This paper discusses evaluation of influence of microscopic uncertainty on a homogenized macroscopic elastic property of an inhomogeneous material. In order to analyze the influence, the perturbation-based homogenization method is used. A higher order perturbation-based analysis method for investigating stochastic characteristics of a homogenized elastic tensor and an equivalent elastic property of a composite material is formulated.As a numerical example, macroscopic stochastic characteristics such as an expected value or variance, which is caused by microscopic uncertainty in material properties, of a homogenized elastic tensor and homogenized equivalent elastic property of unidirectional fiber reinforced plastic are investigated. The macroscopic stochastic variation caused by microscopic uncertainty in component materials such as Young's modulus or Poisson's ratio variation is evaluated using the perturbation-based homogenization method. The numerical results are compared with the results of the Monte-Carlo simulation, validity, effectiveness and a limitation of the perturbation-based homogenization method is investigated. With comparing the results using the first-order perturbation-based method, effectiveness of a higher order perturbation is also investigated.

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a b s t r a c tThis paper describes a methodology for evaluation of influence of microscopic uncertainty in material properties and geometry of a microstructure on a homogenized macroscopic elastic property of an inhomogeneous material. For the analysis of the stochastic characteristics of a homogenized elastic property, the first-order perturbation method is used. In order to analyze the influence of microscopic geometrical uncertainty, the perturbationbased equivalent inclusion method is formulated. In this paper, an analytical form of the perturbation term using the equivalent inclusion method is provided.As a numerical example, macroscopic stochastic characteristics such as an expected value or variance of the homogenized elastic tensor of a unidirectional fiber reinforced plastic, which is caused by microscopic uncertainty in material properties or geometry of a microstructure, are estimated with computing the first order perturbation term of the homogenized elastic tensor. Compared the results of the proposed method with the results of the Monte-Carlo simulation, validity, effectiveness and a limitation of the perturbationbased homogenization method is investigated.

This paper discusses a perturbation-based stochastic homogenization analysis procedure for a fiber reinforced composite material. For the purpose of estimating a stochastic characteristic of a homogenized equivalent elastic constant of composites for a microscopic random variation of a material property or geometry of a microstructure, the first order perturbation technique is applied to the equivalent inclusion method. The homogenized equivalent elastic constants can be computed from a homogenized compliance in case of an orthotropic material, therefore, the perturbation term of the homogenized compliance for a microscopic random variation is also computed. From numerical results, validity and effectiveness of the proposed method are illustrated.