Probabilistic Elastic Characteristics of the Periodic Fiber Composites

The article presented is devoted to computational estimation of the probabilistic effective properties for random fiber-reinforced composites by the Monte-Carlo simulation (MCS) technique. The composite analyzed has randomly defined Young's moduli and Poisson's ratios being uncorrelated Gaussian variables while the heterogeneous medium microgeometry is defined deterministically. Using MCS method linked with the Finite Element procedure, the upper and lower bounds of the fiber composite effective properties as well as direct approximation of the effective characteristics is carried out. The probabilistic sensitivity of the effective properties is analyzed with respect to deterministically varying reinforcement volume as well as to random elastic characteristics of composite constituents. Thanks to such analysis it is observed that even small random fluctuations in all the elastic properties of the fiber and matrix cause significant increase of the second-order probabilistic moments of the effective characteristics; the matrix Poisson's ratio has been detected as the crucial parameter for the effective tensor probabilistic moments.