Fractional viscoplastic model for soils under compression

Sun, Yifei; Sumelka, Wojciech

doi:10.1007/s00707-019-02466-z

Cited by 26 publications

(12 citation statements)

References 49 publications

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“…As fractal theory is now widely used [15][16][17][18][19][20][21][22][23], many researchers [24][25][26][27][28][29][30][31] have found that geomaterials exhibit fractal characteristics, and the rock joints, particle distribution, and pores at different scales have self-similarity, which is also consistent with the evolution of geomaterials under natural conditions. Generally, geomaterials can be regarded as an open non-linear self-organizing system.…”

Section: Introductionmentioning

confidence: 70%

Fractal Analysis of Particle Distribution and Scale Effect in a Soil–Rock Mixture

Ding

Sheng

et al. 2022

Fractal Fract

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A soil–rock mixture (SRM) is a type of heterogeneous geomaterial, and the particle distribution of SRM can be described by fractal theory. At present, it is difficult to quantify the fractal dimension of a particle size distribution and understand the scale effect in SRMs. In this study, the fractal theory and discrete element method (DEM) were introduced to solve this problem. First, the particle gradation of SRM was dealt with by using fractal theory. The fractal structure of particle distribution was studied, and a method of calculation of the fractal dimension is presented in this paper. Second, based on the fractal dimension and relative threshold, the particle gradations of SRMs at different scales were predicted. Third, numerical direct shear tests of SRM at different scales were simulated by using the DEM. The scale effects of shear displacement, shear zone, and shear strength parameters were revealed. Last, taking the maximum particle size of 60 mm as the standard value, the piece-wise functional relationship between shear strength parameters and particle size was established. The results are as follows: for SRM in a representative engineering area, by plotting the relationship between particle cumulative mass percentage and particle size, we can judge whether the SRM has a fractal structure; in Southwest China, the frequency of the fractal dimension of the SRM is in the normal distribution, and the median fractal dimension is 2.62; the particle gradations of SRMs at different scales calculated by fractal dimension and relative threshold can expand the study scope of particle size analysis; when the particle size is less than 70 mm, the strength parameters show a parabolic trend with the particle size increases, and if not, a nearly linear trend is found. The proposed method can describe the fractal characteristics of SRM in a representative engineering area and provides a quantitative estimation of shear strength parameters of SRM at different scales.

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Section: Introductionmentioning

confidence: 70%

Fractal Analysis of Particle Distribution and Scale Effect in a Soil–Rock Mixture

Ding

Sheng

et al. 2022

Fractal Fract

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“…for left-and right-sided fractional Caputo derivatives [216] with n = α . Finally, stress-fractional models for plasticity have found applicability in soil mechanics and geomaterials that follow non-associated plastic flow [217,224], i.e., the yield surface expansion in the stress space does not follow the usual normality rule, and may be non-convex. The work by Sumelka [217] proposed a three-dimensional fractional viscoplastic model, where a fractional flow rule with order 0 < α < 1 in the stress domain naturally models non-associative plasticity.…”

Section: Visco-elasto-plasticitymentioning

confidence: 99%

“…Interestingly, this model recovers the classical Perzyna visco-plasticity as α → 1, and the effect of the fractional flow rule can be a compact descriptor of microstructure anisotropy. Recently, a similar stress-fractional model was developed [224], and successfully applied to soils under compression. We refer the reader to the detailed review work by Sun et al [222] for a review of uses fractional calculus in plasticity.…”

Section: Visco-elasto-plasticitymentioning

confidence: 99%

Fractional Modeling in Action: A Survey of Nonlocal Models for Subsurface Transport, Turbulent Flows, and Anomalous Materials

Suzuki¹,

Gulian²,

Zayernouri³

et al. 2021

Preprint

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Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior with greater efficiency than fully-resolved classical models. In this review article, we first provide a broad overview of fractional-order derivatives with a clear emphasis on the stochastic processes that underlie their use. We then survey three exemplary application areas -subsurface transport, turbulence, and anomalous materials -in which fractional-order differential equations provide accurate and predictive models. For each area, we report on the evidence of anomalous behavior that justifies the use of fractional-order models, and survey both foundational models as well as more expressive state-of-the-art models. We also propose avenues for future research, including more advanced and physically sound models, as well as tools for calibration and discovery of fractional-order models.

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“…e viscoplastic flow direction of soil is simulated by the unit tensor obtained by the fractional derivative of the yield surface. With the increase of fractional order, the predicted compressive shear strength changes, and the transition from pure strain hardening to strain hardening and softening is observed [22]. Liang et al applied the nonorthogonal plastic flow rule to capture the shear expansion behavior of sand.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Damage Constitutive Model for Frozen Red Clay under Uniaxial Compression

Lin

Zhao

2022

Advances in Materials Science and Engineering

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At present, it is in the peak period of infrastructure construction in western China, and due to the natural climate, the soil has been frozen for a long time, but there is little research on frozen red clay at present. Therefore, it is necessary to further study the mechanical properties of frozen red clay. In this paper, taking the remolded red clay as the test material, the change characteristics of uniaxial compression and uniaxial creep of frozen soil under different test factors are studied by artificial freezing method, and the damage theory is introduced to analyze the test results. The results of uniaxial compression test of frozen soil show that temperature has a great influence on the uniaxial compressive strength, and the compressive strength increases with the decrease of temperature, and the damage theory is introduced. It is found that the initial damage stress increases with the decrease of temperature, while the initial strain changes little with temperature. A damage constitutive equation which can well reflect the whole damage process of frozen red clay is established. The experimental research results of this paper can provide some theoretical reference for the engineering of soil quality for freezing red clay.

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Fractional viscoplastic model for soils under compression

Cited by 26 publications

References 49 publications

Fractal Analysis of Particle Distribution and Scale Effect in a Soil–Rock Mixture

Fractal Analysis of Particle Distribution and Scale Effect in a Soil–Rock Mixture

Fractional Modeling in Action: A Survey of Nonlocal Models for Subsurface Transport, Turbulent Flows, and Anomalous Materials

Analysis of Damage Constitutive Model for Frozen Red Clay under Uniaxial Compression

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