A variable-order fractional derivative creep constitutive model of salt rock based on the damage effect

2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Jie Liu ◽  
Fei Wu ◽  
Quanle Zou ◽  
Jie Chen ◽  
Song Ren ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Fractional Derivative ◽  
Damage Effect ◽  
Variable Order ◽  
Salt Rock ◽  
Creep Constitutive Model ◽  
Variable Order Fractional Derivative

scholarly journals On the sub–diffusion fractional initial value problem with time variable order

2021 ◽  
Vol 10 (1) ◽  
pp. 1301-1315
Author(s):  
Eduardo Cuesta ◽  
Mokhtar Kirane ◽  
Ahmed Alsaedi ◽  
Bashir Ahmad
Keyword(s):  
Asymptotic Behavior ◽  
Fractional Derivative ◽  
Initial Value Problem ◽  
Regularity Result ◽  
Time Variable ◽  
Variable Order ◽  
Initial Value ◽  
Integration By Parts ◽  
Integration By Parts Formula ◽  
Variable Order Fractional Derivative

Abstract We consider a fractional derivative with order varying in time. Then, we derive for it a Leibniz' inequality and an integration by parts formula. We also study an initial value problem with our time variable order fractional derivative and present a regularity result for it, and a study on the asymptotic behavior.

Study on the Creep Parameters of Salt Rock Constitutive Function

2014 ◽  
Vol 1079-1080 ◽  
pp. 166-169 ◽  
Author(s):  
Hai Peng Zhang ◽  
Yi Jin ◽  
Long Ma
Keyword(s):  
Constitutive Model ◽  
Creep Test ◽  
Constitutive Equations ◽  
Determination Method ◽  
Salt Rock ◽  
Constitutive Function ◽  
Rock Creep ◽  
Creep Models ◽  
Creep Constitutive Model

Salt rock is a kind ofthe most suitablemedium for energy storages, because of its strongcreep behavior. "Burgers" and "Norton" is the two classic creep models. This paper starts from the establishment of creep constitutive model to obtain the determination method of creep constitutive parameters.Finally, it takes Nanjing salt rock creep test (2003) as an example to solve the parameters in Burgers and Norton constitutive equations.

SM-Algorithms for Approximating the Variable-Order Fractional Derivative of High Order

2017 ◽  
Vol 151 (1-4) ◽  
pp. 293-311 ◽  
Author(s):  
B. P. Moghaddam ◽  
J. A. T. Machado
Keyword(s):  
Fractional Derivative ◽  
High Order ◽  
Variable Order ◽  
Variable Order Fractional Derivative

scholarly journals A Numerical Scheme Based on the Chebyshev Functions to Find Approximate Solutions of the Coupled Nonlinear Sine-Gordon Equations with Fractional Variable Orders

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
MohammadHossein Derakhshan
Keyword(s):  
Fractional Derivative ◽  
Numerical Method ◽  
Numerical Scheme ◽  
Numerical Approximation ◽  
Operational Matrix ◽  
Approximate Solutions ◽  
Variable Order ◽  
Algebraic Equations ◽  
Variable Order Fractional Derivative ◽  
Chebyshev Functions

In this article, a numerical method based on the shifted Chebyshev functions for the numerical approximation of the coupled nonlinear variable-order fractional sine-Gordon equations is shown. The variable-order fractional derivative is considered in the sense of Caputo-Prabhakar. To solve the problem, first, we obtain the operational matrix of the Caputo-Prabhakar fractional derivative of shifted Chebyshev polynomials. Then, this matrix and collocation method are used to reduce the solution of the nonlinear coupled variable-order fractional sine-Gordon equations to a system of algebraic equations which is technically simpler for handling. Convergence and error analysis are examined. Finally, some examples are given to test the proposed numerical method to illustrate the accuracy and efficiency of the proposed method.

A creep constitutive model for salt rock based on fractional derivatives

2011 ◽  
Vol 48 (1) ◽  
pp. 116-121 ◽  
Author(s):  
H.W. Zhou ◽  
C.P. Wang ◽  
B.B. Han ◽  
Z.Q. Duan
Keyword(s):  
Constitutive Model ◽  
Fractional Derivatives ◽  
Salt Rock ◽  
Creep Constitutive Model

scholarly journals A non-linear creep constitutive model for salt rock based on fractional derivatives

2019 ◽  
Vol 23 (Suppl. 3) ◽  
pp. 773-779 ◽  
Author(s):  
Jie Chen ◽  
Dan Lu ◽  
Fei Wu ◽  
Jinyang Fan ◽  
Wei Liu
Keyword(s):  
Constitutive Model ◽  
Creep Property ◽  
Salt Rock ◽  
Whole Process ◽  
Rock Creep ◽  
Non Linear ◽  
Accelerated Creep ◽  
Deep Underground ◽  
Abel Dashpot ◽  
Creep Constitutive Model

The creep property of the salt rock is an important determinant of deep underground repository of energy storage for long-term operatio. Starting from fractional derivative, this paper proposes a new concept of super Abel dashpot based on Abel dashpot. According to the Nishihara model, the non-linear element of super Abel dashpot is introduced, and a new salt rock creep constitutive model is established. The theoretical analytic solution of this model is then deduced. Fitting analysis of the experimental data indicates that the model can well reflect the whole-process creep curve, especially the non-linear accelerated creep stage.

Fractional derivative-based creep constitutive model of deep artificial frozen soil

2020 ◽  
Vol 170 ◽  
pp. 102942 ◽  
Author(s):  
Dongwei Li ◽  
Chaochao Zhang ◽  
Guosheng Ding ◽  
Hua Zhang ◽  
Junhao Chen ◽  
...  
Keyword(s):  
Constitutive Model ◽  
Fractional Derivative ◽  
Frozen Soil ◽  
Creep Constitutive Model
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