Stochastic constitutive modeling of elastic-plastic materials with uncertain properties

Lacour, Maxime; Abrahamson, Norman A.

doi:10.1016/j.compgeo.2020.103642

Cited by 5 publications

(4 citation statements)

References 4 publications

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“…It does not require to precompute the solution for different values on the uncertain input as it is usually done in the non‐intrusive set up, which makes the proposed method practical for large scale systems where only a limited amount of supercomputer run is usually available. The proposed method can further be combined with recently developed stochastic constitutive models as in Lacour and Abrahamson 10 to directly propagate the uncertainty in nonlinear material models, which will be developed in a separate study. The proposed method suffers from the same disadvantages usually found in intrusive methods: the complexity in the solution's representation increases in time and therefore requires the use of local PC expansions over subdomains to maintain accuracy and computational efficiency for long‐time simulations.…”

Section: Resultsmentioning

confidence: 99%

“…The second reason is that it can be difficult to fully propagate the uncertainty in nonlinear material models with limited sampling in a nonintrusive approach. More particularly, in the context of nonlinear stochastic finite elements, 10 the nonlinear behavior of uncertain elastic‐plastic materials in dynamic simulations will lead to solutions that are highly unpredictable (due to the plastification of each element during run time), and we doubt that the solution in that case could be obtained with a nonintrusive approach. The use of an intrusive stochastic constitutive algorithm as developed by Lacour and Abrahamson 10 turns out to be very efficient when used with the proposed intrusive approach for dynamic stochastic finite elements, and it can be extended to allow efficient propagation of the uncertainty in elastic‐plastic material models in dynamic finite‐element simulations, but this extension is beyond the scope of this paper.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic stochastic finite element method using time‐dependent generalized polynomial chaos

Lacour

Bal

Abrahamson

2020

Num Anal Meth Geomechanics

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Summary We present an intrusive formulation for the dynamic stochastic finite‐element method to propagate the epistemic uncertainty in material properties into a finite‐element system over time. The stochastic finite‐element method, originally developed for the static case, uses generalized polynomial chaos (gPC) expansions to represent the uncertainty in both material/load fields and displacement fields and solves for the unknown PC coefficients of displacement at each degree of freedom of the finite‐element system. In this case, the gPC basis used to represent the solution is optimal and can be kept the same throughout the static simulation; however, when integrating a stochastic system over time, it is proven that using gPC tends to break down for integrations over long times. The reason is that the solution's complexity increases in time, and the set of polynomials used in the gPC expansion to represent the solution, therefore, does not stay optimal. In this formulation, new stochastic variables and orthogonal polynomials are constructed as time progresses. These variables are obtained as the Kahrunen‐Loeve expansion of the finite‐element solution at the times of update, thus, optimally representing the distribution of the solution using a minimal set of orthogonal polynomials. The result from the method is a time‐domain polynomial chaos representation of the entire finite‐element solution. A fast post‐processing phase can be used to (a) obtain the probability distribution of the solution at each degree of freedom and (b) generate any number of time series realizations of the solution, which correspond to the same time series that would be obtained from a set of simulations based on direct Monte‐Carlo simulations of the uncertain material properties.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic stochastic finite element method using time‐dependent generalized polynomial chaos

Lacour

Bal

Abrahamson

2020

Num Anal Meth Geomechanics

Self Cite

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“…In order to formulate a stochastic finite element method for nonlinear material models, the same authors have applied a discrete approach to develop a constitutive algorithm which can be implemented on a global level of the context 3D nonlinear stochastic finite element method [10]. In this work, our proposed modeling is done by the continuous stochastic model, and it should be noticed that it has not been treated before in the literature.…”

Section: Introductionmentioning

confidence: 99%

A Stochastic Model of Stress Evolution in a Bolted Structure in the Presence of a Joint Elastic Piece: Modeling and Parameter Inference

Haiek

Ansari

Amrani

et al. 2020

Advances in Materials Science and Engineering

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In this paper, we propose a stochastic model to describe over time the evolution of stress in a bolted mechanical structure depending on different thicknesses of a joint elastic piece. First, the studied structure and the experiment numerical simulation are presented. Next, we validate statistically our proposed stochastic model, and we use the maximum likelihood estimation method based on Euler–Maruyama scheme to estimate the parameters of this model. Thereafter, we use the estimated model to compare the stresses, the peak times, and extinction times for different thicknesses of the elastic piece. Some numerical simulations are carried out to illustrate different results.

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“…In some cases, the calibration uncertainty can be directly implemented into the constitutive laws [9] but it is more common to acknowledge the uncertainty directly to the material parameters -or other data entering the simulation -and perform stochastic simulations. The commonly used approaches to stochastic analysis in geotechnics are the Monte-Carlo method [2,10,11] and Latin hypercube sampling [12].…”

Section: Introductionmentioning

confidence: 99%

Uncertainty of material parameters for clay and its influence on simulation results

Janda

Proceedings of the Seventeenth International Conference On Civil, Structural and Environmental Engineering Computing

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The paper presents how the uncertainty of material parameters of fine grained soils propagate to the results of numerical simulation. In particular, the posterior distribution describing the uncertainty of the five basic parameters of the hypoplastic model for clay is considered in two scenarios. In the first scenario, only the marginal distributions material parameters are considered independently and no correlation between them are assumed. In the second approach the complete multivariate posterior distribution is assumed in which the parameters are mutually correlated. This posterior distribution shows relatively low correlation between most of the parameter pairs with exception to the slope of primary consolidation line φ and its intercept N . The significantly higher variance of the simulation results obtained for the uncorrelated marginal distribution show that the correlations within the posterior distribution need to be considered in stochastic geotechnical simulations.

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Stochastic constitutive modeling of elastic-plastic materials with uncertain properties

Cited by 5 publications

References 4 publications

Dynamic stochastic finite element method using time‐dependent generalized polynomial chaos

Dynamic stochastic finite element method using time‐dependent generalized polynomial chaos

A Stochastic Model of Stress Evolution in a Bolted Structure in the Presence of a Joint Elastic Piece: Modeling and Parameter Inference

Uncertainty of material parameters for clay and its influence on simulation results

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