Journal ArticleDOI
An improved Maxwell creep model for rock based on variable-order fractional derivatives
Fei Wu,Jianfeng Liu,Jun Wang +2 more
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TLDR
For describing the time-dependent mechanical property of rock during the creep, a new method of building creep model based on variable-order fractional derivatives is proposed in this article, where the order of the fractional derivative is allowed to be a function of the independent variable (time), rather than a constant of arbitrary order.Abstract:
For describing the time-dependent mechanical property of rock during the creep, a new method of building creep model based on variable-order fractional derivatives is proposed. The order of the fractional derivative is allowed to be a function of the independent variable (time), rather than a constant of arbitrary order. Through the segmentation treatment, according to different creep stages of the experimental results, it is found that the improved creep model based on variable-order fractional derivatives agrees well with the experimental data. In addition, the fact is verified that variable order of fractional derivatives can be regarded as a step function, which is reasonable and reliable. In addition, through further piecewise fitting, the parameters in the model are determined on the basis of existing experimental results. All estimated results show that the theoretical model proposed in the paper properly depicts the creep properties, providing an excellent agreement with the experimental data.read more
Citations
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A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications
TL;DR: In this article, a survey of the recent relevant literature and findings in primary definitions, models, numerical methods and their applications is provided, which can help the readers for the selection of appropriate definition, model and numerical method to solve specific physical and engineering problems.
Journal ArticleDOI
Applications of variable-order fractional operators: a review
TL;DR: This review provides a concise and comprehensive summary of the progress made in the development of VO-FC analytical and computational methods with application to the simulation of complex physical systems.
Journal ArticleDOI
A nonlinear creep damage model for salt rock
TL;DR: In the creep tests, stress is no longer a constant and increases gradually under the influence of damage occurring during accelerating creep, which is a slow-loading process rather than a conventio...
Journal ArticleDOI
Fractional viscoelastic models for power-law materials
TL;DR: In this article, the authors provide a clear and accessible description of fractional viscoelastic models for a broad audience, and demonstrate the ability of these models to deliver a unified approach for the characterisation of power-law materials.
Journal ArticleDOI
Creep constitutive models for viscoelastic materials based on fractional derivatives
Huanying Xu,Xiaoyun Jiang +1 more
TL;DR: The results demonstrate that the fractional PoyntingThomson model is optimal in simulating the creep behavior of viscoelastic materials and it also shows that the interior-point method is effective in the inverse problem to estimate parameters of fractional viscoELastic models.
References
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Journal ArticleDOI
A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity
Ronald L. Bagley,Peter J. Torvik +1 more
TL;DR: In this article, the authors established a link between molecular theories that predict the macroscopic behavior of certain viscoelastic media and an empirically developed fractional calculus approach to visco-elasticity.
Journal ArticleDOI
Applications of Fractional Calculus to the Theory of Viscoelasticity
TL;DR: The relation entre le calcul fractionnaire and the theory of l'equation integrale d'Abel for les materiaux a memoire is discussed in this paper.
Journal ArticleDOI
On the Fractional Calculus Model of Viscoelastic Behavior
Ronald L. Bagley,Peter J. Torvik +1 more
TL;DR: In this paper, a mathematical model of the viscoelastic phenomenon employing derivatives of fractional order is examined in light of its consistency with thermodynamic principles, which leads the model to predict realistic sinusoidal response as well as realistic relaxation and creep responses.
Journal ArticleDOI
A creep constitutive model for salt rock based on fractional derivatives
TL;DR: In this article, a new creep constitutive model is proposed on the basis of time-based fractional derivative, which is based on the Newtonian dashpot in the classical Nishihara model.