Non‐normality and induced plastic anisotropy under fractional plastic flow rule: a numerical study

Sumelka, Wojciech; Nowak, Marcin

doi:10.1002/nag.2421

Cited by 54 publications

(15 citation statements)

References 68 publications

(92 reference statements)

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“…The interpretation of the virtual surrounding in a stress state depends on the specific material (see [28]), but in general it could be understood as a (homogenized) phenomenological measure of some instability, e.g., for metallic materials it is connected with dislocation nucleation [32][33][34], nucleation of voids [35] or breakup of grains [36][37][38] (see review paper [39]). By way of illustration, Figure 1 shows the cross-section of this virtual neighbourhood in the σ 2 − σ 3 plane.…”

Section: Methodsmentioning

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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Section: Methodsmentioning

confidence: 99%

Numerical Study of Dynamic Properties of Fractional Viscoplasticity Model

2018

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“…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]. To consider the state dependence, the state-dependent fractional plasticity model was then proposed [14] by empirically incorporating ψ, which however made the parameters of the obtained stress-dilatancy equation lack physical meaning.…”

Section: Introductionmentioning

confidence: 99%

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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“…This mathematical approach has been introduced in describing the viscous behavior of materials, (cf. [21] and references therein), non-normal plastic flow [22], or finally spatial non-locality [23][24][25][26][27][28][29]. In the latter case, to the best of the authors' knowledge, the comparison with the Born-Von Karman model has not been studied before.…”

Section: Introductionmentioning

confidence: 99%

One-dimensional dispersion phenomena in terms of fractional media

2016

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Abstract. It is well know that structured solids present dispersive behaviour which cannot be captured by the classical continuum mechanics theories. A canonical problem in which this can be seen is the wave propagation in the Born-Von Karman lattice. In this paper the dispersive effects in a 1D structured solid is analysed using the Fractional Continuum Mechanics (FCM) approach previously proposed by Sumelka (2013). The formulation uses the Riesz-Caputo (RC) fractional derivative and introduces two phenomenological/material parameters: 1) the size of non-local surrounding l f , which plays the role of the lattice spacing; and 2) the order of fractional continua α, which can be devised as a fitting parameter. The results obtained with this approach have been compared with the reference dispersion curve of Born-Von Karman lattice, and the capability of the fractional model to capture the size effects present in the dynamic behaviour of discrete systems has been proved.

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Non‐normality and induced plastic anisotropy under fractional plastic flow rule: a numerical study

Cited by 54 publications

References 68 publications

Numerical Study of Dynamic Properties of Fractional Viscoplasticity Model

Numerical Study of Dynamic Properties of Fractional Viscoplasticity Model

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

One-dimensional dispersion phenomena in terms of fractional media

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