Various approaches in probabilistic homogenization of the CFRP composites

Abstract

A variety of the homogenization methods is collected here and contrasted to determine the basic probabilistic characteristics of the CFRP composite in a presence of Gaussian uncertainty in its components material characteristics. We compare algebraic approximations of the effective elasticity tensor components with these calculated by using of two different FEM strategies. One may find in this elaboration a comparison of the Voigt–Reuss versus Hashin–Shtrikmann upper and lower bounds, the results of spatial averaging of this composite RVE, Mori–Tanaka, Vanishing Fiber Diameter as well as the Self-Consistent homogenization theories together with two independent FEM solutions of the so-called cell problem. Symbolic probabilistic analysis is implemented according to the generalized tenth order stochastic perturbation technique supported by the Response Function Method. Polynomial basis with statistically optimized order enables determination of the analytical functions relating effective tensor components with material parameters of the composite constituents. The expected values series confirm fundamental tendencies observed before in deterministic comparisons of these theories, an analysis of the coefficients of variations shows the resulting uncertainty level and sensitivity of the effective characteristics, while skewness and kurtosis show that Gaussian character of the homogenized tensor prevails in this problem.