined successfully. The fitting curve and the experimental data of the two specimens both approximately consist with each other, indicating the rationality and correctness of the improved model. Therefore, the improved model can give a better description of the thermal coupling characteristics of the salt rock and overcome the deficiency of the classical Nishihara model that can not describe the accelerated creep accurately. The creep deformation curve of salt rock can be simulated by changing the value of model parameters, thereby providing the theoretical basis of the salt rock destroying characteristic and the countermeasures of prevention and control.

中文翻译：

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一种考虑热效应的蠕变损伤分数 Nishihara 型新模型

摘要 本文的主要目标是研究基于Caputo分数阶导数的蠕变损伤温度相关Nishihara型模型(TDNM)。Vogel-Fulcher-Tammann (VFT) 定律被认为是由于其介于粘弹性和温度之间的特性。因此，结合热效应的改进的 Nishihara 型模型由 Caputo-Mainardi 缓冲器和 VFT-Caputo-Mainardi 缓冲器重新组装，而不是经典缓冲器。根据威布尔分布统计理论和连续介质损伤力学理论，提出了热损伤有效应力来描述加速蠕变阶段。拉普拉斯变换的采用提供了一种方便的方法来求解所提出的模型并推导出其应变方程。借助数值模拟软件，成功地确定了改进的分数TDNM的参数。两个试件的拟合曲线和实验数据基本一致，说明改进模型的合理性和正确性。因此，改进后的模型可以更好地描述盐岩的热耦合特性，克服了经典西原模型不能准确描述加速蠕变的不足。通过改变模型参数的取值，可以模拟盐岩蠕变变形曲线，从而为盐岩破坏特征及防治对策提供理论依据。两个试件的拟合曲线和实验数据基本一致，说明改进模型的合理性和正确性。因此，改进后的模型可以更好地描述盐岩的热耦合特性，克服了经典西原模型不能准确描述加速蠕变的不足。通过改变模型参数的取值，可以模拟盐岩蠕变变形曲线，从而为盐岩破坏特征及防治对策提供理论依据。两个试件的拟合曲线和实验数据基本一致，说明改进模型的合理性和正确性。因此，改进后的模型可以更好地描述盐岩的热耦合特性，克服了经典西原模型不能准确描述加速蠕变的不足。通过改变模型参数的取值，可以模拟盐岩蠕变变形曲线，从而为盐岩破坏特征及防治对策提供理论依据。改进后的模型可以更好地描述盐岩的热耦合特性，克服了经典西原模型不能准确描述加速蠕变的不足。通过改变模型参数的取值，可以模拟盐岩蠕变变形曲线，从而为盐岩破坏特征及防治对策提供理论依据。改进后的模型可以更好地描述盐岩的热耦合特性，克服了经典西原模型不能准确描述加速蠕变的不足。通过改变模型参数的取值，可以模拟盐岩蠕变变形曲线，从而为盐岩破坏特征及防治对策提供理论依据。