Kriging-based approximate stochastic homogenization analysis for composite materials

Sakata, Sei-ichiro; Ashida, Fumihiro; Zako, Masaru

doi:10.1016/j.cma.2007.12.011

Cited by 79 publications

(31 citation statements)

References 12 publications

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“…Figure 2 shows the relative estimation error between the results of the exact and the approximate Monte-Carlo simulation with the first order approximation using the different numbers of samples. Referring to the previous report 9) , and this paper aims to construct the surrogate model with fewer samples, 5, 11 and 21 samples are used for approximation. The legends than that with 11 samples.…”

Section: Accuracy Of Stochastic Homogenization Analysis With a Convenmentioning

confidence: 99%

“…The approximation-based stochastic homogenization methods have been proposed by Sakata et al (9) or Kaminski (10) , but in those reports, a non-parametric flexible approximation or a higher order approximation was employed. Of cause if many samples can be used and a flexible approximation can be usable with higher stability, those approaches will be effective for the approximate stochastic homogenization.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic Homogenization Analysis of a Particle Reinforced Composite Material using an Approximate Monte-Carlo Simulation with the Weighted Least Square Method

Sakata

Ashida

Iwahashi

2013

JCST

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This paper describes a stochastic homogenization analysis of a particle reinforced composite material using an approximation technique. In order to analyze the influence of a microscopic random variation of an elastic property of a component material on the homogenized elastic property of a particle reinforced composite material, the Monte-Carlo simulation is employed. Since the conventional Monte-Carlo simulation sometimes involves a higher computational cost, an approximate stochastic homogenization method using the Monte-Carlo simulation combined with a polynomial-based approximation technique is employed, and accuracy of the approximate Monte-Carlo simulation is investigated. In order to apply a lower order approximation to the approximate Monte-Carlo simulation effectively, the weighted least square method is proposed, and its effectiveness is discussed with the numerical results.

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Section: Accuracy Of Stochastic Homogenization Analysis With a Convenmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stochastic Homogenization Analysis of a Particle Reinforced Composite Material using an Approximate Monte-Carlo Simulation with the Weighted Least Square Method

Sakata

Ashida

Iwahashi

2013

JCST

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“…(2) , Xu (3) or Sakata (4) reported several results with respect to the stochastic homogenization problem of composite materials or a heterogeneous material. In addition to a conventional method using the Monte-Carlo simulation (4)(5) , the perturbation-based homogenization method (6)- (9) or an approximation-based stochastic analysis method (10) (11) for solving the stochastic homogenization problem has been reported.…”

Section: Introductionmentioning

confidence: 99%

Influence of Random Variation in Volume Fraction of Fiber on Stochastic Property of Equivalent Elastic Property of Unidirectional Fiber Reinforced Composite Material

Sakata

Ashida

2010

JMMP

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This paper describes stochastic analysis on a homogenized elastic property of a unidirectional fiber reinforced composite material considering uncertainty in material and geometrical properties of component materials. The influence of the microscopic uncertainties on the stochastic characteristics of a homogenized elastic property is analyzed with the perturbation-based analysis using the equivalent inclusion method. Especially, influence of a volume fraction variation on the stochastic characteristics is discussed in this paper. Also, as an example of a design considering the influence of a volume fraction variation, a limit of the random variation of the volume fraction of fiber for controlling a random variation of a homogenized elastic property of a composite to be less than random variations of elastic properties of component materials is discussed.

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“…Complementary, systems with random material properties quantified by random variables and deterministic (or slightly perturbed) geometry of the representative volume can be treated employing numerical techniques of stochastic mechanics such as MonteCarlo simulations [20], perturbation-based methods [22,35] or approaches based on an empirical probability distribution function [36]; see also [21] for a systematic overview. Most generally, uncertainties in spatial distribution and material properties of individual phases can be jointly characterized when resorting to random field description [42].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Modeling of Chaotic Masonry via Mesostructural Characterization

Lombardo

Zeman

Šejnoha

et al. 2009

Int J Mult Comp Eng

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Abstract. The purpose of this study is to explore three numerical approaches to the elastic homogenization of disordered masonry structures with moderate meso/macrolengthscale ratio. The methods investigated include a representative of perturbation methods, the Karhunen-Loève expansion technique coupled with Monte-Carlo simulations and a solver based on the Hashin-Shtrikman variational principles. In all cases, parameters of the underlying random field of material properties are directly derived from image analysis of a real-world structure. Added value as well as limitations of individual schemes are illustrated by a case study of an irregular masonry panel.

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Kriging-based approximate stochastic homogenization analysis for composite materials

Cited by 79 publications

References 12 publications

Stochastic Homogenization Analysis of a Particle Reinforced Composite Material using an Approximate Monte-Carlo Simulation with the Weighted Least Square Method

Stochastic Homogenization Analysis of a Particle Reinforced Composite Material using an Approximate Monte-Carlo Simulation with the Weighted Least Square Method

Influence of Random Variation in Volume Fraction of Fiber on Stochastic Property of Equivalent Elastic Property of Unidirectional Fiber Reinforced Composite Material

Stochastic Modeling of Chaotic Masonry via Mesostructural Characterization

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