Stochastic homogenization analysis on elastic properties of fiber reinforced composites using the equivalent inclusion method and perturbation method

Sakata, Sei-ichiro; Ashida, Fumihiro; Kojima, Tomoyuki

doi:10.1016/j.ijsolstr.2008.08.017

Cited by 41 publications

(10 citation statements)

References 10 publications

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“…A number of results in analytical stochastic homogenization were obtained in the works of Andrianov et al, Castañeda and Galipeau, and Sakata et al Here, we would like to highlight also the rapidly developing general perturbation method . Nowadays, the perturbation method is one of the most popular stochastic techniques.…”

Section: Introductionmentioning

confidence: 92%

Fuzzy‐stochastic FEM–based homogenization framework for materials with polymorphic uncertainties in the microstructure

Pivovarov

Oberleiter

Willner

et al. 2018

Numerical Meth Engineering

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Summary Uncertainties in the macroscopic response of heterogeneous materials result from two sources: the natural variability in the microstructure's geometry and the lack of sufficient knowledge regarding the microstructure. The first type of uncertainty is denoted aleatoric uncertainty and may be characterized by a known probability density function. The second type of uncertainty is denoted epistemic uncertainty. This kind of uncertainty cannot be described using probabilistic methods. Models considering both sources of uncertainties are called polymorphic. In the case of polymorphic uncertainties, some combination of stochastic methods and fuzzy arithmetic should be used. Thus, in the current work, we examine a fuzzy‐stochastic finite element method–based homogenization framework for materials with random inclusion sizes. We analyze an experimental radii distribution of inclusions and develop a stochastic representative volume element. The stochastic finite element method is used to obtain the material response in the case of random inclusion radii. Due to unavoidable noise in experimental data, an insufficient number of samples, and limited accuracy of the fitting procedure, the radii distribution density cannot be obtained exactly; thus, it is described in terms of fuzzy location and scale parameters. The influence of fuzzy input on the homogenized stress measures is analyzed.

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Section: Introductionmentioning

confidence: 92%

Fuzzy‐stochastic FEM–based homogenization framework for materials with polymorphic uncertainties in the microstructure

Pivovarov

Oberleiter

Willner

et al. 2018

Numerical Meth Engineering

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“…Since this paper considers both random variations in volume fraction of inclusions and material properties of a microstructure, the perturbationbased approach with the equivalent inclusion method [7] is employed for stochastic homogenization analysis in a microscopic scale.…”

Section: Perturbation-based Stochastic Homogenization Analysis With Tmentioning

confidence: 99%

“…Several reports on the Monte-Carlo simulation [1,2], the perturbation analysis with the homogenizationbased finite element analysis [3][4][5][6] or the equivalent inclusion method [7,8] have been reported. Also, other approaches for stochastic homogenization analysis [9,10] or approximationbased stochastic homogenization analysis [11,12] have been reported.…”

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confidence: 99%

Hierarchical stochastic homogenization analysis of a particle reinforced composite material considering non-uniform distribution of microscopic random quantities

Sakata

Ashida

2011

Comput Mech

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This paper discusses a stochastic homogenization problem for evaluation of stochastic characteristics of a homogenized elastic property of a particle reinforced composite material especially in case of considering a nonuniform distribution of a material property or geometry of a component material and its random variation. In practice, some microscopic random variations in composites may not be uniform. In this case, a non-uniformly distributed random variation of a microscopic material or geometrical property should be taken into account. For this problem, this paper proposes a hierarchical stochastic homogenization method. This method assumes that a two-phase composite material can be separated into three-scales, and propagation of the randomness through the different scales can be evaluated with the perturbation-based technique. As an example, stochastic characteristics of homogenized elastic properties of a glassparticle reinforced plastic are estimated using the proposed approach. With the numerical results, importance of the problem and validity of the proposed method are discussed.

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“…Alternative stochastic perturbation-based approaches for the determination of the effective properties of random composites can be found. 10,11 Xu and Graham–Brady 12 developed a stochastic computational method which combines a fast iterative numerical method with stochastic decomposition techniques in order to compute the effective elastic behavior of composite materials with a spatially random Young’s modulus. Tootkaboni and Graham–Brady 13 proposed a spectral stochastic computational scheme for linking the global properties of multi-phase periodic composites to the geometry and the random material properties of their microstructural components.…”

Section: Introductionmentioning

confidence: 99%

Assessment of the effect of microstructural uncertainty on the macroscopic properties of random composite materials

Savvas

Stefanou

2016

Journal of Composite Materials

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The linking of microstructural uncertainty with the random variation in the response of heterogeneous structures at the macroscale is particularly important in the framework of the stochastic finite element method. In this work, the effect of uncertainty in the constituent material properties and the geometry of the microstructure, on the macroscopic properties of composite materials is assessed through computational homogenization. Based on Hill–Mandel homogeneity condition, the homogenization procedure utilizes the excellent synergy of the extended finite element method and the Monte Carlo simulation. In this way, the computation of the statistical characteristics of the homogenized elasticity tensor of random composite materials reinforced with arbitrarily shaped inclusions is performed in a computationally efficient manner. The effect of stochastic variation in the elastic properties of the constituents as well as the effect of inclusion shape on the statistical characteristics of the homogenized elasticity tensor is assessed through probabilistic sensitivity analysis. A comparison is performed with regard to the relative influence of material and geometrical uncertainty which are considered separately. More realistic results are obtained by considering simultaneously material and geometrical uncertainty in the microstructural modeling of composite materials. The results can be further exploited in the stochastic finite element analysis of composite structures where material properties with random characteristics obtained by the presented multiscale homogenization procedure will be assigned to each finite element.

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Stochastic homogenization analysis on elastic properties of fiber reinforced composites using the equivalent inclusion method and perturbation method

Cited by 41 publications

References 10 publications

Fuzzy‐stochastic FEM–based homogenization framework for materials with polymorphic uncertainties in the microstructure

Fuzzy‐stochastic FEM–based homogenization framework for materials with polymorphic uncertainties in the microstructure

Hierarchical stochastic homogenization analysis of a particle reinforced composite material considering non-uniform distribution of microscopic random quantities

Assessment of the effect of microstructural uncertainty on the macroscopic properties of random composite materials

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