On Perturbation-Based Stochastic Homogenization Analysis for a Homogenized Equivalent Elastic Constant of FRP Using the Equivalent Inclusion Method

Abstract

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.

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

“…Accuracy of the PEI for a certain volume fraction and relationship between the accuracy and a degree of random variation in a material or geometrical property of component materials have been reported by Sakata et al (13) , however, influence of the volume fraction of fiber on the accuracy has not been reported yet. Since this paper discusses a stochastic property for every volume fraction which can be realized using PEI, it should be evaluated at first.…”

“…On the other hand, the perturbation based approach will be still effective for a large numbers of random variables, since an approximation model will be difficult to be constructed for many random variables. From this viewpoint, Sakata et al proposed the perturbation-based stochastic homogenization analysis approach using the equivalent inclusion method especially for a geometrical random variation (12) (13) .…”

Stochastic Analysis of Microscopic Stress in Fiber Reinforced Composites Considering Uncertainty in a Microscopic Elastic Property

“…(4) Sakata (5)- (7) or Xu (8) . Also, approximation based stochastic homogenization analysis (9) (10) or perturbationbased stochastic homogenization analysis using the equivalent inclusion method (11) (12) have been reported.…”