A new fractional Nishihara-type model with creep damage considering thermal effect

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.