Constitutive Model of Granular Soils Using Fractional-Order Plastic-Flow Rule

Sun, Yifei; Shen, Yang

doi:10.1061/(asce)gm.1943-5622.0000904

Cited by 58 publications

(21 citation statements)

References 35 publications

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“…Note that detailed derivations of Eqs. (25) and (26) can be found in Sun and Shen [21] and Sun et al [49], thus not repeated here for simplicity.…”

Section: Bounding Surface and Loading Directionmentioning

confidence: 99%

“…α is the fractional order and should be at least less than two due to the thermodynamic restriction for a positive plastic dissipation [27]. As discussed in Sun and Shen [21], α represents the extent of non-associativity between plastic flow and loading directions as well as the degree of state dependence of material deformation. σ is the current effective stress, while σ c is the corresponding critical-state stress.…”

Section: Fractional Derivative and Yielding Surfacementioning

confidence: 99%

“…Undeniably, this approach can always substantially improve the model performance; however, the empirical correlation between the state variable and the existing constitutive parameters would inevitably result in more model parameters. It was found that the fractional mechanics was an efficient way to capture the relaxation [17], diffusion [18][19][20], and stress-strain [14,21] behaviour of materials. To reduce the number of model parameters without the loss of modelling capability, Sun and Shen [21] proposed a non-associated plastic flow rule for granular soil by simply conducting fractional-order derivatives of the yielding surface, where the obtained vector (plastic flow direction) was no longer normal to the yielding surface, even without using an additional plastic potential.…”

Section: Introductionmentioning

confidence: 99%

“…It was found that the fractional mechanics was an efficient way to capture the relaxation [17], diffusion [18][19][20], and stress-strain [14,21] behaviour of materials. To reduce the number of model parameters without the loss of modelling capability, Sun and Shen [21] proposed a non-associated plastic flow rule for granular soil by simply conducting fractional-order derivatives of the yielding surface, where the obtained vector (plastic flow direction) was no longer normal to the yielding surface, even without using an additional plastic potential. This non-normality increased as the fractional order (α) decreased [14,22,23].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Fractional-order modelling of state-dependent non-associated behaviour of soil without using state variable and plastic potential

Sun

Zheng

2019

Adv Differ Equ

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It was found that the constitutive behaviour of granular soil was dependent on its density and pressure (i.e. material state). To capture such state dependence, a variety of state variables were empirically proposed and introduced into the existing plastic potential functions, which inevitably resulted in the complexity and meaninglessness of some model parameters. The purpose of this study is to theoretically investigate the state-dependent non-associated behaviour of granular soils without using predefined plastic potential and state variable. A novel state-dependent non-associated model for granular soils is mathematically developed by incorporating the stress-fractional operator into the bounding surface plasticity. Unlike previous studies using empirical state variables, the soil state and non-associativity in this study are considered via analytical solution, where a state-dependent plastic flow rule and the corresponding hardening modulus without using additional plastic potentials are obtained. Possible mathematical connection with a well-known empirical state variable is also discussed. The non-associativity between plastic flow and loading directions as well as material hardening is found to be controlled by the fractional-derivative order. To validate the proposed approach, a series of drained and undrained triaxial test results of different granular soils are simulated and compared, where a good agreement between the model predictions and the corresponding test results is observed.

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“…Note that detailed derivations of Eqs. (25) and (26) can be found in Sun and Shen [21] and Sun et al [49], thus not repeated here for simplicity.…”

Section: Bounding Surface and Loading Directionmentioning

confidence: 99%

Section: Fractional Derivative and Yielding Surfacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fractional-order modelling of state-dependent non-associated behaviour of soil without using state variable and plastic potential

Sun

Zheng

2019

Adv Differ Equ

Self Cite

View full text Add to dashboard Cite

show abstract

“…On the other hand, the space-fractional models are successfully used in mechanics to describe the deformation of a harmonic oscillator [12], deformation of an infinite bar subjected to a self-equilibrated load distribution [13], modeling plane strain and plane stress elasticity [14], Euler-Bernoulli beam [15], Darcy's flow in porous media [16] and fractional strain formulation [17]. Finally, the stress-fractional models [18,19] and their finite element implementations were used to study the granular soils under drained cyclic loading [20], and monotonic triaxial compression [21]. Concluding, one should emphasize that regardless of the specific formulation, the fractional operators have one common feature, namely, the 'change' of a selected variable is based on integration over a closed interval, thus extending the definition of integer order derivative (defined in a point) and simultaneously introducing a non-locality in a given space.…”

Section: Introductionmentioning

confidence: 99%

Numerical Study of Dynamic Properties of Fractional Viscoplasticity Model

2018

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Abstract:The fractional viscoplasticity (FV) concept combines the Perzyna type viscoplastic model and fractional calculus. This formulation includes: (i) rate-dependence; (ii) plastic anisotropy; (iii) non-normality; (iv) directional viscosity; (v) implicit/time non-locality; and (vi) explicit/stress-fractional non-locality. This paper presents a comprehensive analysis of the above mentioned FV properties, together with a detailed discussion on a general 3D numerical implementation for the explicit time integration scheme.

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A homogenization‐based state‐dependent model for gap‐graded granular materials with fine‐dominated structure

Shi

Zhao

Gao

2021

Num Anal Meth Geomechanics

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Gap‐graded granular soils are common natural soils composed of cohesionless granular matrix and rock aggregates. Since they are widely used as construction materials worldwide, their deformation behavior is crucial for the design of civil infrastructures. There have been rare constitutive models reported for gap‐graded granular soils in the literature. This study presents a homogenization‐based state‐dependent model within the elastoplastic framework. The model features a homogenization equation with a structure parameter and a novel state‐dependent dilatancy function to describe the behavior of granular matrix. Simulations of the model reveals that the initial stiffness and peak shear strength of gap‐graded soils rely on both the coarse fraction and the initial density of granular matrix. The structure parameter is related to the internal structure of gap‐graded soils, and it varies with the particle shape, and particle size distribution of rock aggregates. A higher value of the structure parameter indicates a more distinct coarse fraction effect of rock aggregates, that is, higher initial stiffness, higher peak shear strength, and higher residual shear strength. For a given coarse fraction, the critical states can be well fitted by a straight line through the origin, and the critical state strength parameter Mm increases with the rising rock fraction. A practical method is further proposed for the critical state line of gap‐graded granular soils in e‐p′ compression plane. The proposed model is validated by using experimental data from the literature, including the soils with various densities of sand matrix, different particle size, and particle size distribution of rock aggregates. Comparison between measured data and model predictions indicates that the proposed model can well reproduce the stress‐strain relationship and volumetric deformation behavior of sand‐gravel mixtures and soil‐rock mixtures.

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Constitutive Model of Granular Soils Using Fractional-Order Plastic-Flow Rule

Cited by 58 publications

References 35 publications

Fractional-order modelling of state-dependent non-associated behaviour of soil without using state variable and plastic potential

Fractional-order modelling of state-dependent non-associated behaviour of soil without using state variable and plastic potential

Numerical Study of Dynamic Properties of Fractional Viscoplasticity Model

A homogenization‐based state‐dependent model for gap‐graded granular materials with fine‐dominated structure

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