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This paper describes stochastic homogenization analysis of a uni-directionally aligned short fiber reinforced composite material. In case of a short fiber reinforced composite material, length or orientation of the short fiber will be a random variable in addition to elastic properties of component materials, volume fraction or cross-sectional shape of fiber. Especially, a stochastic homogenization problem considering the length or fiber orientation variation is analyzed in this paper. For the purpose of this analysis, the first-order perturbation-based stochastic homogenization method is employed. Since the perturbation term with respect to the length or the orientation variation cannot be explicitly obtained in using the homogenization method, a finite differential technique is used for approximation of the perturbation term. From the numerical results, validity, effectiveness and problem of the perturbation-based analysis are discussed. Also, influence of the length variation on a stochastic characteristic of a homogenized elastic property of a short fiber reinforced composite material is discussed.

First Order Perturbation-based Stochastic Homogenization Analysis for Short Fiber Reinforced Composite Materials