基于分数阶导数的盐岩流变本构模型

Zhou, Hongwei; Wang, ChunPing; Duan, ZhiQiang; Zhang, Miao; Liu, Jianfeng

doi:10.1360/132011-616

Cited by 25 publications

(7 citation statements)

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“…The constitutive equation based on the fractional derivative [32] is established as. σt=ηndnεfalse(tfalse)dtn,0≤n≤1 where the stress σ remains constant; that is, σ=const.…”

Section: Construction Of Concrete Nonlinear Creep Damage Constitutmentioning

confidence: 99%

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Nonlinear Creep Damage Constitutive Model of Concrete Based on Fractional Calculus Theory

Zhang

Zhu

et al. 2019

Materials

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Concrete creep has become one of the major problems that threatens concrete structural development and construction. However, a reasonable and accurate calculation model for numerical analysis is the key to control and solve the creep deformation of concrete. To better describe the concrete nonlinear creep damage evolution rule, the visco-elasticity Plasticity Rheological Theory, Riemann Liouville Theory and Combined Model Theory are quoted, and the Able dashpot is used to reconstruct fractional-order soft-body composite elements to propose the expression of the stress-strain relationship of the elastomer, visco-elasticity plasticity body, and Viscoplasticity body, considering the evolution of the concrete compression damage process. A nonlinear creep damage constitutive model of concrete, based on fractional calculus theory, is conducted, and the parameters of the specific calculation method of the model are given. The influence of stress level σ, fractional order n and material parameter α on the concrete creep process is determined by a sensitivity analysis of the model parameters. The creep process and deformation amount of concrete in practical engineering can be effectively controlled by the results of the proposed sensitivity analysis. The research results can be used to provide guidance and reference for the safe construction of concrete engineering in actual practice.

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“…The constitutive equation based on the fractional derivative [32] is established as. σt=ηndnεfalse(tfalse)dtn,0≤n≤1 where the stress σ remains constant; that is, σ=const.…”

Section: Construction Of Concrete Nonlinear Creep Damage Constitutmentioning

confidence: 99%

“…According to the theory of fractional calculus [32,36], the following can be obtained:εvp=σ−σS2η2ntnsans-serifΓfalse(1+nfalse)…”

Section: Construction Of Concrete Nonlinear Creep Damage Constitutmentioning

confidence: 99%

Nonlinear Creep Damage Constitutive Model of Concrete Based on Fractional Calculus Theory

Zhang

Zhu

et al. 2019

Materials

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“…其中Hansbo的分段幂函数型与Swartzendruber连续指数型方程广泛应用于固结分析问题 [12][13][14] . [15,16] 基于分数阶微积分理论, 构建了盐岩分数阶流变的本构模型; Chen 等人 [17] 构建了分数阶反常扩散方程来描述钢筋混凝土结构中氯离子的扩散过程; Tian等人 [18] 利用分数阶方法研究了分形孔隙介质条件下的径向渗流问题. 可见, 分数阶微积分方法在研究非线性问题提供了新的…”

Section: -2unclassified

The study on non-Darcy seepage equation of low velocity flow

Wang¹,

Zhou²,

Zhong³

et al. 2017

Sci. Sin.-Phys. Mech. Astron.

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Effect of thermal radiation on mixed convection of a nanofluid from an inclined wavy surface embedded in a non-Darcy porous medium with wall heat flux Propulsion and Power Research 7, 147 (2018); Darcy-Forchheimer relation in Casson type MHD nanofluid flow over non-linear stretching surface Propulsion and Power Research 9, 159 (2020); An unsteady seepage flow model considering kickoff pressure gradient for low-permeability gas reservoirs Petroleum Exploration and Development 35, 457 (2008); Effects of velocity and thermal wall slip on magnetohydrodynamics (MHD) boundary layer viscous flow and heat transfer of a nanofluid over a non-linearly-stretching sheet: a numerical study

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“…The parameters of Fq. (24) are shown in Table 1. Let n = 1,6,8.31,10, a series of creep curves can be plotted in Fig.…”

Section: Experimental Data Analysis and Verificationmentioning

confidence: 99%

A Nonlinear Viscoelastic-Plastic Rheological Model for Rocks Based on Fractional Derivative Theory

Chen

Wang

et al. 2013

Int. J. Mod. Phys. B

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The soft-matter element between the ideal solid and the ideal liquid is established and is described based on the definition of the fractional derivatives. By replacing a component in the generalized Kelvin model with the soft-matter component and connecting it in series with a nonlinear visco-plastic body, a nonlinear viscoelasto-plastic rheological model is proposed based on the fractional derivatives in order to describe the rheological behaviors of rocks. The data obtained from the triaxial creep tests of a typical rock are simulated with this model and the fitting result is good. The model can describe well three rheological stages of the rock during the triaxial creep tests. The validity of this model is then discussed. In this model, the fractional order ß controls creep strain rate in the stable creep stage under the condition of low stress; while the creep index n controls creep rate of the accelerated rheological stage under the condition of high stress. Few parameters and good simulation results manifest the outstanding performance of the model. The model also adopts the damage theory to describe the progressive deterioration of rock viscous coefficient of the accelerated creep stage. The model can also give an excellent description of the three rheological stages of rocks, especially the accelerated creep stage., .-.

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基于分数阶导数的盐岩流变本构模型

Cited by 25 publications

References 0 publications

Nonlinear Creep Damage Constitutive Model of Concrete Based on Fractional Calculus Theory

Nonlinear Creep Damage Constitutive Model of Concrete Based on Fractional Calculus Theory

The study on non-Darcy seepage equation of low velocity flow

A Nonlinear Viscoelastic-Plastic Rheological Model for Rocks Based on Fractional Derivative Theory

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