Probabilistic yielding and cyclic behavior of geomaterials

Sett, Kallol; Jeremić, Boris

doi:10.1002/nag.870

Cited by 9 publications

(6 citation statements)

References 22 publications

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“…The most general, rate form of the constitutive equation for an uncertain, elastic‐plastic material, when written in the probability density space, becomes 2 coupled FPK PDEs of the following forms:

\begin{matrix} right \frac{\partial P (σ, t)}{\partial t} & left = - \frac{\partial}{\partial σ_{m n}} [N_{{(1)}_{m n}}^{σ^{e q}} (σ, q; t) P (σ, t)] & right \\ right & left + \frac{\partial^{2}}{\partial σ_{m n} \partial σ_{a b}} [N_{{(2)}_{m n a b}}^{σ^{e q}} (σ, q; t) P (σ, t)], \end{matrix}

\begin{matrix} right \frac{\partial \tilde{P} (q, t)}{\partial t} & left = - \frac{\partial}{\partial q_{i}} [N_{{(1)}_{i}}^{{I V}^{e q}} (σ, q; t) \tilde{P} (q, t)] & right \\ right & left + \frac{\partial^{2}}{\partial q_{i} \partial q_{j}} [N_{{(2)}_{i j}}^{I V}] \end{matrix}

…”

Section: The Fpk Equations In Probabilistic Elasto‐plasticitymentioning

confidence: 99%

“…The most general, rate form of the constitutive equation for an uncertain, elastic-plastic material, when written in the probability density space, becomes 2 coupled FPK PDEs of the following forms 3,4,8,9,16 :…”

Section: The Fpk Equations In Probabilistic Elasto-plasticitymentioning

confidence: 99%

“…It also avoids the small variance requirement and closure problem associated with the regular perturbation approach. FPK approach to probabilistic elasto‐plasticity has been used to simulate both monotonic and cyclic hardening and softening type uncertain material behaviors . It has also been successfully integrated with the spectral approach of the stochastic finite element (FE) method to probabilistically solve stochastic elastic‐plastic boundary value problems …”

Section: Introductionmentioning

confidence: 99%

“…FPK approach to probabilistic elasto-plasticity has been used to simulate both monotonic and cyclic hardening and softening type uncertain material behaviors. 8,9 It has also been successfully integrated with the spectral approach of the stochastic finite element (FE) method to probabilistically solve stochastic elastic-plastic boundary value problems. 10,11 Traditionally, in mechanics, an FPK equation is solved numerically using the finite difference or FE technique.…”

Section: Introductionmentioning

confidence: 99%

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Efficient solution algorithms for multiaxial probabilistic elasto‐plastic constitutive simulations of soils

Sadrinezhad

Sett

Hariharan

2017

Num Anal Meth Geomechanics

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Summary A Fokker‐Planck‐Kolmogorov (FPK) equation approach has recently been developed to probabilistically solve any elastic‐plastic constitutive equation with uncertain material parameters by transforming the nonlinear, stochastic constitutive rate equation into a linear, deterministic partial differential equation (PDE) and thereby simplifying the numerical solution process. For an uniaxial problem, conventional numerical techniques, such as the finite difference or finite element methods, may be used to solve the resulting univariate FPK PDE. However, for a multiaxial problem, an efficient algorithm is necessary for tractability of the numerical solution of the multivariate FPK PDE. In this paper, computationally efficient algorithms, based on a Fourier spectral approach, are presented for solving FPK PDEs in (stress) space and (pseudo) time, having space‐independent but time‐dependent coefficients and both space‐ and time‐dependent coefficients, that commonly arise in probabilistic elasto‐plasticity. The algorithms are illustrated by probabilistically simulating 2 common laboratory constitutive experiments in geotechnical engineering, namely, the unconfined compression test and the unconsolidated undrained triaxial compression test.

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\begin{matrix} right \frac{\partial P (σ, t)}{\partial t} & left = - \frac{\partial}{\partial σ_{m n}} [N_{{(1)}_{m n}}^{σ^{e q}} (σ, q; t) P (σ, t)] & right \\ right & left + \frac{\partial^{2}}{\partial σ_{m n} \partial σ_{a b}} [N_{{(2)}_{m n a b}}^{σ^{e q}} (σ, q; t) P (σ, t)], \end{matrix}

\begin{matrix} right \frac{\partial \tilde{P} (q, t)}{\partial t} & left = - \frac{\partial}{\partial q_{i}} [N_{{(1)}_{i}}^{{I V}^{e q}} (σ, q; t) \tilde{P} (q, t)] & right \\ right & left + \frac{\partial^{2}}{\partial q_{i} \partial q_{j}} [N_{{(2)}_{i j}}^{I V}] \end{matrix}

…”

Section: The Fpk Equations In Probabilistic Elasto‐plasticitymentioning

confidence: 99%

Section: The Fpk Equations In Probabilistic Elasto-plasticitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient solution algorithms for multiaxial probabilistic elasto‐plastic constitutive simulations of soils

Sadrinezhad

Sett

Hariharan

2017

Num Anal Meth Geomechanics

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“…They showed that by considering the uncertainty in yield stress, the average (mean) constitutive response and the most probable (mode) constitutive response show nonlinear behavior from the very beginning, even for the simplest elastic-perfectly plastic material model [18]. To make this method more general, Sett and Jeremi´c also discussed the effect of probabilistic yielding on constitutive simulation under cyclic loading [19] . In 2014, Sadrinezhad and Sett extended the one-dimensional framework to a multi-dimensional framework to simulate the probabilistic elastic plastic constitutive behaviour of soils [20,21].…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Elastic–Plastic Cam Clay Response of Soils

Sadrinezhad¹,

Sett²

2017

Proceedings of the 2nd World Congress on Civil, Structural, and Environmental Engineering

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-This study uses Cam Clay model to investigate the influence of uncertainties in soil properties on simulated undrained triaxial constitutive response. To this end, recently developed Fokker-Planck-Kolmogorov (FPK) equation approach to probabilistic elasto-plasticity is employed. The most general form of the three dimensional elastic-plastic constitutive rate equation is written in probability density space, resulting in a multi-dimensional FPK equation. The resultant FPK equation is specialized to undrained stress path. Given the second order statistics of the uncertainties in soil properties and assuming Cam Clay elastic-perfectly plastic constitutive model, the specialized FPK equations are solved to obtain second order accurate evolutionary (with pseudotime/ strain) joint probability density function of the stress response. Marginal statistics -marginal probability density function, marginal mean, and marginal standard deviation -of the stress components are then obtained from the multivariate probability density function using standard integration techniques.

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